University of Nevada, Reno
Electromagnetic Energy Harvesting In Pursuit of Heat Radiation
A dissertation submitted in partial fulfillment of the Requirements for the degree of Doctor of Philosophy in Electrical Engineering
By
Richard A. Bean
Dr. Banmali S. Rawat, Ph. D., Dissertation Advisor
May, 2019
Copyright by Richard A. Bean 2019
All Rights Reserved THE GRADUATE SCHOOL
We recommend that the dissertation Prepared under our supervision by
Richard A. Bean
entitled
Electromagnetic Energy Harvesting in Pursuit of Heat Radiation
be accepted in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Banmali S. Rawat, Ph. D., Advisor Bruno S. Bauer, Ph. D., Committee Member Yantao Shen, Ph. D., Committee Member Jihwan Yoon, Ph. D., Committee Member David M. Leitner, Ph. D., Graduate School Representative David W. Zeh, Ph. D., Dean, Graduate School
May, 2019 i
Abstract
This dissertation explores the potential harvesting of electrical energy from heat radiation.
Heat is an abundant form of energy that occurs naturally. It is spontaneously emitted from the matter in a material surface, and its random photonic emissions aggregate. It is transferred from material surfaces to other material surfaces in the form of heat radiation.
This heat radiation transfers through free space in the form of plane waves. These plane waves are electromagnetic in character and are fully described by Maxwell’s equations.
Electromagnetic (EM) plane waves are routinely utilized in communication, radar, and optical systems. This dissertation posits that heat radiation can be captured by antennas, conducted by coax cables, and then converted to hybrid TE-TM waves inside microstrip printed circuit boards. These EM waves can be subsequently rectified using electronic devices known as Schottky diodes. The resultant direct current (DC) can be stored and used to power electronic devices and electrical machinery.
This dissertation analyzes the theoretical foundations of heat radiation. Using Planck’s
Law, the likely power magnitudes from material surfaces are predicted. Passive antennas, geometrical relationships, and bandwidth aggregation can concentrate these power magnitudes. Using these passive gains, effective rectification can be achieved.
Complementing this mathematical and logical analysis, physical measurements of power were made for multiple antennas types, for different temperatures, and for different ii distances from the material surfaces. Multiple power meters and measurement applications were used.
To confirm the feasibility of harvesting electrical energy from heat radiation multiple rectifier and rectenna designs and circuits were designed, fabricated, and tested.
Prevailing views of energy aggregation were adopted and then compared with the actual performance in the electronic circuits.
Finally, the applied research in this dissertation has successfully generated DC electricity by harvesting ambient radiation using electrical engineering technology and techniques.
Because photons of heat radiation are indistinguishable from the photons from other sources in the microwave frequency range, this dissertation logically examines the potential sources removing the increasingly improbable sources such that heat radiation remains a likely source. Further, the harvesting technology was tested in an anechoic chamber where the manmade radiation sources from outside the chamber were greatly reduced by metallic shielding and signal absorbing materials.
iii
Acknowledgements
Every endeavor is the product of numerous contributors. These contributions include ideas, coursework, discussions, encouragement, and frameworks for analysis. I wish to acknowledge the assistance I have received and to express my gratitude for the help.
I gratefully acknowledge the continued support and guidance of my advisor, Dr. Banmali
S. Rawat. His weekly participation in my progress has provided a forum for discussions, and his feedback has guided my investigations. He provided the coursework foundations in electromagnetic waves, microwaves, and optical communications. These foundations and support were instrumental in harvesting the noise energy that is often treated as a detriment to electrical engineering.
I also acknowledge Dr. Indira Chatterjee whose courses in distributed systems and antennas theory figured prominently in my dissertation research. My original exposure to rectennas was through her courses.
Dr. Miles Greiner’s course in radiative heat transfer provided my first recognition that heat radiation might produce enough power to be harvested. Dr. David Leitner’s course in Quantum Mechanics reinforced the role of spontaneous emissions and reaffirmed the recognition that heat photons were the same as plane waves in the radio frequency through visible light wave-lengths.
Finally, I would like to recognize the support of my wife and family who have been partners in my dissertation research. iv
TABLE OF CONTENTS
Abstract ...... i
Acknowledgements ...... iii
Table of Contents ...... iv
Table of Tables ...... x
Table of Figures ...... xi
1 Introduction ...... 1
1.1 A Conceptual Design for A Simple Electrical Generator ...... 2
1.2 Heat: An Abundant Energy Source ...... 4
1.3 Why Use Heat Radiation? ...... 5
1.4 Research in Support of This Conceptual Design ...... 6
1.5 Antennas as Electromagnetic Energy Harvesters ...... 9
1.6 Rectification...... 9
1.7 The Need for Engineering Gain ...... 10
1.8 Heat Radiation in Theory...... 11
1.9 Stefan-Boltzmann Equation ...... 13
1.10 Storage of Heat Energy ...... 16 v
1.11 Planck’s Law: Frequency Spectrum of Thermal Radiation ...... 18
1.12 “kbTB” Noise Equation ...... 26
1.13 Disparate Power Predictions ...... 27
1.14 Early Power Measurements ...... 29
1.15 Conclusions from Heat Theory, Literature, and Early Measurements ...... 31
2 Engineering Gains Useful to Harvesting Heat Radiation ...... 33
2.1 Conservation of energy and Engineering Gains ...... 33
2.2 Antennas ...... 34
2.3 Emitting Area ...... 39
2.4 Heat Geometries ...... 39
2.5 Predictive Equations for Power ...... 43
2.6 Reflections ...... 45
2.7 Impedance Matching ...... 47
2.8 Bandwidth Aggregation ...... 49
2.9 Potential Gains from Convolution ...... 51
2.10 Other Gain Techniques ...... 55
2.11 Predictive Engineering ...... 56
2.11.1 Radiance Predictions ...... 58 vi
2.11.2 FRIIS Predictions ...... 59
2.11.3 Heat View Predictions ...... 60
2.11.4 Summary of Radiometry, FRIIS, and Heat View Approaches ...... 61
2.11.5 Measurement and Known Factor Approach...... 62
2.11.6 Summary of Predictive Engineering ...... 66
3 Power Measurements of Heat Radiation ...... 68
3.1 Measurement Chronology ...... 68
3.2 Measurement Set-up ...... 71
3.3 Measurement Results ...... 73
3.4 Measurement Anomalies ...... 75
3.5 Interpretation of the Spectrum Display from the FieldFox Meter...... 76
3.6 Resolution Bandwidth ...... 78
3.7 Temperature Impact on Spectrum Power Measurements ...... 81
3.8 Power Spectrum Measurement for Various Antennas Types ...... 83
3.9 Impact of Distance from the Heat Source ...... 84
4 Antenna Considerations for Harvesting Heat Radiation...... 87
4.1 Aperture Antennas ...... 87
4.2 Near and Far Fields ...... 87 vii
4.3 Incident Power Densities...... 88
4.4 Rectangular Wave Guides ...... 90
4.5 Modeling a Wire Through Rectangular Wave Guide ...... 93
5 Rectifier Design and Fabrication ...... 96
5.1 Rectification Foundations ...... 96
5.1.1 Schottky Diodes ...... 96
5.1.2 Relationship between Power Level and Voltage ...... 101
5.1.3 Line Width Impacts on Impedances for Microstrip PCBs ...... 103
5.1.4 Diode Basics ...... 105
5.2 Rectifier Design Objectives and Choices ...... 109
5.3 Sufficient Voltage from the Power Source Is Key to Rectification ...... 111
6 Measurements, Experimental Results, and Discussion ...... 117
6.1 Harvesting 0 Hz Power ...... 117
6.1.1 Voltage Doubler Rectifier Using NXP BAT86113 Diode ...... 117
6.1.2 Version 1 Rectifier ...... 120
6.1.3 “Version 1” vs Breadboard Rectifier Measurements ...... 123
6.2 Harvesting In the 26 to 50 GHz Range ...... 126
6.2.1 Design Considerations for Harvesting at 26 GHz and Beyond ...... 126 viii
6.2.2 Thermal Noise Modeling ...... 129
6.2.3 V2 Rectifier ...... 132
6.2.4 V3 Rectifier ...... 137
6.2.5 V4 Rectifier ...... 140
6.2.6 V5 Rectifier ...... 148
6.3 Harvesting in the 75 GHz Range ...... 151
6.3.1 V1 Rectenna ...... 151
6.3.2 V2 Rectenna ...... 155
6.4 Natural versus Manmade Radiation ...... 160
6.4.1 Anechoic Chamber Testing ...... 163
6.4.2 Hot Pot Testing...... 165
6.4.3 Logical Exclusions of Manmade Sources ...... 168
6.5 Experiment Inconsistencies ...... 169
6.5.1 Equipment and Fabrication Limits ...... 169
6.5.2 Measurement Inconsistencies ...... 170
6.5.3 Aggregation: The Missing Power ...... 173
7 Conclusions and Next Steps ...... 174
7.1 Summary ...... 174 ix
7.2 Next Steps ...... 176
7.2.1 Step 1: Create an Improved Quad Rectangular Patch Rectenna ...... 177
7.2.2 Step 2: Scale through An Array of Rectangular Patch Rectennas ...... 177
7.3 Additional Experiments to Further Confirm Source as Heat Radiation ...... 178
7.4 Conclusions...... 179
References ...... 180
x
Table of Tables
Table 2-A: Antenna Gain Computed via Different Techniques ...... 38
Table 2-B: Comparison of Radiometry, FRIIS, and Heat View Techniques ...... 62
Table 2-C: Measured Average and Peak Powers ...... 63
Table 2-D: Known and Unknown Factors (in dB) Affecting Measurements ...... 66
Table 4-A: The Equivalent Incident Powers for 1 mW of Measured Power ...... 89
Table 5-A: Characteristics of Various Schottky Diodes ...... 100
Table 5-B: Peak Voltage for a Given Sinusoidal Power Level ...... 102
Table 5-C: Line Widths for Various Impedances of RO4003 Microstrip Boards ...... 104
Table 5-D: RMS Voltage Associated with a Given Power Level ...... 112
Table 5-E: Characteristics of Schottky Diodes Used in Rectifiers in this Dissertation ... 113
Table 6-A: Measurements and Comparisons for Version 4 Rectifier ...... 144
xi
Table of Figures
Figure 1.1: A Simple Electrical Generator ...... 3
Figure 1.2: Rectenna Basics...... 10
2 Figure 1.3: Emitted Power (W/m ) for Temperature Range of Liquid H2O ...... 14
Figure 1.4: Emitted Power (W/m2) for Temperature Range 0oC to 1500oC ...... 15
Figure 1.5: Water as an Energy Storage Source ...... 18
-2 Figure 1.6: Power (in dBmm ) per Planck’s Law (5 MHz of Resolution Bandwidth) .... 21
Figure 1.7: Planck Power (for a 1 m2) Area and Power Thresholds ...... 23
Figure 1.8: Planck Power (in dBm) with Area and Bandwidth Aggregation Gains ...... 25
Figure 1.9: Measurements of Version 4 and 5 Rectifiers ...... 26
Figure 1.10: Planck vs kTB Power Predictions per Hertz ...... 29
Figure 1.11: Power Spectrum Measurements with LadyBug Power Meter ...... 30
Figure 1.12: Two Possible Methods to Predict Power ...... 31
Figure 2.1: Antenna Gain for an Aperture Antenna ...... 35
Figure 2.2: WR-340 and WR-187 Antenna Gains (in dB) as a Function of Frequency ..... 37
Figure 2.3: View Factors for a Simple Heat Source and Antenna Aperture Surface ...... 41
Figure 2.4: Heat Source Gain Obtained thru COMSOL Simulation ...... 42
Figure 2.5: Predicted Power (in dBm) per Planck’s Law with and without Gains ...... 44
Figure 2.6: Predicted Power (in dBm) for Two Temperatures (295K and 2500K) ...... 45
Figure 2.7: Implied Power from Measured Power Due to Reflections ...... 47 xii
Figure 2.8: Power Gain Achievable with Parallel Wire Connection to Waveguide ...... 49
Figure 2.9: Mixing Two Signals ...... 52
Figure 2.10: MATLAB Simulation of Noise Convolution ...... 53
Figure 2.11: Noise in Time Domain ...... 53
Figure 2.12: Spectral Product of Noise Convolved with Noise ...... 54
Figure 3.1: Example of the CCDF View for Planck Radiation ...... 71
Figure 3.2: Measurement Environment ...... 72
Figure 3.3: Major Capabilities of Agilent N9918A FieldFox Meter ...... 73
Figure 3.4: Spectrum Power Measurement for WR-340 at 55oF ...... 74
Figure 3.5: Spectrum Power Measurement for WR-340 at 72oF ...... 75
Figure 3.6: Interpretation of the Spectrum Display from the FieldFox Meter ...... 77
Figure 3.7: Channel Power Measurement at 26.3 GHz for a 5 MHz RBW ...... 79
Figure 3.8: Measured Power for Various Resolution Bandwidths (RBW) ...... 80
Figure 3.9: Spectrum Power Measurements at 55oF and 72oF ...... 82
Figure 3.10: Power Spectrum Measurements for Various Antennas ...... 84
Figure 3.11: Power Measurements at 50 and 100 cm Distances from Wall ...... 85
Figure 4.1: Antenna Array at 2.45 GHz Required to Power Mobile Phone ...... 90
Figure 4.2: Position of Waveguide Tap Alters the Wave Pattern and Magnitudes ...... 92
Figure 4.3: "Through Wire" Probe for a WR-187 ...... 95
Figure 5.1: Equivalent Circuits for a Schottky Diode...... 98
Figure 5.2: I-V Diode Curve for NXP's BAT86113 Diode ...... 107
Figure 6.1: Circuit Schematic for Voltage Doubler Rectifier ...... 118 xiii
Figure 6.2: Photograph of the Breadboard Circuit Voltage Doubler ...... 119
Figure 6.3: Voltage Output from Breadboard Rectifier across Frequency Range ...... 120
Figure 6.4: Board Layout for Discrete Components from ADS ...... 122
Figure 6.5: Photograph of Full Wave Rectifier Implemented as a PCB ...... 123
Figure 6.6: Measurements from the Version 1 PCB and Breadboard Rectifiers ...... 125
Figure 6.7: Gerber Output for the Version 2 Rectifier ...... 133
Figure 6.8: Photograph of Version 2 Rectifier ...... 133
Figure 6.9: Version 2 Rectifier Design Error Example ...... 135
Figure 6.10: Measured Power from Antenna for Version 2 Rectifier ...... 136
Figure 6.11: Output from 40 GHz MSG As Measured by FieldFox Meter ...... 138
Figure 6.12: Photograph of Version 3 Rectifier ...... 139
Figure 6.13: DC Output Voltage from V3 Rectifier ...... 139
Figure 6.14: I-V Curves for Schottky Diodes Used in Version 3 and 4 Rectifiers ...... 141
Figure 6.15: Photograph of Version 4 Rectifier ...... 142
Figure 6.16: Version 4 DC Output (in mV) Using Aritsu Microwave Signal Generator .. 143
Figure 6.17: Manufacturer’s S12 Curve for BAT-24 Diode Used in Version 4...... 146
Figure 6.18: Power Range for Measured Voltages ...... 147
Figure 6.19: Noise Equivalent Model ...... 148
Figure 6.20: Genesys Layout for the V5R1 Rectifier ...... 149
Figure 6.21: V5 and V4 Rectifiers Driven by MSG ...... 150
Figure 6.22: Measurements of V5 vs V4 Rectifiers ...... 151
Figure 6.23: Predictive Differences between V5 Rectifier and V1 Rectenna ...... 153 xiv
Figure 6.24: Simulated Resonance and Bandwidth of V1R0 Rectenna ...... 153
Figure 6.25: Genesys Microstrip Board Layout for the V1R0 Rectenna ...... 154
Figure 6.26: V1 Rectenna Performance Compare to the V5 Rectifier ...... 155
Figure 6.27: V2R0 vs V1R0 Improvements ...... 156
Figure 6.28: Rectangular vs Square Patch Antennas ...... 156
Figure 6.29: Genesys Layout of the V2R0 Rectenna ...... 157
Figure 6.30: Performance of V2R0 Rectenna...... 158
Figure 6.31: Genesys Microstrip Board Layout for the V2R1 Rectenna ...... 159
Figure 6.32: Performance for V2 R1 Rectenna ...... 160
Figure 6.33: Apparatus for Hot Pot Test ...... 166
Figure 6.34: Rectifier V4R1 Output from Hot Pot Test ...... 167
Figure 6.35: Power Measurements Using the Agilent N1911A Power Meter ...... 172 1
1 INTRODUCTION
This dissertation explores the direct harvesting of electrical energy from the heat that radiates from all matter. This heat radiation is by nature electromagnetic (EM) radiation in the microwave through infrared frequencies for room temperatures. EM radiation transfers energy through space in the form of EM plane waves. When these waves encounter matter, the wave energy can be reflected, transmitted, or absorbed by the matter. If absorbed, the energy is transferred to the electrons in the matter.
Because energy cannot be created nor destroyed, generating electricity is by definition the conversion of energy from one form to another. Traditionally, heat in mechanical heat engines, such as turbines or pistons, is used to indirectly turn magnetic induction generators. The hypothesis of this dissertation is: Electricity can be generated directly by harvesting heat radiation from material surfaces thereby moving electrons in electronic circuits. 2
1.1 A CONCEPTUAL DESIGN FOR A SIMPLE ELECTRICAL GENERATOR
Any engineering solution begins with an idea. The idea is founded on theory, mathematics, and most often previous technological achievements that are adapted to the idea. The underlying theory for this dissertation can be summarized in the following chain of physics principles:
. All matter radiates heat from its external surfaces as a function of its temperature.
. This heat energy transfers through free-space in the form of electromagnetic
radiation.
. This electromagnetic radiation can be readily captured by antennas.
. Antennas are passive electrical devices that convert electromagnetic radiation
into the oscillating movement of electrons.
. The oscillating movement of the electrons in antennas can be rectified into direct
current electricity using diodes.
As can be seen in Figure 1.1: A Simple Electrical Generator, this simple system illustrates the idea for directly generating electricity from heat radiation. In this conceptual model heat radiation produces electron movements in the antenna. The energy from these electron movements is subsequently rectified into direct current. This simple system looks and behaves much like a communication system with a transmitter (heat source), a radiative medium (air), an antenna (receiving antenna), and a receiver (rectifier). Given this analogous behavior, it is natural for an electrical engineer to apply the FRIIS equation
[1] to quantify the power magnitudes and to engineer the system components. 3
Figure 1.1: A Simple Electrical Generator
Electricity is a core technology for the industrial economies of the world. Today the dominant technology for generating electricity is the rotary magnetic induction generator.
Electricity is generated by rotating magnets past coils of wire per Faraday’s Law [2]. The rotation can be produced through a hand crank using human muscle power or more commonly through a heat engine, such as a turbine. Turbines can use water, steam, or gases as the “fluid” that kinetically turns the turbine blades. Steam and gas turbines directly rely on chemical combustion, nuclear fission, and sunlight (nuclear fusion) for the heat source. Water turbines rely upon nature’s evaporation and precipitation cycles.
These weather cycles are energized by the heat of sunlight to indirectly elevate water to 4 higher levels behind dams. Whether the “fluid” is directly or indirectly energized by heat, heat energy is the primary energy source for most of today’s electricity generation.
1.2 HEAT: AN ABUNDANT ENERGY SOURCE
To harvest energy one has to have an energy source. Heat is an abundant energy source.
It is produced naturally by the sun and geothermally by the earth’s interior. It can be readily produced by chemical combustion and nuclear reactions. All matter readily stores heat energy with some doing so better than others. Because of its abundance, any system or process for harvesting energy would be well served to use heat energy as the source for any conversion to electricity.
Heat is fundamentally electromagnetic in character. Heat is stored in matter in the form of vibrations and motion of atoms and molecules. The electric fields of protons and electrons create spring like compressions and repulsions in atoms and molecules that collide or are oscillating adjacent to each other. The electrical and heat conductivities of matter are intertwined. The best conductors of electricity are also among the best conductors of heat [3]. Heat also naturally converts the vibrational and kinetic energy into thermal radiation energy. Thermal radiation is better known in electrical engineering as electromagnetic waves. Because of its omnipresence, it enters many electronic systems. It is also commonly referred to as “Johnson noise,” “thermal noise,” or more simply as “noise.” While it has characteristics in common with these types of circuit noise, it is also distinctive. 5
By definition the movement of electrons constitutes electricity, and this movement allows the transfer of electrical power and energy. Electrons inherently produce electric fields, a form of potential energy. When electrons move from one potential energy level to another, their movement, a form of kinetic energy, generates magnetic fields. When electrons oscillate periodically, the associated electric and magnetic fields can generate electromagnetic waves. These principles of physics are well defined by Maxwell’s
Equations and are well understood. They are the foundation of all electrical engineering.
1.3 WHY USE HEAT RADIATION?
There are many types of energy and several forms of energy transfer. Heat energy is transferred from mass to mass via three mechanisms: conduction, convection, and radiation [4]. Given these alternatives, why explore the potential of heat radiation?
First and foremost, heat radiation is abundant and readily available. The sun delivers over a kilowatt of heat radiation per square meter for much of the earth’s latitudes [5]. The
U.S. Energy Information Administration reports that the typical household in 2015 used
29.6 kilowatt-hours per day [6]. This consumption is equivalent to a few square meters of sunshine on much of the earth, assuming efficient heat-to-electricity conversion.
Geothermal heat flows from the earth’s core to the surface are approximately 60 to 100
-2 mWm almost anywhere on earth [7-8]. The U.S. Department of the Interior reports that the average depths of ground water wells in Oregon are on the order of 100 feet or so [9]. Similar ground water depths are found throughout the U.S. The geothermal heat 6 flows can be captured from ground water as well as artesian wells. Absent abundant, natural occurring heat, chemical combustion and nuclear fission can generate tremendous amounts of heat from fossil and nuclear fuels.
Secondly, heat radiation offers significant potential for higher energy efficiencies. Heat engines, such as steam engines and gas turbines, are used to turn today’s electrical generators. Steam engines have efficiencies on the order of 37% [10]. Gas turbines approach efficiencies in the range of 40-55% [11]. While rotary magnetic induction generators approach 90%+ efficiencies, when coupled with a lower efficiency heat engine the overall system is reduced to roughly 30-50% efficiencies. By way of comparison, patch antennas convert electromagnetic radiation to electric currents with efficiencies that have been reported to exceed 92% [12]. Matter naturally converts heat energy to radiation with high efficiencies, and insulation around any heat reservoir can preserve large portions of the heat energy until it is needed.
Thirdly, heat transfer via radiation occurs as a function of temperature to the fourth power while heat transfer via conduction and convection transfers as a linear function of temperature. If one seeks to engineer maximum transfer of heat energy, heat radiation is the best mechanism for maximum transfer.
1.4 RESEARCH IN SUPPORT OF THIS CONCEPTUAL DESIGN
Research into generating electricity directly from heat radiation is relatively thin. The energy harvester adapted in this dissertation looks like a radio system, however. A radio 7 system modulates, transfers, and demodulates signal energy using electromagnetic waves. Extracting signal power from the radiation background is the primary objective for such communication systems. In the “Simple Generator System” the signal being captured is the noise from heat radiation. Ironically, one of the competitors to successful communications is heat radiation, commonly known as “noise.” Industry research for communications has been greatly focused on the mitigation, prevention and reduction of
“noise” rather than its constructive use.
Tesla was one of the earliest technical pioneers to explore the transfer of electric power wirelessly [13]. Wireless Power Transfer (WPT) has had extensive research as this history shows [14]. With the advent of the space program in the 1960’s, the engineering community revisited WPT looking for commercial applications to economically fund the development of space exploration. Orbital generation of electricity using solar cells coupled with the wireless power transfer to earth became one of the technical dreams of that era [15]. A subset of WPT is the transfer of power to mobile platforms such as helicopters, drones and balloons. This subset is known as Mobile Power Transfer (MPT), and several prototypes have demonstrated the technical feasibility [ 16 ]. While technically feasible, however, wireless power transfer has been slow to develop economically. Given that anyone with an antenna might extract power from the air, commercial businesses have not solved how to prevent giving their power away for free.
Delivering electric power to remote areas is an inherent benefit of WPT. Yet, the 8 economics have been haunted by the distance squared power losses inherent in the propagation of electromagnetic radiation.
Recently, rectennas have been the technological darling that has garnered research interest. A rectenna, often called a rectifying antenna, combines technology using antennas and rectifying circuits on microstrip printed circuit boards (PCB). Conceptually, there is little that inhibits reduction to MMIC scales much like LCD screen technology.
Much of the rectenna research literature centers on the 2.4 GHz spectrum given its availability for testing [17-18]. The evolution from theory to circuit testing has led to numerous antenna and rectifying circuits being tested. The test environment often uses a signal generator to power the transmitting antennas [19]. This testing environment is essentially WPT where traditional AC electricity is used to power the microwave signal generators.
The latest evolution in the industry research is the fascination with energy harvesting.
Photoelectric solar cells harvest electricity from sunlight. Thermoelectric and piezoelectric sensors have been employed to harness temperature gradients and mechanical vibrations. While there has been some activity centered upon harvesting ambient RF signals [20], there has been a paucity of research into harvesting heat radiation as a source. 9
1.5 ANTENNAS AS ELECTROMAGNETIC ENERGY HARVESTERS
Antennas are passive devices that use conductors to guide electromagnetic (EM) waves to periodically excite electrons in the conductors. The oscillating EM waves excite the individual electrons in the conductors creating electric currents. Based upon antenna geometries these alternating currents are passively reinforced producing resonance and signal gains. To generate electricity from an antenna, radiation must irradiate the effective aperture of the antenna. The radiation from the incoming EM waves can then be converted to electrical voltages and currents associated with each of the incoming frequencies.
1.6 RECTIFICATION
Electromagnetic waves captured by an antenna produce movement of electrons in the antenna’s conductors. This movement alternates based upon the frequency of the electromagnetic waves. Because the frequencies of heat radiation are very high, this form of alternating current needs to be converted to lower frequencies. Frequencies such as
60 Hz or direct current, are commonly used by commercially available devices. The electron movement can be readily converted from alternating current to direct current by passing the received signal through a semiconductor device known as a diode.
Electrons with a voltage above the threshold voltage of the diode pass through the diode while the electrons from the reverse direction are blocked. The resultant direct current electricity subsequently can be converted to useable alternating current, or it may be stored and used directly as direct current. 10
Figure 1.2 illustrates a basic rectenna. Power from an electromagnetic plane wave excites electrons in an antenna. A diode rectifies the oscillating electrons charging a capacitor with repeated oscillations. A load in the form of a resistor drains the charged capacitor performing useful work. The key to the rectenna’s success and utility is capturing enough power to generate input voltages greater than the voltage threshold of the diode.
Figure 1.2: Rectenna Basics
1.7 THE NEED FOR ENGINEERING GAIN
Heat radiation emanating from a “transmitting” surface may have insufficient power to clear the voltage threshold of a diode. Consequently, a power system must be engineered to effectively harvest the radiating heat energy. A weak input power signal (such as -50 dBm per m2) emanating from a heat surface (transmitter), when scaled through passive 11 engineering gain techniques (+50 dB), could conceptually enter a rectifier (receiver) with a power of 1 mW (+0 dBm). Per conservation of energy and power constraints, these passive gains cannot produce more energy or power. Instead passive gains are derived from aggregation of wave fronts, geometric areas and volumes, and frequency bandwidth.
For example, the voltage maximum for a standing wave inside of a waveguide is twice the amplitude of the wave entering the waveguide even though the power entering the waveguide does not change. Such engineering gains are essential for harvesting input signals with low power densities.
EM waves travel through free space with an impedance of 377 Ω. When these EM waves enter a 50 Ω rectifier, much of the free space power is reflected. As a result, the power level of +0 dBm measured at a rectifier is +3.8 dBm in free space. A power level of +0 dBm entering a rectifier can generate a RMS (root mean squared) voltage level approaching 0.224 V. Without reflections from the impedance boundaries more of the free space power could reach the rectifier. If the rectifier could be engineered for 377 Ω, the RMS voltage could approach 0.954 V.
1.8 HEAT RADIATION IN THEORY
Any exploration of heat radiation as a direct power source requires an estimate of the power that emits from a surface. If one turns to physics literature, one finds that the
Planck’s Equation quantifies the energy that is emitted from a material surface for a given emission frequency [21]. Given the temperature of the material and a surface property 12 called emissivity, one can calculate the energy that is likely from a surface. This equation is well tested, and it is the cornerstone of Einstein’s Coefficients used in quantum physics, the foundation for oscillators, and the impetus for stimulated emissions in lasers [22].
If one turns to electrical engineering literature, one is likely to encounter the formula for
Johnson noise or thermal noise power, commonly known as the “kBTB” equation [23-24].
This allows one to model noise in an electronic circuit as an equivalent resistor for a given temperature. Using the ambient temperature of the circuit for this temperature is correct for an electronic circuit. When used to model noise entering an antenna, however, the ambient temperature of the antenna and the antenna noise temperature are different.
Often missed is that the antenna noise temperature needs to be based on actual measurements.
While the rest of this chapter on “Heat Radiation in Theory” provides encouragement and promise to the direct harvesting of heat, it provides only theoretical confidence in the end. Nagging in back of the minds of almost every scientist and engineer: “It already would have been discovered if there was a way to directly harvest heat radiation. There just is not enough power there to be practically useful.”
Given this doubt, only the fundamental rule of electrical engineering can dispel it. The fundamental rule of practical electrical engineering can be summarized as: “When in doubt – Measure.” The magnitude of ambient radiation that looks like a noise floor was measured during this dissertation research. 13
1.9 STEFAN-BOLTZMANN EQUATION
Success in energy harvesting rests on two questions: “Is there any power to harvest?” and
“Is the power enough to be useful?” While engineering a solution in theory can be intellectually rewarding, it can take significant time and resources to eventually discover that the results are only “interesting.” The Stefan-Boltzmann Equation [25] provides a quick way to assess the potential results that might be realized before attempting any engineering efforts. Basic physics observes that the hotter matter becomes, as measured by its temperature, the more thermal power (j*) it radiates per unit area. This thermal power radiates across a broad range of frequencies spanning, if hot enough, from radio through microwave, infrared, light, ultraviolet, and then X-rays. The Stefan-Boltzmann
Equation predicts the radiated power for all frequencies as a quartic function of temperature1. Its simplicity is conducive to “back of the envelope” assessments and reasonableness comparisons.
As an example of the equation’s utility, the human body with an average temperature of
98.6oF (310.2K) radiates 525 W/m2. Given that the average human body has a surface area of approximately two square meters, the average human body radiates roughly a kilowatt of thermal radiation. Another physics law will be introduced later in this chapter that allows the prediction of power in a frequency range. Using this law, approximately
2 W (0.2% or -27 dB) of this kilowatt of power emanates in the 20 to 100 GHz range, and
* 4 8 1 2 4 1 j T Where 5.6704 10 Js m K and T is the temperature in degrees Kelvin. 14 the 20 to 50 GHz range produces roughly 80 mW (0.01% or -41 dB). Of course, the surrounding air at an ambient temperature of 72oF (295.4K) also radiates, and the human body absorbs this energy of 863 W for a net transfer of 187 W to the atmosphere. To maintain the average temperature of 98.6oF the human body must chemically metabolize food.
2 Emitted Power (W/m ) for Temperature Range of Liquid H20 1200
1000 ) 2
618 W/m2, 50 oC 800
600 ThermalPower (in W/m 400
525 W/m2, 98.7 oF
200 280 300 320 340 360 Temperature (in oK)
2 Figure 1.3: Emitted Power (W/m ) for Temperature Range of Liquid H2O
Figure 1.3 graphs the Stephan-Boltzmann equation for the temperature range of liquid water (roughly 0oC to 100oC). As can be seen in Figure 1.3, a cubic meter of water at 50oC 15
(323.2K) radiates 619 W from each of the six faces of a cubic meter, if the faces are perfectly black (i.e., have and emissivity equal to one). Without an inbound source of energy, the temperature of the cubic meter of water drops as it cools due to the radiated heat.
Emitted Power (W/m2) for Temperature Range 0oC to 1500oC
1000000 ) 2 100000
10000
1000 Thermal Power (in W/m (in Power Thermal
100 400 600 800 1000 1200 1400 1600 Temperature (in oK)
Figure 1.4: Emitted Power (W/m2) for Temperature Range 0oC to 1500oC
Figure 1.4 graphs this equation from 100oC to 1500oC (373K to 1773K). As the temperature of a material surface rises to 1500oC (1773K), the emitted thermal radiation rapidly rises to nearly a megawatt per square meter, as shown in Figure
1.4. The temperature of any material can be raised by natural heating through 16 sources such as the sun. It can also be raised by chemical combustion. For example, wood burns at roughly 450K to 600K. The burning wood at these temperatures produces between 1 to 10 kW/m2 of thermal radiation. This radiation explains the perceived warmth standing in front of a campfire on a very cold day while the back side of the one’s body is freezing. The power industry is rapidly shifting its electric power generation to natural gas because of its abundance, energy content, economic, and environmental characteristics. The combustion temperature of natural gas is approximately 2000oC (2273K) making it a very attractive source of heat energy. Modern technology produces very high combustion temperatures that can produce lots of thermal radiation. Harvesting techniques can be applied to natural as well as combustion generated heat sources.
1.10 STORAGE OF HEAT ENERGY
Every volume of matter has a capacity to store heat. This capacity is known as the volumetric Specific Capacity of Heat. For water the volumetric capacity at 25oC is 4.1796
J·(cm3K)-1, and at 100oC it is 4.2160 J·(cm3K)-1 [26]. While the heat capacity of water varies somewhat by the temperature between the freezing and boiling states, an average of 4.2
J·(cm3K)-1 can be used to estimate the storage capacity. Using this approximation, the heat that can be stored in a cubic meter of water can be estimated as 100 kWh between
96oC and 10oC. The temperature delta between these two temperatures offers the
-3 energy storage potential of 100 kWhm . By way of comparison, commercially available 17 lead acid batteries (e.g., Power Stream BP12-12 with a price of $46.10 and a volume of
3 -3 1391 cm ), yield approximately 104 kWhm [27]. Given this rough equivalence in energy density, water could be used as an alternative medium to store energy if that heat energy could be economically converted to electricity on demand. Unlike battery technology which is limited by deterioration through charge/discharge cycles, however, water can sustain a significantly greater number of charge/discharge cycles without wearing out.
Figure 1.5 illustrates the heat capacity of water for a 75oC delta in temperature. While state changes alter the capacity at freezing and boiling temperatures, the energy storage works for the temperature range away from these transitions. This temperature gradient could store the electric energy (in a few cubic meters of water) that a typical house in the
U.S. consumes across three days. Direct electricity from heat radiation could economically address one of the power industry’s biggest challenges of better matching power supply with demand. 18
Figure 1.5: Water as an Energy Storage Source
1.11 PLANCK’S LAW: FREQUENCY SPECTRUM OF THERMAL RADIATION
A black-body, material surface spontaneously emits heat radiation across a broad frequency range depending upon the temperature of the surface. Individual photons are randomly emitted as individual “rays” from the material surface. The statistical average of these emissions forms a hemispherical pattern for any differential surface. Planck’s
Law [21] can be used to predict the power magnitude of these black-body emissions for any given frequency and temperature. These emissions are independent of any inbound emissions from the environment that may occur. 19
Planck’s Law for a hemispheric ray is as follows:
2 hf3 n 2 EPL_ f fT, 2 [1.1] c hf exp 1 kT
Where h is Planck’s constant, f is the frequency of emission, n is the refractive index of the medium (for air n=1), c is the free space speed of light, k is the Boltzmann constant, and T is temperature in Kelvin of the emitting material surface.
This equation predicts the energy per square meter for a hemisphere from the surface.
1 To predict the energy of an individual ray path a factor is needed to adjust the hemispherical energy portion of the equation included in the brackets. To obtain the hemispheric power magnitude that is emitted from a frequency range one integrates this energy equation across a frequency range. The equation for this computation is as follows:
rbw f0 P f, T2 E fT, df [1.2] PL_ f 0 f rbw PL_ f 0 2
Where f0 is the center frequency of the frequency range and rbw is resolution bandwidth.
Figure 1.6 shows the power prediction (in dBm·m-2) for a 5 MHz resolution bandwidth across the electromagnetic spectrum for two material surfaces: one at 295K (solid blue line) and one at 2500K (dashed red line). Emissivity is treated as 1.0 (a perfect black-body) 20 in the examples in this dissertation. If a meter squared area is selected, the per meter squared term is cancelled out. Visually, one can see that 1 nW (-60.0 dBm) is predicted at roughly 26.3 GHz for a 1 m2 area. There are three broad observations for the graph of these predictions:
1. For frequencies reaching into the infrared range (300 GHz to 430 THz) the power
emitted at a given frequency from a material surface is relatively linear for a log
scale of frequency.
2. The temperature difference between 295K (-60.0 dBm) and 2500K (-50.8 dBm)
produces roughly +9 dB greater power at a given frequency (e.g. 26.3 GHz).
3. The predicted power output is in the pW to nW (-90 to -40 dBm) range per m2 for
5 MHz segments of the microwave spectrum (1 GHz to 300 GHz). 21
-2 Figure 1.6: Power (in dBmm ) per Planck’s Law (5 MHz of Resolution Bandwidth)
These observations would lead one to believe that useful power in the nano-watt to micro-watt range could be obtained from heat radiation in the 1-300 GHz range of frequencies using current engineering technologies such as antennas. Using engineering gains through bandwidth aggregation, even higher amounts of power could be harvested.
Planck power is also remarkably stable for ambient temperature ranges including temperatures at -128oC (145 K). The Planck power magnitudes are indirectly confirmed by radio engineering. Since heat radiation appears as “noise” in communications systems, noise measurements in pW’s currently set a “noise floor” for communications. This floor limits effective distances between the receiver and transmitter. Antennas, as an operating practice, are generally pointed away from the ground and any objects that are also radiating heat. Ground noise is a well-recognized noise source that can be picked up 22 by the side lobes of antennas when pointing low in the horizon [28]. It is not unusual to see +30 dB higher powers between sky 0o and ground 90o azimuths.
While there is substantial power in aggregate across all frequencies for a given
-2 temperature (459 Wm at 300K per the Stefan-Boltzmann Equation), small ranges of frequency individually produce relatively little power. Figure 1.7 illustrates the engineering challenge for harvesting power from a 1 m2 area. Electronic processing of signals is currently limited to below 20 THz or so. Above this frequency level, optical processing techniques are used. State of the market Schottky diodes become increasingly ineffective for rectification as the operating frequencies rise above 100 GHz. The diode effectiveness at 100 GHz is less than 10%. Even the best, low-barrier diodes need 1 µW or so of power to turn-on for rectification. While signals less than 1 µW can be detected, this often requires voltage biasing that is incompatible with rectification applications.
Power levels need to reach 1 mW levels to become interesting and 1 W levels to become seriously useful.
Engineering gains between + 50 and +80 dB are needed to reach the seriously useful level.
Heat radiation would be hard to harvest without substantial gains through engineering.
Fortunately, engineering gains exist. 23
Figure 1.7: Planck Power (for a 1 m2) Area and Power Thresholds
Since a simple energy harvesting system looks very much like a communication system, the FRIIS Radiation Equation [29] is a well-recognized equation that can be adapted to estimate power magnitudes entering a rectifier. The FRIIS equation is as follows:
2 1 c PfTR,, PfTGG T RT 4 r f [1.3]
Where: PT is the power of the heat radiation emitted from heat surfaces for a given frequency (f) and temperature (T), r is the distance from the heat surfaces to the effective aperture, G is the engineering gains of the receiving and transmitting systems, and PR is the power received at the rectifier. 24
In theory the transmitting system within this energy harvesting system can be any material surface such as the laboratory wall used during this dissertation research. The gains for radiation emitted from this wall and entering an antenna aperture are on the order of +15 dB, as will be explained later in this dissertation. Antenna gains for highly directional, aperture antennas can be +25 dB. Gains from bandwidth aggregation have been measured during experiments for this dissertation as high as +25 dB. These bandwidth gains are directly related to the bandwidth that an antenna can receive. The combination of these gains approach +65 dB, and the combination can substantially raise the power predicted by Planck’s Law. Of course, these gains are offset by losses due to reflections, single polarities, connectors, and rectifier inefficiencies. These losses were measured at nearly -24 dB for the WR-187 and the Version 4 Rectifier during the research for this dissertation. Figure 1.6 shows that Planck’s Law predicts nano-watt (-60 dBm) power levels at 26.3 GHz for a 5 MHz frequency segment for a 1 m2 area. Figure 1.8 combines Planck’s Law with the net +41 dB gains (+65 dB - 24 dB) to suggest that roughly
-20 dBm power that can be obtained from a wall. As can be seen in Figure 1.8, the predicted power magnitude climbs to almost +0 dBm at 100 GHz. These power projections were matched by subsequent measurements with the WR-187 waveguide connected to the V4 and V5 rectifiers fabricated during this dissertation. 25
Figure 1.8: Planck Power (in dBm) with Area and Bandwidth Aggregation Gains
Figure 1.9 shows the performance measurements for the Version 4 and 5 Rectifiers fabricated during this dissertation in comparison to the Planck’s Law prediction of -60 dBm per m2 at 26.3 GHz. The average power and the peak power were measured with the N1911A power meter. The peak power measurement was duplicated by the Channel
Program using the FieldFox meter. The differences are the computed magnitudes between the predicted Planck’s Law and the measured average as well as the measured average and the measured peak. The Version 4 Rectifier was not impedance matched between the low pass filter and the diodes. The Version 5 Rectifier corrected this mismatch, and the output voltage substantially improved. 26
V4 Rectifier V5 Rectifier
Operating Frequency (in GHz) 26.3 26.3
Planck's Law (dBm per m2) -60.1 -60.1
Difference Between Planck's Law and Average Power 13.8 13.8
Measured Average Power (dBm) -46.3 -46.3
Difference Between Average and Peak Power 25.0 25.0
Measured Peak Power (dBm) -21.3 -21.3
Theoretical Voltage (in mV) 19.3 19.3 Measured Voltage (in mV) 7 19.0 Effective Rectification 36.4% 98.7%
Figure 1.9: Measurements of Version 4 and 5 Rectifiers
1.12 “KBTB” NOISE EQUATION
Quantifying the power that is available from heat radiation is an essential task on the road to harvesting the power of “noise.” The “kBTB” equation is extensively used within electrical engineering. Agilent Technology publishes Application Notes and is renowned for their measurement leadership. The Agilent publication on noise introduces this equation and uses it extensively [30]. RF Café, a website (www.rfcafe.com) which extensively covers RF and microwave topics, refers to this equation as Thermal Noise
Power [31]. This equation allows the modeling of thermal noise in a circuit as a Thevenin equivalent resistor and voltage source using Nyquist’s Law. Some publications caution 27 that this equation is a minimum power that must be augmented with noise measurements to get an actual thermal power received by antennas and to arrive at an equivalent antenna temperature [32]. Irrespective of its intended use and the associated caveats, engineers often use such equations and rules of thumbs to gauge feasibility.
Traditionally, noise power can be represented in circuit models as follows:
N kTBB [1.4]
Where N is noise power, kB is Boltzmann Constant, T is temperature (in K), and B is bandwidth.
For a 72oF (22.2oC) environment this formula predicts 0.02 pW (-106.9 dBm) of noise power being generated in a 5 MHz bandwidth.2 While this is the noise power of a resistor at room temperature, the actual power received from an antenna is likely to be much different. To match the power predicted by Planck’s Equation at 26.3 GHz and ambient temperatures the antenna temperature in the “kBTB” equation would have to be
1.45 million degrees Kelvin, a temperature far hotter than the sun’s 5780 K.
1.13 DISPARATE POWER PREDICTIONS
The disparate difference in predictions (+57 dB) between the traditional noise power equation (-106.9 dBm) and Planck’s Law (-60.0 dBm) at 26.3 GHz presented a dichotomy early in the research for this dissertation. The existing research literature provided no
2 N k TB(1.38 1023 J / K ) 295.4 K 5 MHz 0.02 pW B 28 noise measurements to guide the assessment of which prediction to believe.
Fascinatingly, radio engineering references from over seventy years ago used the traditional noise power equation to predict a noise floor of -104 dBm for a ham radio station that also measured the noise floor as -111 dBm [33-34]. For a 120 MHz signal with a 10 kHz bandwidth and a 295 K temperature, Planck’s Law predicts -133.9 dBm and the kBTB formula predicts -133.9 dBm.
Figure 1.10 plots the kTB formula and Planck’s equation on a logarithmic scale for a 1 Hz bandwidth. At frequencies under 200 MHz the two methods yield similar results. As the frequencies increase, however, Planck’s equation rapidly diverges in the predicted power levels for noise. This divergence explains the need for an equivalent noise temperature greater than that of the sun in the kTB formula. Planck solved the “ultraviolet catastrophe”
(infinite energy problem) associated with the kTB formula. Planck’s law predicts less power at higher frequencies than the kTB formula while agreeing at low frequencies. 29
Figure 1.10: Planck vs kTB Power Predictions per Hertz
1.14 EARLY POWER MEASUREMENTS
The initial measurement of the power spectrum was performed using a LadyBug power meter. The frequency span of the meter was 10 MHz to 10 GHz, and the power measurements were manually recorded for each measurement frequency. The meter also has a power measurement range of -60 dBm to +20 dBm. The resolution bandwidth, the frequency span of an individual measurement, was 100 kHz.
A WR-340 rectangular waveguide and a patch antenna salvaged from a Buffalo wireless router were used as antennas. The measurement results are shown in Figure 1.11. While frequencies below the frequency cutoff (fc) are reflected out of a waveguide, the effective cutoff frequency is generally 20% higher because the impedance inside the waveguide 30 becomes infinite as one approaches the frequency cut-off from above [35]. Since the effective cutoff frequency for a WR-340 waveguide is roughly 2 GHz (fc = 1.736 GHz), the measured floor was roughly -60 dBm for the WR-340 waveguide up to 2 GHz. Since – 60 dBm was the minimum limit for power measurements with the meter, this result was expected. At 10 GHz the meter measured -34 dBm of power for the WR-340. The microstrip patch antenna salvaged from the Buffalo wireless router registered -4.4 dBm at 10 GHz. As can be seen in Figure 1.11, linear extrapolation from the WR-340 measurements, however, clearly indicated that power more than +0 dBm was probably achievable.
Figure 1.11: Power Spectrum Measurements with LadyBug Power Meter
31
1.15 CONCLUSIONS FROM HEAT THEORY, LITERATURE, AND EARLY MEASUREMENTS
The power of -4.4 dBm at 10 GHz was measured in a preliminary measurement using a relatively low-cost power meter with a limited frequency range and a Wi-Fi patch antenna.
This measurement exceeded the prediction of Planck’s Law by +56 dB and the prediction of the traditional noise formula by +97 dB. Intellectually, gains from an antenna (+25 dB) and other engineering gains (+35 dB) seemed to feasibly explain the gap between Planck’s
Law (-60 dBm) and the best measurement (-4.4 dBm). This added further support to
Planck’s Law. Finally, the reputation of Planck’s Law and its theoretical underpinning of quantum physics gave further weight to using Planck’s Law for modeling the power magnitudes for heat radiation. Figure 1.12 summarizes the disparate power predictions.
Figure 1.12: Two Possible Methods to Predict Power
32
Unfortunately, there is a disparate difference (+57 dB) in the predictions Planck’s Law and
o o the “kBTB” equations for an environment temperature of 72 F (22.2 C). The existing research literature provided no measurements to guide the assessment of which prediction to believe. Using the traditional noise formula prediction of -106.9 dBm, one would quickly consider harvesting from heat radiation as infeasible. It is likely that many electrical engineers have followed this path. Using the Planck’s Equation, the -60.0 dBm prediction offers hope for using thermal noise as an energy source. When in doubt, engineering caution suggested that the power should be further measured.
33
2 ENGINEERING GAINS USEFUL TO HARVESTING HEAT RADIATION
2.1 CONSERVATION OF ENERGY AND ENGINEERING GAINS
The conservation of energy (power) is one of the most fundamental principles of physics.
Engineers routinely use the FRIIS equation to estimate the power that is delivered to a receiver by multiplying the transmitter power by the gains associated with the transmitting and receiving antennas adjusted by distance related attenuation. These types of passive gains are engineering “gains.” Since It is impossible to create energy through mathematics, these engineering “gains” are really techniques to quantify the aggregation of energy and power that may be distributed in wave fronts, geometric areas and volumes, and frequency spans. They are often relative to a comparison standard such as the power associated with an isotropic radiator or an area of one meter squared. For example, a parabolic antenna dish with an area of 4 m2 concentrates the received power density intercepted by the dish resulting in four times the power density relative to a square meter being delivered to a receiver. While more power is physically delivered to the receiver, it comes from capturing a greater area of radiating power. Engineering gains like this are mathematical simplifications for far more complex energy and power aggregation techniques that are consistent with energy and power conservation. 34
2.2 ANTENNAS
Antennas use conductors and geometry to capture the power of incoming electromagnetic waves by aggregating the changes in the EM fields in a volume of space.
Antennas achieve this aggregation by harnessing and reinforcing periodicity from the incoming electromagnetic waves. This periodicity can create an electrical signal that concentrates the energy and power in an EM wave. This gain varies for every type of antenna. Since this gain is an aggregation of EM waves across wave fronts within a volume of space, the conservation of energy and power are preserved.
Rectangular waveguides belong to a class of antennas known as “aperture antennas.”
Figure 2.1 contains photographs of a rectangular waveguide and a coax adapter for a rectangular waveguide. The gain of an aperture antenna depends primarily on the input frequency and the dimensions of the aperture. While the conversion efficiency of the antenna depends on many factors, 90 to 100% is a common efficiency assumption used in modeling. The area of a WR-340 waveguide is 3.4 in x 1.7 in (37.3 cm2). The equations for computing the antenna gain and its gain in dB for an aperture antenna [36] are as follows: 35
2 f G f 4 Area a a aperture c [2.1]
GfadB10 log Gf a [2.2]
Where a is the antenna efficiency, f is the frequency, and c is the speed of light.
The computed antenna gains using these formulas at 26.3 GHz for the WR-340 waveguide using a 90% efficiency were calculated as follows:
GaWR340 26.3 GHz 324.6 [2.3]
GaWR340 dB 26.3 GHz 25.1 [2.4]
Figure 2.1: Antenna Gain for an Aperture Antenna
36
The antenna gains for the WR-187 waveguide using 99% efficiency can be similarly computed:
GaWR187 26.3 GHz 108.4 [2.5]
GaWR187 dB 26.3 GHz 20.3 [2.6]
When plotted on a frequency logarithmic scale, Figure 2.2 shows the theoretical, linear, gain impact in dB of the WR-340 and the WR-187 waveguide antennas. Antennas are often engineered so that the operating frequencies are within the TE10 mode of the antenna. The operating range of the TE10 mode for a WR-340 waveguide is 1.7 to 3.4
GHz. Higher frequencies activate higher modes within the waveguide. This equation also does not apply for frequencies below the cutoff frequency as a result. 37
Figure 2.2: WR-340 and WR-187 Antenna Gains (in dB) as a Function of Frequency
The gain and the beam width of an antenna are related. The formula for the gain (GA) of an antenna is as follows:
4 GA AA D A [2.7] SA
Where A is the electrical efficiency of the antenna, DA is the directivity of the antenna,
and SA is the solid angle associated with the beam width.
The efficiency of an antenna can be estimated to be near 100% since it is dependent on the low electrical resistance of the antenna’s conductors. As a result, the gain and the directivity of the antenna are roughly equivalent. Solid angles and gains are therefore 38 inversely related. Consequently, smaller solid angles yield smaller beam widths and higher gains.
For radiometry where the luminance sources are often celestial bodies, areas adjacent to the emitting body tend to be vacuums. As a result, the radiation received from the emitting body is fully contained in the diameter of the body, and solid angles are tied to the diameter of that body. For heat radiation from broad surface areas, however, the normal components from radiation originating outside the beam width also make contributions. Using the Lambert cosine to obtain the normal contributions from the emanations outside the beam width, heat views provide the solid angles for heat radiation.
The solid angles for the WR-340 and WR-187 waveguides can be computed using the radiometry, the antenna gain Equation [2.1], and heat view approaches. The distance of
1.0 m was used in computing the solid angles and the associated gains. Table 2-A reflects the different results in antenna gain.
Table 2-A: Antenna Gain Computed via Different Techniques
Gain (in dB) Type of Aperture Area FRIIS Radiometry Heat View Waveguide (in m2) Equation WR-340 0.003729 35.0 25.5 34.4 WR-187 0.001130 40.0 20.3 48.1 39
2.3 EMITTING AREA
Planck’s Law predicts a power magnitude for a surface area that is emitting power, such as 1 nW·m-2 (-60 dBm·m-2). The surface can be real or virtual in space. A meter squared of area generates 1 nW. By engineering to select a larger area more power can be harvested. An area of 4.1 m2 generates 4.1 nW. An area of 4.1 m2 relative to a 1 m2 comparison translates to a gain of +6.1 dB yielding a Planck floor of -54 dBm for a power density (-60 dBm per m2) at 26.3 GHz and 5 MHz bandwidth.
2.4 HEAT GEOMETRIES
The geometry of a heat source surface relative to the antenna’s effective aperture create gains much like a parabolic antenna does. In a parabolic antenna the parabolic surface reflects and concentrates EM radiation into the antenna’s aperture. The parabolic surface increases the effective aperture. This analogous, passive gain technique is known in the literature of heat theory as heat “View Factors” [37]. These view factors are integral to computing radiative heat transfer. While these are techniques for estimating and engineering heat transfer, they equally apply to the energy transfer of microwaves since microwaves are an electromagnetic radiation subset of heat radiation.
View factors, commonly represented as Fij, are founded on the concept that one can define a view of power flow from one surface (subscript i) irradiating another surface
(subscript j). The sum of all views from a surface to all other surfaces in a system totals to one, as represent by the formula: 40
F1 j 1 j2 n
Where j identifies the other real or virtual surfaces in the system.
For a simple geometry there is a heat source surface (i=1) and an antenna aperture (a virtual surface of j=2). There is one other virtual surface of the surrounding air (j=3). In this case the view factors reduce to two surfaces:
F{ aperture } F { surrounding _ air } 1 12 13 [2.8]
Figure 2.3 illustrates the geometry relationships between two surfaces in radiative heat transfer. For two surfaces facing in arbitrary directions, two cos function adjustments are needed to obtain the normal component that irradiates the differential area dA2. If the two surface areas (A1 and A2) are perpendicular to each other, then the two cos terms reduce to a single cos term, as reflected in equation [2.9].
1 1 F cos dA dA [2.9] 12A s2 2 1 1 A1, A 2
Where s is the distance between the differential surfaces of the heat source and the aperture, and cos (α) is the component of the ray from the heat source surface to the normal entering the aperture. 41
Figure 2.3: View Factors for a Simple Heat Source and Antenna Aperture Surface
Using vector analysis, the distance (s) and the cos (α) can be obtained as:
2 2 2 sxyz(, ,) xx1 2 yy 1 2 zz 1 2 [2.10]
xx 2 yy 2 cosxyz , , 1 2 1 2 [2.11] sxyz(, ,)
Combining the individual equations, the full equation is obtained as:
w h w h 2 2 1 1 2 2 2 2 2 2 1 xx yy 1 1 2 1 2 F dy dx dy dx [2.12] 12 2 1 1 2 2 A1 wh w h sxyz(,,) sxyz (,,) 22 1 1 22 2 2 42
Using a software package for numerical integration called MATHCAD, the following results were obtained:
-3 w1 = 5.0 ft w2 = 3.4 in F12_1m (w1, h1, w2, h2, z1, z2) = 1.155 x 10 -7 h1 = 2.5 ft h2 = 1.7 in F12_NG (w2, h2, w2, h2, z1, z2) = 4.146 x 10 z1 = 0.0 m z2 = 1.0 m Ghsg340 = 2785 (+34.4 dB)
By computing the ratio of the view factor of F12_1m divided by the view factor F12_NG (a projection of a virtual A2 area on the A1 surface), the gain due to the larger A1 can be obtained. As the geometry becomes more complex software tools, such as COMSOL, can be used to simulate the geometries, as shown in Figure 2.4.
Figure 2.4: Heat Source Gain Obtained thru COMSOL Simulation 43
2.5 PREDICTIVE EQUATIONS FOR POWER
Predictive equations are often useful in engineering. It was hypothesized that area, bandwidth, and antenna gains were applicable to the predictions from Planck’s Law.
Area, bandwidth, and antenna gains can passively increase signals through aggregation of wave fronts, geometries, and multiple frequencies. Equation [2.13] and Equation [2.14] include the wall area (A1), the bandwidth gain (Gbw), and the antenna gain (GA). This is a predictive equation where the WR-187 curve is fitted to the two measurement points by the 0.854 factor. The closeness of fit for the two data points suggest that there may be predictive utility. This equation uses a resolution bandwidth of 5 MHz. The gain (Gbw) from bandwidth corresponds to 3% of the operating frequency divided by 5 MHz. The equations used to predict this plot are as follows:
f rbw 2 PfT, A 0.854 EfTGfdfGf , ppp 1 bf A bw [2.13] f rbw 2
Pppp fT, PdBmppp fT, 10 log [2.14] mW
2 Where Pppp is the Planck predicted power, A1 (4.1 m ) is the area emitting Planck radiation,
Ebf(f,T) is the function described by Equation [1.1], and GA(f) is the function described by
Equation [2.1]. T is the temperature (295K) of the surface area A1 and f is the operating frequency. 44
Figure 2.5 shows the predicted power (in dBm) at the coax adapter for the WR-340 (in red dotted) and WR-187 (in blue solid) waveguides.
Figure 2.5: Predicted Power (in dBm) per Planck’s Law with and without Gains
Figure 2.6 uses equation [2.14] to predict the power (in dBm) available in the 5 MHz
segments around each frequency in the power spectrum that is produced at the two
temperatures of 295K and 2500K. The engineering implication of this power
projection: There is a lot of power in the microwave and infrared frequency ranges
awaiting effective harvesting. Even more power is available at the higher frequencies
if the state of the rectification technology could harvest it. 45
Figure 2.6: Predicted Power (in dBm) for Two Temperatures (295K and 2500K)
2.6 REFLECTIONS
Electromagnetic radiation in the microwave and higher frequencies are subject to power reflections and the associated reductions in power transmissions. Power reflections are determined by the voltage reflections squared (Γ2). These phenomena are triggered by changes at impedance boundaries, and the coefficients that impact the voltage magnitudes are determined by the following equations:
Z1 Z 2 Z1, Z 2 Voltage Reflection Coefficient [2.15] Z1 Z 2
TZZ 1, 2 1 ZZ 1 , 2 Voltage Transmission Coefficient [2.16] 46
EM radiation travelling through free-space encounters an intrinsic impedance of 377 Ω.
The impedance within an antenna varies by the antenna type and dimensions. Coax adapters are commonly used to connect antennas to electronic circuits such as receivers and rectifiers. Two common impedances for coax adapters are 50 Ω and 75 Ω. Reflections occur as the EM plane waves encounter the change in impedances from the free-space to antenna to coax adapter to electronic circuit.
Figure 2.7 illustrates the reflection and transmission implications of a rectangular waveguide (377 Ω entering the waveguide) and a 50 Ω coax boundary. About 77% of the free-space voltage entering the waveguide is reflected at the coax boundary, and 23% is transmitted to the electronics beyond the coax adapter. If the electronics beyond the coax adapter is a meter measuring the power, then the measured power is only 41% (1-
Γ2) of the free-space power. Reflections at disparate impedance boundaries thus reduce the overall power reaching the measurement circuit. Consequently, the actual power in free space is +3.8 dB higher than a measured magnitude of +20 dBm at a meter given the transition from 377 to 50 Ω. 47
Figure 2.7: Implied Power from Measured Power Due to Reflections
2.7 IMPEDANCE MATCHING
As a result of reflections at impedance boundaries, many microwave and infrared systems are impedance matched to minimize the signal losses due to these reflections. Standard circuits are used, such as the quarter-wave transformer and stub tuning circuits, to minimize the losses for a given operating range of frequencies. These types of circuits are optimized to a specific frequency. Heat radiation spans a very large frequency range where these circuits will periodically alternate between ranges that harvest power and ranges that do not. For sinusoidal signals this characteristic suggests engineering ladders 48 of band-select circuits that select specific ranges where impedance matching is implemented within the selected frequency range. Alternatively, one can impedance match for the major boundaries and take what happens for all others. Since filters have inherent insertion losses, the crude approach might be good enough since more sophisticated filters may incur greater losses. Given the temporal randomness of Planck radiation, however, impedance matching can be compromised by the non-sinusoidal behavior of the resultant signals. Ideally, a rectenna for maximum power capture should be engineered to match the intrinsic impedance of free-space as close as possible.
Engineering for maximum power suggests using a different boundary condition for the connection to the rectangular waveguide. The 50 Ω impedance for coax adapters is determined by the physical dimensions of the adapter and the connecting coax. Parallel wires have a different impedance dictated by the physical dimensions. If a parallel wire is somehow connected to the waveguide and the impedance is engineered to be close to the 377 Ω inside the waveguide, then more of the free-space power could reach the rectification circuitry. As an example of a commonly use alternative, the impedance of a parallel wire connection is given as follows:
Z Z o cosh1 D [2.17] p d r
Where Zo is the impedance of free-space (377Ω), εr is the relative permittivity of the material around the transmission space, D is the distance between the parallel wires, and d is the diameter of the wire. 49
Figure 2.8 shows an example of dimensions in a parallel wire connection between a rectangular waveguide and the rectifying circuitry. If the parallel wire connection achieves a 442 Ω impedance, then 99.4% of any free-space power would reach the rectifying circuitry. While exploring the 0 Hz power measurements, the parallel wire connection in combination with the “wire probe through” the waveguide was considered.
Figure 2.8: Power Gain Achievable with Parallel Wire Connection to Waveguide
2.8 BANDWIDTH AGGREGATION
Each segment of frequency contains a magnitude of power. While each segment of frequencies has relatively the same average power as the previous segment, Planck’s Law predicts a difference of +20 dB between the powers at 26.3 GHz and 100 GHz. When a 50 span of bandwidth contains multiple segments, then the power aggregates. By choosing a wider bandwidth the total power can be controlled. The aggregate power and the associated voltages can be estimated with the following equations:
BW Paggregate P segment [2.18] RBW
BW V V [2.19] aggregate segment RBW
Where P is power, V is voltage, BW is the selected frequency bandwidth, and RBW is the resolution bandwidth of the segment.
The use of passive filters allows the selection of a bandwidth range that enters a rectifier.
For example, a 30 GHz bandwidth has 6000 segments with a resolution bandwidth of 5
MHz for each segment. If the power in a 5 MHz segment was 1 µW (7 mVrms), then the noise power in 30 GHz would be 6000 times greater or 6 mW (0.548 Vrms). The diodes used in the rectifiers also behave like filters. The Schottky diodes used in the Version 4 rectifier behaved as band-pass filters as can be seen in the manufacturer’s S12 curve shown in Figure 6.17 on page 146. All diodes have similar S12 curves with different values for each of the frequencies. 51
2.9 POTENTIAL GAINS FROM CONVOLUTION
Mixers are electronic circuits that mix a carrier frequency with a signal to create inter- modulation frequencies. Diodes are often passively used to create inter-modulation using the nonlinearity’s associated with this circuit element. Rectangular waveguides
(RWG’s) also have nonlinearities caused by imperfections and discontinuities that can create inter-modulation products [38]. Metal-oxide-metal diodes are a class of modern diodes that look materially like the imperfections in RWG’s. This is an example where a bad thing in communications could turn into a good result when harvesting heat “noise.”
During this dissertation’s measurements, anomalies surfaced that begged for explanation.
One example was: “How could +18.82 dBm of power be measured at 0 Hz?” The possibility of passive inter-modulation products was one possible explanation that was explored. Passive inter-modulation productions are known to be triggered by disparate types of metals at connections, oxides between metals at connectors, non-linear transmission lines, and faulty connectors [38-40].
A signal mixed with another signal generates inter-modulation products including a spectral component at 0 Hz. Using MATLAB, Figure 2.9 illustrates the mixing of two signals: one at 500 Hz and another at 2.1 kHz. The spectrum of the inter-modulation products is illustrated in the lower right of the graphic. Predictably, the largest spectral component of these inter-modulation products appears at 0 Hz. 52
Figure 2.9: Mixing Two Signals
A simple MATLAB simulation using the signals workshop was constructed to examine the results of mathematical convolution on “noise.” Figure 2.10 shows the model where a
“Random Source” is passed through the “Convolution” tool and the resultant spectral product is displayed on a MATLAB scope. Noise is the “Random Source,” and the time domain display of this signal is shown in Figure 2.11. The average voltage of the noise in the time domain as shown in Figure 2.11 is 0.44 V (+5.9 dBm). 53
Figure 2.10: MATLAB Simulation of Noise Convolution
Figure 2.11: Noise in Time Domain
54
Figure 2.12 shows the spectral product of noise convolved with noise. The resulting
“noise floor” is roughly -35 dB (-65 dBm). There is a spectral component at 0 Hz, however, that is roughly +6 dB (-24 dBm). This mathematical result suggests a potential convolution gain of roughly +40 dB.
Figure 2.12: Spectral Product of Noise Convolved with Noise
Triggering nonlinearities that result in inter-modulation products from “heat noise” could generate large power magnitudes around 0 Hz if the mathematical results could be physically captured. While diodes inherently do this, their efficiency wanes at higher frequencies. Other techniques might prove more effective. This improvement from other 55 techniques would allow power diodes designed for lower frequencies and kilowatts to be used to rectify the radiation.
2.10 OTHER GAIN TECHNIQUES
Several other gain techniques were examined. Some of the techniques required fabrication and assembly technology beyond what was available in this dissertation research. Others added rectenna complexity adding new points of potential confusion or failure. Two promising techniques that were considered were:
. Standing Waves within Waveguides and Microstrip lines (+3 dB), . Using a radiation medium other than air (e.g. water) between the surface and antenna (+9.5 dB),
Standing waves form on transmission lines, such as microstrip lines, when open and short circuits are encountered. Different frequencies have different wavelengths resulting in frequency specific maxima at different lengths of a transmission line. Placement of diodes in parallel at the maxima on a transmission line, for example, could be used to create rectifiers that are frequency selective. Using these voltage sources that are “in parallel” could permit greater harvesting currents for greater power yields.
The power magnitude predicted with Planck’s Law is dependent upon the refractive index,
2 n. The refractive index squared (n ) and relative permittivity (εr) are equivalent. The use of a dielectric material instead of air between the material surface and an antenna would increase the refractive index term of Planck’s Law. Since the area of the emitting surface 56 impacts the heat source gain, a large slab of dielectric material (or a container of water,
εr = 9) would have been required. Engineering trade-offs are usually available in most projects. Proving that rectification could be achieved was viewed as more important in this dissertation research than maximizing the gain that could be achieved with different materials other than air.
2.11 PREDICTIVE ENGINEERING
Engineering is founded upon theories, models, calculations, and estimates to predict the results of design changes. When working in areas where the phenomena is still being understood or where measurements do not match predictions, the tools available can be rudimentary or can even generate “wrong” and misleading predictions.
The harvesting of heat radiation is a new frontier. The disciplines of radiometry, communications systems, and heat transfer have established techniques for estimating the power that should be expected to enter an antenna aperture. Radiometry is well documented for celestial bodies where any power from an emitting source traverses on the order of 1012 meters of vacuum. Communications systems use the FRIIS equation to predict the received power from a source that traverses on the order of 105 meters of air.
Heat View techniques are used to predict the radiative transfer from sources of power that traverse on the order of meters of transparent materials. 57
Several characteristics of heat radiation complicates the analysis. Heat is composed of spontaneous photonic emissions. The orderly, sinusoidal behaviors that are expected in communications engineering do not occur with heat radiation. For example, differences exceeding +25 dB were measured between the average and peak powers for heat radiation. While EM waves of heat radiation form plane waves at far-field distances, the omni-directional and omni-frequency composition makes analysis of radiation and circuit paths far more complex. Radiation that is close to tangential to an antenna still has components that are normal to the antenna surface. Further, radiation coming from outside of an antenna beam-width can be and is reflected into the received beam.
Additionally, the intervening air absorbs and randomly reemits heat radiation. Air participates in the power being contributed, received, measured and rectified. Air contributions while testing within an anechoic chamber were present. Since the walls, floor, and ceiling of the anechoic chamber had absorbent materials that suppressed emissions and reflections, at least some of the EM radiation that was measured in the chamber had to be coming from the intervening air.
The radiometry, FRIIS, and heat views approaches all seek to simplify the model of the environment to mathematically simplify the predictions for the power transfer. While identifying and quantifying all the contributors to a predictive model is often desirable, sometimes being close with factors derived from measurements are used. Many equations used within microwave engineering, antennas, and microstrip lines are measurement based and have such factors. 58
2.11.1 Radiance Predictions
Radiometry is used heavily in the field of measuring luminance from celestial bodies such as the sun. The equation is as follows:
1 Lm P planck Area E SA [2.20]
Where Lm is the luminance, Pplanck is the Plank power, AreaE is the area emitting the radiation, and ΩSA is the solid angle illuminating an area of interest.
For a source of heat radiation emitted at 26.3 GHz in a 5 MHz bandwidth at 295 K, the
Planck power would be -60 dBm per m2 (0.983 nW per m2). The computation using luminance is as follows:
2 160 1.872in 1 L 1010 mW m2 4.1 m 2 1.45 pW m 2 2 m
If the source included 1 GHz of bandwidth, then the Planck power would be -37 dBm per m2 (196.6 nW per m2), and the computation for the luminance is as follows:
2 137 1.872in 1 L 1010 mW m2 4.1 m 2 289.1 pW m 2 2 m
While this computation predicts far more power than the “kBTB” formula, this is far short of the microwatts that were harvested using the V5 rectifier that was tested in this dissertation. Either the radiometry equation is missing some components, or multiple measurement instruments and techniques gave erroneous results. 59
Heat radiation is random and emits radiation in directions other than the normal to the area of emission. The non-normal emissions also make contributions to the luminance, yet the radiometry technique does not capture the contributions. The Lambert’s cosine technique is commonly used to include the contributions of the normal components from the 0o to 89o emissions. Consequently, one would expect the radiometry technique to be less accurate by ignoring the non-normal contributions.
2.11.2 FRIIS Predictions
Traditional communication and radar systems use the FRIIS equation and its variants to predict the received power in a system. Using this equation, the power received can be computed as follows:
2 Pr GGP T R planck 4 r
37 1 10 2 2 PrWR187 4 108 10 mWmm 4.1 1. 0 110. 5 W
When the power from the transmitter antenna fits within the aperture of the receiver antenna, distance squared attenuation goes to zero. Under this condition, as can be engineered in WPT, the attenuation term (enclosed in parenthesis in blue) of the FRIIS equation approaches unity. For a WR-187 waveguide the received power per the FRIIS equation approaches 110.5 µW for a 1 GHz (3.8% of 26.3 GHz) bandwidth. While greater than the measured powers in this dissertation, this magnitude is more in line with the measured magnitudes that were around -21.3 dBm (7.4 µW) to -18.2 dBm (15.1 µW). 60
Interestingly, the luminance from radiosity and the FRIIS equations are related.
Luminance is defined in Equation [2.20] and can be inserted into the FRIIS equation in the following sequence of algebra and substitutions:
1 Lm PPL_ f Area wall wall
2 PWR187 LGG m wall WR 187 4 R
4 Gwall wall
2 1 4 PWR187 PArea PL _ f wall wall G WR1 87 wall 4 R
2 2 PWR187 0.984 nW m 4.1 m 4 108.4 1.0 1.749 W
2.11.3 Heat View Predictions
The gains for heat views are higher than the antenna gains that are typically seen using
-3 the FRIIS equations. For the WR-187 waveguide the heat view F12 is 1.352·10 . This heat view factor yields a gain of 9,295 (+39.7 dB). This translates to a 9.7 mW power level for a 1 GHz bandwidth at 26.3 GHz.
3 F12 _ 1m _ WR 187 1.352 10
Pplanck P Area G G r HV E r t 61
4 4 G 9952 39.7 dB r 3 F12 1.352 10
Pplanck 4 P Area G r HV E t F12
37 2 2 4 P 1010 mW m 4.1 m 4 9.7 mW rHV _ WR 187 3 1.352 10
For the WR-340 waveguide the associated computations are as follows:
3 F12 _ 1m _ WR 340 1.155 10
4 4 G 10880 40.4 dB r_ WR 340 3 F12 1.155 10
37 2 2 4 P 1010 mW m 4.1 m 4 11.3 mW rHV _ WR 340 3 1.155 10
2.11.4 Summary of Radiometry, FRIIS, and Heat View Approaches
The radiometry, FRIIS and heat view techniques provide three ways to estimate the power that reaches the antenna aperture. The radiometry technique has the narrowest selection of power where no power rays outside the solid angle are included. The FRIIS technique allows some. The heat view technique considers both the rays within the beam width and those outside that have normal components inside the beam width. Table 2-B compares the techniques by antenna gains and by predicted powers for 5 MHz and 1 GHz frequency spans. Given the measured powers of -21.3 dBm (7.5 µW) to -18.2 dBm (15.1
µW), the FRIIS Equation and the Heat View techniques appear to generate predictions 62 that are closer to the measurements of multiple meters and the harvested magnitudes of power.
Table 2-B: Comparison of Radiometry, FRIIS, and Heat View Techniques
Gain (in dB) Type of Aperture Area FRIIS Radiometry Heat View Waveguide (in m2) Equation WR-340 0.003729 35.0 25.5 34.4 WR-187 0.001130 40.0 20.3 48.1
Antenna and Power (in FRIIS Radiometry Heat View Bandwidth nW·m2) Equation WR-187 at 5 MHz 1 1.5 pW 1.8 µW 48.6 µW WR-187 at 1 GHz 199.5 289.1 pW 110.0 µW 9.7 mW
2.11.5 Measurement and Known Factor Approach
This approach begins with a series of measurements. Table 2-C shows the measurements for (1) the LadyBug power meter connected to a Wi-Fi patch antenna salvaged from a
Buffalo Wi-Fi router and (2) the WR-187 waveguide connected to the N1911A. Since the noise floor is hypothesized to be Planck radiation, the differences between Planck’s Law and the Average Power as well as the differences between the Average Power and Peak
Power are computed. The fields highlighted in yellow are measured values, and the floors predicted by Planck’s Law are also highlighted in yellow. The difference lines are computed. The average power for the LadyBug Patch configuration was not measured and is a computed value based the upon estimated values for known factors as a result. 63
Table 2-C: Measured Average and Peak Powers
LadyBug Patch V4 Rectifier V5 Rectifier
Operating Frequency (in GHz) 10.0 26.3 26.3
Planck's Law (dBm per m2) -68.5 -60.1 -60.1
Difference Between Planck's Law and Average Power 36.9 13.8 13.8
Measured Average Power (dBm) -31.6 -46.3 -46.3
Difference Between Average and Peak Power 27.2 25.0 25.0
Measured Peak Power (dBm) -4.4 -21.3 -21.3
Theoretical Voltage (in mV) 19.3 19.3 Measured Voltage (in mV) 7 19.0 Effective Rectification 36.4% 98.7%
Power (in mW) at Measured Power 0.007 0.007 Voltage (in V) 0.007 0.019 Current (in mA) 1.1 0.4
Power Harvested (in mW) 0.001 0.006
The theoretical and measured voltages are included for the V4 and V5 Rectifiers. Based upon the board impedance (50 Ω) at 26.3 GHz, the theoretical voltage can be computed as 19.3 mV. The measured voltages using a voltmeter of 7 mv and 19 mV for the V4 and
V5 Rectifiers, respectively, suggest that 1 and 7 µW were harvested. By comparison the
Radiometry, FRIIS, and Heat View techniques all predicted power levels different from what was physically measured. 64
Once measurements have been made, the differences can be decomposed into the known and unknown factors that can be identified which are likely to impact the power measurements. Table 2-D summarizes the sum in dB of the known and unknown factors that affect the power. The estimated area of 4.1 m2 translates to 6.1 dB. Wall gain is 4x which yields the +6 dB. The antenna gain of the Ladybug patch configuration was on the order of 21.0 dB. Since the patch antennas were designed for 2.45 GHz and 5 GHz frequencies, a 10 GHz signal being received by the patch antennas would have been over- moded increasing the gain from an expected +12 dB. The antenna gain of the WR-187 waveguide was computed as 20.34 dB per Equation [2.6]. Both the patch antenna and the WR-187 capture only a single polarity of the input radiation for a loss of -3 dB. The power loss for free space power crossing a 50 Ω impedance boundary is a loss of -3.8 dB.
The power loss for the intervening connectors and coax cables in the measurement setup was -5.5 dB, and the power losses in the rectifiers for the low pass filters and the diodes was -7 dB from Genesys and SPICE models. The sum of these type of known factors for the WR-187 and V4 Rectifier produced a 0.6 dB difference on the average power to
Planck’s Law relationship. This dB difference is equivalent to a 0.8x adjusting multiplier where the knowns exceed the unknowns. This adjusting multiplier is similar to the 0.854 factor used in Equation [2.13], although the 0.854 factor was cruder with a greater number of unknowns.
There was a +16.1 dB from unknown factors in the gap difference for the LadyBug Patch measurements. This is a perplexing result that will garner additional experimentation in 65 future rectennas. Two things occurred with this configuration that may yield additional insights for gains associated with heat radiation. One, the patch antennas in Wi-Fi applications are designed with wider bandwidths to capture both the 2.45 GHz and the 5
GHz frequencies of Wi-Fi. The 26% bandwidth used in this table reflects this type of dual bandwidth engineering. Two, when the patch antennas capture two frequency ranges with a center at 10 GHz, the bandwidth gain is much higher. This table also shows an estimated antenna gain of +21 dB when the typical patch antenna is in the range of +9 dB.
This higher estimate is suggested by over-mode effects of receiving a 10 GHz signal within antenna areas configured for 2.45 and 5 GHz. Even with this higher estimate, however, this leaves the unknown gap of +16.1 dB between the Planck floor and the average power received. The greater bandwidth gains suggest that using a lower gain antenna may achieve better results. Generally, higher gain antennas have narrower bandwidths. 66
Table 2-D: Known and Unknown Factors (in dB) Affecting Measurements
Known Attenuations and Gains LadyBug Patch V4 Rectifier V5 Rectifier
Board Impedance (in Ohm) 50 50 50 Gains Wall Area 6.1 6.1 6.1 Wall 6.0 6.0 6.0 Antenna 21.0 20.3 20.3
Attenuations Polarity -3.0 -3.0 -3.0 Impedance Losses (377 to Board) -3.8 -3.8 -3.8 Measured Connectors -5.5 -5.5 -5.5
S21 Losses (LPF and Diodes at fo) -7.0 -7.0 Impedance Mismatch (9 to 54 Ohm) Net Gain (Loss) from Planck's Law 20.8 13.1 13.1
Implied Bandwidth (in GHz) 2.600 1.575 1.575 % of Operating Frequency 26.0% 6.0% 6.0% Bandwidth Aggregation (in dB) 27.2 25.0 25.0
Unknowns for Average Power Difference 16.1 0.6 0.6 Unknowns for Peak Power Difference 0.0 0.0 0.0
2.11.6 Summary of Predictive Engineering
Given the variability associated with the Radiometry, FRIIS and Heat View techniques for estimating the received power from Planck radiation, the Measurement and Known
Factor technique was used extensively to engineer the V4 Rectifier, V5 Rectifier, and the
V1R0 through V2R1 Rectennas. The high variability in the behavior of the ambient radiation suspected to be heat and the random characteristics of the ambient radiation were not captured in the traditional techniques for predicting power. Additionally, the absence of power attenuation for the distances and geometries used in this dissertation 67 also rendered the FRIIS equation less effective in predicting the received power. Rather than making changes without some predictive foundation for the next iteration, experimental measurements proved more helpful than the theoretical predictions. 68
3 POWER MEASUREMENTS OF HEAT RADIATION
3.1 MEASUREMENT CHRONOLOGY
The early extrapolations from the manual measurements with the Ladybug meter showed the potential for obtaining harvestable power above 10 GHz. Because of the limited frequency range of the LadyBug power meter, an Agilent N1911A power meter was obtained. This meter has an upper limit of 40 GHz, and it can be controlled by external software such as LABVIEW. A LABVIEW routine was written to turn the meter into a spectrum analyzer by stepping thru the frequency range of the meter measuring and recording the power at each step. Unfortunately, a LABVIEW interface to the Agilent
N1911A power meter did not come with the meter. After writing an interface and developing the spectrum analyzer application, automated measurements showed “flat- lined” power at -40 dBm across the spectrum irrespective of whether the power meter was connected to or disconnected from an antenna. When connected to the microwave signal generator, the power of frequencies below 3 GHz was accurately measured. A connection to the antenna should have yielded a curve like Figure 1.11. The dubious nature of a “- 40 dBm flat line” for both a connected and disconnected cable suggested that there was a circuit continuity issue. This led to replacement of coax cables, connectors, waveguides, etc. Power from a microwave signal generator with an upward limit of 3 GHz was accurately measured by this meter creating a paradox as to why the 69 power from an antenna and from an open connection could be the same without regard to the frequency. Another possible source for the flat-line behavior was an error in the interface software to the power meter, although manual measurements also reflected the “flat-lined” behavior. Meaningful measurements with the Agilent N1911A and
LabView were never obtained. In hindsight, it is likely that the meter was damaged during the development of the automated measurement application. The antenna power during application testing could have exceeded the allowed maximum burning out the measurement circuitry for power above 3 GHz.
Subsequently, an Agilent FieldFox N9918A meter was obtained. An attenuator (-30 dB) was inserted between the antenna and the meter to guard against excessive input power.
Additionally, the FieldFox is designed to insert additional attenuation in 5 dB increments to further protect the meter from damage by inadvertent inputs of power greater than
+23 dBm. Power spectrums were successfully obtained for multiple antenna types, temperatures, and measurement distances. The FieldFox meter automatically inserted attenuations (5 and 10 dB) on occasion to protect the internal circuitry from power overload. Given the fixed attenuator (30 dB) and the meter inserted attenuations, the input power from the waveguides had to be greater than the power limit of +23 dBm for the FieldFox.
When BenchVue was obtained, additional analysis of the measured power was performed.
BenchVue is a software product from Keysight that consolidates and displays data captured from Keysight instruments. The N1911A power meter and the FieldFox meter 70 are Keysight instruments. BenchVue has a graphing tool that analyzes and displays the distribution of peaks to the average power. Normal sinusoidal power has a predictable
+1.5 dB peak to average ratio, and the RMS average of voltage is 0.707 of the peak amplitude. The BenchVue displays show that harvested radiation had a measured peak to average ratio as great as +25 dB. Figure 3.1 shows the CCDF vs Gaussian analysis for the WR-187 waveguide. A peak of +24.2 dB occurs 0.0001% of the time at 26.3 GHZ. This translates to over 26,000 over-voltages per second if the average input signal is +0 dBm.
These peaks appear to be related to the captured bandwidth of the antenna in use. This roughly +25 dB difference corresponds to capturing 6% of the bandwidth at 26.3 GHz. An antenna and rectifying circuit with too large a bandwidth could be a hazard to a diode with a small reverse breakdown voltage. 71
Figure 3.1: Example of the CCDF View for Planck Radiation
3.2 MEASUREMENT SET-UP
Figure 3.2 illustrates the test equipment and environment for the experiments to measure the power spectrum for heat radiation. Laboratory walls were used as the sources for the heat radiation. The paint on the walls was white interior latex with a likely emissivity in the range of 0.6 to 0.8 (-2.2 to -1.0 dB). A standard WR-340 (and a WR-187) rectangular waveguide section with a 50 Ω coaxial adapter was used as an antenna. The 72 open mouth of the waveguide was positioned one meter from the wall. An attenuator (-
30 dB) was placed in the coax path to the Agilent Technologies N9918A FieldFox Meter.
Figure 3.3 provides a photograph of the FieldFox meter and a summary of its major capabilities. The Spectrum Analysis (SA) application was used to measure the power spectrum from 0 Hz to 26.5 GHz, the frequency range of the meter. The measurements were captured at two different room (wall) temperatures of 55oF (12.8oC) and 72oF
(22.2oC).
Figure 3.2: Measurement Environment
73
Figure 3.3: Major Capabilities of Agilent N9918A FieldFox Meter
3.3 MEASUREMENT RESULTS
Figure 3.4 shows the measured power spectrum at 55oF, and Figure 3.5 shows the measured power spectrum at 72oF. These graphs are displays generated by the FieldFox meter. The resolution bandwidth was 5 MHz. This is the bandwidth that the meter used and plotted for each frequency measurement. Both plots show power ranging from roughly -35 dBm through -5.677 dBm for 0 Hz to 26.5 GHz (the frequency measurement range of the N9918A FieldFox meter). The safety circuitry of the meter inserted an additional 5 dB of attenuation to protect the meter from power overload (The label Atten
5 dB at the top of each of the plots indicates this insertion). The reported magnitudes are the actual measured magnitudes after correcting for the inserted attenuation. 74
Figure 3.4: Spectrum Power Measurement for WR-340 at 55oF
75
Figure 3.5: Spectrum Power Measurement for WR-340 at 72oF
3.4 MEASUREMENT ANOMALIES
Interestingly, the largest power measured was +18.82 dBm at 0 Hz, as can be seen in the
M1 Marker for both Figure 3.4 and Figure 3.5. This corresponds to 76.4 mW. This power magnitude might have triggered the insertion of 5 dB of additional attenuation. The M2
Marker also shows +14.52 dBm at 5,000 kHz. The second largest power magnitude beyond the 0 Hz ranges was measured as -5.677 dBm at 26.3 GHz for a 5 MHz segment. 76
The FieldFox computes the spectral content of input signals by making power measurements in the time domain and by using the Fast Fourier Transform (FFT) to compute the power in the frequency domain. This DC signal was a computed magnitude that mathematically predicted the spectral content of the time domain measurements.
Given the measurement circuit from the waveguide’s coax adapter through the meter, there is no physical path for steady state DC current (0 Hz). As a result, any DC spectral power could not be steady state. If real, this power would manifest itself as a transient current until the circuit reaches the stabilizing charge separation. Alternatively, it could have been a mathematical artifact in the meter’s method of measurement. Efforts to measure the associated DC voltage with a digital volt meter or to measure a transient were unsuccessful.
3.5 INTERPRETATION OF THE SPECTRUM DISPLAY FROM THE FIELDFOX METER
The Spectrum Analysis application for the FieldFox meter generates a display with many pieces of information. Figure 3.6 shows the FieldFox’s display on the left side of the figure and is color annotated with explanations on the right for key pieces of measurement information. The power spectrum ranges from roughly -35 to -5 dBm based upon the scale on the left. Each measurement sample is 5 MHz in resolution bandwidth as indicated by the “Res BW” label highlighted by a teal blue box in the lower left corner of the FieldFox display. The red boxes highlight the 5 dB of attenuation that was inserted by the meter to prevent overload. The power at 0 Hz is indicated by the +18.83 dBm power measured by marker M1. The maximum power for the FieldFox is +23 dBm. The green 77 box highlights the -6.534 dBm of power measured at 26.3 GHz as indicated by marker M6.
This power measurement is the actual power level without the 5 dB of attenuation. The
FieldFox adjusts its measurements to offset the 5 dB of physical attenuation that is inserted.
Figure 3.6: Interpretation of the Spectrum Display from the FieldFox Meter 78
3.6 RESOLUTION BANDWIDTH
Microwave power meters measure the power in a frequency segment for a given frequency. The parameter that controls this measurement range for a frequency segment is called the resolution bandwidth (RBW). For some meters, such as the LadyBug, a RBW is fixed by the manufacturer. For others, such as the FieldFox meter, the user is provided the ability to set this parameter within an allowable range. Most of the measurements performed in this dissertation were done for a RBW of 5 MHz around each measurement frequency.
While trying to resolve why the “Version 3” rectifier fabricated in this dissertation did not work when connected to the antenna, the Channel Power application on the FieldFox meter was used to measure the noise power coming from the waveguide antenna for various resolution bandwidths for the 26.3 GHz frequency. Figure 3.7 shows an example of the output from this measurement tool on the FieldFox. 79
Figure 3.7: Channel Power Measurement at 26.3 GHz for a 5 MHz RBW
Individual measurements were made and recorded for various resolution bandwidths and measurement frequencies. Figure 3.8 shows the measurement results. The immediate conclusion from the plots is that the measured powers are linear as the RBW’s are increased. At a given frequency such as 26.3 GHz, the measured power doubles (+ 3 dB) as the RBW doubles from the 5 MHz segment baseline. This result strongly reinforced the idea that the power and voltage aggregates with greater spans of frequency. If a frequency span (RBW) of 5 MHz yields -25 dBm (13 mV RMS) and 10 MHz yields -22 dBm
(18 mV RMS), then it would be logical to conclude that 3.0 GHz of power would also yield a linearly scaled result. 80
Measured Power vs Frequency for Various Resolution BandWidths (RBW) 0 -5 -10 -15 -20 -25 -30 -35 Power dBm) (in -40 -45 -50 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Frequency (in GHz)
5 MHz 10 MHz 20 MHz 40 MHz 80 MHz 100 MHz
Figure 3.8: Measured Power for Various Resolution Bandwidths (RBW)
The measurements with the Channel Power application also raised a measurement oddity.
As can be seen in Figure 3.5, the Spectrum Analyzer application showed – 5.677 dBm (112 mV RMS) at 26.3 GHz for a 5 MHz RBW. Correspondingly, as can be seen in Figure 3.7, the Channel Power application showed -21.3 dBm (19.3 mV RMS) of power. This is a roughly 15 dB difference in measured power from the same FieldFox meter and measurement setup. The difference can in part be explained by the effects of averaging for the average power and averaging for the peak power. BenchVue showed large variations between the “average” and the “peak” powers. Depending on what 81 percentage of the peaks are included in the “average” peak, one can have a peak that is somewhere between +10 and +15 dB higher.
3.7 TEMPERATURE IMPACT ON SPECTRUM POWER MEASUREMENTS
Power measurements were performed at two temperatures to quantify the impact of temperature on the generation of the suspected “heat noise” by the wall. Figure 3.9 shows the side-by-side FieldFox displays for the two temperatures: 55oF (Figure 3.4) and
72oF (Figure 3.5). (See Figure 3.4 and Figure 3.5 for greater legibility.) For the 17oF (9.4oC) difference in temperature, the FieldFox meter measured a 0.9 dB difference in power, a
23% increase with the higher temperature. This difference in power magnitude comports with the expectations from Planck’s Law, and it lends credence to the hypothesis that this measured noise is Planck radiation. 82
Figure 3.9: Spectrum Power Measurements at 55oF and 72oF
While the measured power is relatively stable for a design range in temperatures, any harvesting design needs to consider the maximum and minimum temperatures to avoid power overloads on a hot day or insufficient power on a cold day. A safety margin of +3 dB in power offers roughly 325oF of flexibility between a maximum temperature of 395oF
(200oC) and an operating temperature of 72oF (22oC). A safety margin of -3 dB in power offers roughly 249oF of flexibility between a minimum temperature of minus 145oF (-
128oC) and an operating temperature of 72oF. 83
3.8 POWER SPECTRUM MEASUREMENT FOR VARIOUS ANTENNAS TYPES
While most of the measurements for the dissertation were performed with waveguides as the antenna type, various antenna types were measured. Waveguides were chosen because of their inherent high directivity and large antenna gains. They also have relatively high cut-off frequencies that inherently screen out ambient RF. Figure 3.10 shows the measured power for various antennas. Remarkably, the measured powers were within 5 dB of each other even though the rated antenna gains for some antenna types were often greater than 20 dB from other antenna types. This result was unexpected, but it demonstrates the interrelationship between directivity and large antenna gains. A highly directive antenna, such as a waveguide, captures the electromagnetic radiation from a narrow solid angle. An omnidirectional antenna, such as a half dipole, captures the electromagnetic radiation from a 360o radius of the antenna.
If the walls of a room are at the same temperature, the gains from a portion of one wall can be matched by the gains from four walls even though some of the walls are farther away. Further, the air in the room also emits blackbody radiation from its molecules thereby offsetting some of the gain advantages from a highly directive antenna. 84
Figure 3.10: Power Spectrum Measurements for Various Antennas
3.9 IMPACT OF DISTANCE FROM THE HEAT SOURCE
Power is expected to attenuate with the distance squared between a source and a receiver. Power was measured for the distances of 50 and 100 cm during this dissertation.
Consequently, the 50 cm power measurements were expected to be four times (+ 6 dB) the 100 cm measurements. Figure 3.11 shows the results of the distance measurements.
Visually, there is little, if any, discernable difference in the 50 vs 100 cm measurements. 85
Figure 3.11: Power Measurements at 50 and 100 cm Distances from Wall
Wireless Power Transfer (WPT) has shown that distance squared attenuation does not occur if the beam width of the transmitting antenna fits inside the aperture of the 86 receiving antenna [41]. The percentage of power transferred without attenuation is determined by the following equations:
2 P 1 e [3.1]
Where P is the percentage of power transferred without attenuation and
A A 2 t r [3.2] D 2
Where At is the area of the transmitter, Ar is the area of the receiver, is the wave length of the signal, and D is the distance between the transmitter and the receiver.
For 2 values greater than 2.0, wireless transfer is nearly 100% resulting in power transfers without distance attenuation. This characteristic of WPT explains the absence of distance squared attenuations in the measurement results from the experiment.
87
4 ANTENNA CONSIDERATIONS FOR HARVESTING HEAT RADIATION
4.1 APERTURE ANTENNAS
Aperture antennas are a class of antennas that capture electromagnetic radiation through an opening. Generally, aperture antennas are highly directive and can smoothly conform to aerodynamic surfaces. The opening can be physical or virtual. They often use reflectors to direct the electromagnetic waves to the aperture. Waveguides, horn antennas, and patch antennas are all examples of aperture antennas. Patch antennas can be implemented using microstrip technology and have been used heavily in rectenna research.
4.2 NEAR AND FAR FIELDS
The EM fields near the antenna surfaces are in transition at microwave frequencies from largely surface currents in the conductors to fully formed plane waves in free space. Near the antenna (the near field) these EM fields are reactive and longitudinal in character.
The full transition to plane waves (the far field) occurs by twice the wave-length of the radiation [42]. For 26.3 GHz radiation this far-field distance in free space is 2.3 cm or less than an inch. Consequently, the measurements from the experiments in this dissertation all measured far-field radiation. 88
4.3 INCIDENT POWER DENSITIES
The power densities incident upon an antenna’s aperture are often used in the research literature for performance comparisons. The measured power density that is equivalent to the literature for the WR-340 rectangular waveguide at 26.3 GHz can be computed using the following equation:
Pmeasured 1mW mW W Pden WR340 ( lP , measured ) 0.027 27 [4.1] 0.5l20.5 3.7in 2 cmcm 2 2
Similarly, the WR-187 can be computed as:
Pmeasured 1mW mW W Pden WR187 ( lP , measured ) 0.089 89 0.5l20.5 1.87in 2 cmcm 2 2
By way of comparison, power densities of ambient RF in the urban areas of London has
-2 been reported in the 0.18 to 84.0 nWcm range for signals in the 2.45 GHz frequency range [43]. The incident power density in the literature is often at a free-space impedance of 377 Ω, and the measured power in this dissertation is at 50 Ω. Consequently, much of the incident, free-space power is reflected from the antenna. As can be seen in Table 4-A, the equivalent power densities that are incident upon the waveguide’s aperture are 65
-2 and 214 µWcm for the WR-340 and WR-187 respectively. These predicted power densities of thermal noise at 26.3 GHz are over +30 dB (1000 times) greater than ambient
RF in London at 2.45 GHz. If the antennas used for measurement in London were pointed at heat surfaces and were operating at 26.3 GHz, the noise would most likely overwhelm 89 the signals. At 2.45 GHz the power of the ambient noise is predicted by Planck’s law to
-2 be 0.85 fWcm . This low power density for “noise” is why most manmade radiation is
- below 5.0 GHz. Successful communications in London occurs because the noise (fWcm
2 -2 ) is substantially smaller than the useful signals (nWcm ).
Table 4-A: The Equivalent Incident Powers for 1 mW of Measured Power
Wave Aperture Area Power Density (in µW/cm2) Power (in mW) Guide Inches CM 50 Ω 377 Ω 50 Ω 377 Ω Type Squared Squared WR-187 1.75 11.28 89 214 1.00 2.42 WR-340 5.78 37.29 27 65 1.00 2.42
-2 By way of comparisons geothermal power densities are 6 µWcm for most of the North
American continent. This power density makes geothermal noise useful for harvesting.
Wi-Fi noise floors of -80 dBm have been reported in San Francisco [44]. With Wi-Fi transmission powers of +24 dBm and +12 dB signal-to-noise margins above the noise floors, this provides link margins of 92 dB. Path losses at 2.4 GHz are 86 dB for 200 m of travel in free-space. Travel through walls with metal studs can quickly attenuate the remaining 6 dBm of link margin. The combined power of the signal-to-noise margin and
-2 the remaining link margin translates to approximately 100 to 400 µWcm that is
-2 harvestable. The London research [43] reported 0.18 nWcm for Wi-Fi at 2.4 GHz. The power density report in the London research leads to power magnitudes of 7 nW and 90 voltages of 0.6 mV per antenna. Unlike thermal radiation that emits from a broad range of frequencies, Wi-Fi is concentrated in relatively narrow bands. While Wi-fi power densities can be harvested, antenna sizes for harvesting 2.45 GHz Wi-Fi are unfortunately on the order of 6 in2. Figure 4.1 shows the practical impact of the antenna size [45]. This picture shows the antenna array that is required to power a cell phone with 2.45 GHz Wi-
Fi harvesting.
Figure 4.1: Antenna Array at 2.45 GHz Required to Power Mobile Phone
4.4 RECTANGULAR WAVE GUIDES
Rectangular wave guides (RWG) are a subset of aperture antennas. Figure 2.1 on page 35 shows a picture of a RWG along with a coax adapter that translates the TE and TM waves 91 that propagate in the waveguide into TEM waves within a coax cable. RWG’s can transfer very high power and are dimensionally well suited for microwave frequencies. They also inherently behave like high pass filters where frequencies above the cutoff for the fundamental mode pass through relatively unimpeded. Signals within 20% above the cutoff frequency are increasing attenuated as the cutoff is approached from above.
Signals below cutoff are reflected. The physical dimensions of the aperture determine the cutoff frequency for a RWG. The TE10 cutoff frequencies for the two RWG’s (WR-340 and WR-187) that were used heavily in this dissertation, are 1.735 GHz and 3.156 GHz respectively.
RWG’s that are closed at one end with a metal plate will establish standing waves within the interior of the waveguide and can serve as antennas. Creating a standing wave doubles (+3 dB) the voltage at the maxima of the standing wave. By using a probe into the interior of a waveguide through a slot in the exterior, the electric field strength can be measured.
In order to explore engineering ideas, a finite element model (FEM) of a RWG antenna was created in a computer simulation using COMSOL. Figure 4.2 shows a summary of the simulation results for a RWG where a 1 mW plane wave enters the waveguide from the left in this figure. The upper left graphic shows the intensity of the electric field inside the waveguide as seen from the top. The dark red areas are the maxima, and the dark blue areas are the minima for a given input signal. The lower left graphic shows the electric 92 field strength along the center length of the waveguide. The peaks in this graphic correspond to the maxima in the upper left graphic.
Figure 4.2: Position of Waveguide Tap Alters the Wave Pattern and Magnitudes
The graphic in the upper right illustrates the impact of inserting a vertical metal probe into the interior as a signal tap. With the insertion of the tap all the maxima drop in 93 intensity, and the tap becomes the area of the greatest electric field (the dark red dot on the right side of the RWG). The graphic on the lower right of the figure shows the magnitudes of the electric field along the center length of the RWG. As a result of the tap, the maxima are approximately 45 V/m in the lower right graphic having dropped from roughly 48 V/m in the lower left graphic. The electric field at the tap is roughly 175 V/m, a gain of 3.6 (+5.6 dB) over the lower left graphic.
The key observation from the COMSOL modeling is that the interior of the RWG is altered by the measurement probe. Equation [2.1] for calculating gain of an aperture antenna does not reflect this alteration partially explaining why the rated gains of the RWG are higher than this equation for the TE10 mode.
4.5 MODELING A WIRE THROUGH RECTANGULAR WAVE GUIDE
The measurement anomaly associated with 0 Hz inspired a potential engineering solution to the absence of a DC path of electrical continuity in a RWG. Rather than a vertical coax probe that only provides an AC connection, why not run a wire through the waveguide being careful to insulate the wire from the walls of the waveguide. The electric fields within the interior of the waveguide would conceptually continue to activate electrons in the wire including the DC component reported by the FieldFox measurements. Unlike the vertical coax probe that partially enters the waveguide, a “through wire” probe would provide two points of connectivity allowing a traditional DC circuit connection. 94
Rather than physically altering a RWG to reflect a wire through the waveguide, a COMSOL simulation was explored. A WR-187 RWG was modeled. The “a” dimension of the WR-
187 is 1.87 inches and the “b” dimension is half of the “a” dimension. Figure 4.3 shows a vertical view of the standing electric field for a 1 mW EM wave entering from the right in this graphic. The “through wire” is in the center of the waveguide roughly 0.01 from the left in Figure 4.3 of the graphic. This probe alters the interior of the waveguide such that the electric field surrounds the wire while going to zero at the wire boundaries. This behavior persisted irrespective of attempts to center the “through wire” in the electric field maxima by moving the location of the “through wire” probe. What seemed like a good idea to resolve the absent DC connectivity did not work. 95
Figure 4.3: "Through Wire" Probe for a WR-187
96
5 RECTIFIER DESIGN AND FABRICATION
5.1 RECTIFICATION FOUNDATIONS
5.1.1 Schottky Diodes
Schottky diodes are passive devices where a metal is placed adjacent to a typically doped
N-type semiconductor. The reverse recovery times are greatly reduced by this metal and semiconductor junction allowing for frequencies into the gigahertz ranges. Metal on metal oxide junctions allow even higher frequencies into the terahertz range. Turn-on voltages positioned for detector applications are typically 0.15 to 0.45 V, although low- barrier Schottkys can turn-on as low as a few mV of voltage.
One of the applications for Schottky diodes is signal detection. The current generation of
Schottky diodes that are designed for signal detection turn-on at voltages as low as a few mV, permit current flows that follow the “voltage squared law,” and have low breakdown voltages. Because of voltage breakdown characteristics, low or zero barrier diodes as well as high barrier diodes are offered by manufacturers. The high barrier diodes require external biasing to create low voltage turn-on characteristics while providing somewhat higher breakdown voltages. To their advantage higher breakdown voltages are desired for defense applications where electronic jammers by the opposing forces can burn out unprotected detection circuits. When a high barrier diode and voltage biasing is used in a rectifer application, however, the biasing hobbles the ability to create a full-wave 97 rectifier. The more sensitive detection benefit yields lower efficiencies associated with half-wave rectifiers. This is not as important in a detector application, but a 50 % hit in efficiency is not as acceptable in a rectification application for WPT. For energy harvesting the 50% efficiency of half-wave rectification is acceptable when the “free” energy is ambient and the unused 50% is reflected back into the originating heat source.
Figure 5.1 illustrates (a) a simplified equivalent circuit for a Schottky diode and (b) a more complex equivalent circuit. The basic circuit is a resistance (RS) in series with a in parallel variable resistance (RD or RP) and a capacitance (CJ or CT where CT = CJ + CO). The more complex equivalent circuit has multiple capacitances, summarized as CO, in parallel with the junction capacitance (CJ). Performance of a Schottky diode, as predicted by the simplified equivalent circuit, is dominately dependent on the frequency. The following equation describes the frequency cut-off for Schottky diodes modelled by this equivalent circuit:
1 1 fc or fc [5.1] 2 RS C j 2 RS CT
Where: Rs is the series resistance, Cj is the junction capacitance, and CT is the sum of the junction with the other capacitances. 98
Figure 5.1: Equivalent Circuits for a Schottky Diode
For the HSMS 282X series of Schottky diodes manufactured by AVAGO, Inc., when one uses the junction capacitance and series resistances quoted in the data sheets, the approximate frequency cut-off is predicted as follows:
1 1 f 37.89 GHz [5.2] c 2 R C 2 6 0.7 pF S J
AVAGO’s specifications recommend this diode for applications, such as signal detectors, up to 4 GHz. The specifications also cite a device capacitance of 2.0 pF. If one adds this capacitance with the junction capacitance for a total device capacitance of 2.7 pF, a value of 9.8 GHz cut-off is predicted. This 9.8 GHz cut-off value is more in line with AVAGO’s recommendations for detector applications under 4.0 GHz. This type of interpretation of 99 parameters is common. The manufacturer’s positioning statements often convey more information than one can infer from the models, equations, and SPICE parameters.
Table 5-A provides a table of various discrete component Schottky diodes that were commercially available at the start of this dissertation research. The diodes used in the
“Bread Board” and “Version 1” rectifier are highlighted. It includes their theoretical frequency cut-offs. Actual measurements in the lab for this dissertation showed much lower frequency cut-offs. The blanks in the table illustrates how often manufacturers leave characteristics out of the specification sheets. They also often provide different parameters such as Co, Cj, Cd, and CT for capacitance making comparisons of alternative diodes more difficult. Some diodes have application notes, and occassionally the manufacturer provides statements that position the diodes for certain applications.
Occasionally, the manufacturers will even provide SPICE model parameters. Rectification of microwave signals is not an application that manufacturers yet see as “big” in the discrete component market. Guidance through application notes for microwave rectifiers is uncommon. 100
Table 5-A: Characteristics of Various Schottky Diodes
Minimum Maximum Maximum C -Based C -Based Diode Model j T VBR (V) Vf (mV) Cr (pF) CJ (pF) Rs (Ω) fc (GHz) fc (GHz) Application HSMS 280x 75 410 2.00 1.60 30.00 3.3 2.7 HSMS 282x 15 340 1.00 0.70 6.00 37.9 26.5> -20 dBm, <4 GHz HSMS 285x 3.8 250 0.30 0.18 25.00 35.4 21.2<1.5 GHz Detector HSMS 286x 7 350 0.30 0.18 6.00 147.4 88.4>4 GHz HSMS 810x 4 350 0.26 0.17 6.00 156.0 102.0Optimized 10 - 14 GHz
MA 1N5711 70 410 2.00 Mixer Detector MA 4E1340 70 410 1.50 MA 4E2037 7 700 0.05 0.02 4.00 1989.4 884.2 MA 4E2054 3 350 0.14 0.13 17.00 72.0 66.9Mixer Detector MA 4E2200 1.5 220 0.25
DDC 2353 4 210 0.20
NXP BAT15 4 250 0.30 NXP BAT54 30 320 10.00 NXP BAT62 40 430 0.35 NXP BAT64 40 320 4.00 NXP BAT86113 50 300 8.00 NXP BAT120 25 400 100.00 NXP 1PS70SB20 40 550 90.00 NXP PMEG1020EV 10 255 37.00 NXP PMEG2002AESF 20 245 25.00 Trr=1.9ns
Teledyne 03020 5 700 0.03 0.01 5.00 3248.1 994.7355 x 88 microns, < 2 THz
Parameters such as “Maximum Vf” are dependent upon a forward voltage and current level combination such as “340 mV at a current of 1 mA.” Other diodes use other current levels such as “100 mA”. Even manufacturers of detector diodes are vague as to the lowest turn-on voltage, possibly because the detection circuits often use voltage biasing to achieve turn-on sensitivity.
101
5.1.2 Relationship between Power Level and Voltage
The relationship between spectrum power level and voltage is an algebraic application of
Ohms’ Law. Spectrum power is the product of voltage times current, and current can be represented by the voltage divided by the resistance. This yields a familiar form of power reflected in the following equation:
V 2 P V I [5.3] R
Power in dBm (PdBm) can be converted to power in mW via the following equation:
PdBm P10 10 mW [5.4]
By using algebra and the relationships in Equations [5.3] and [5.4] to solve for voltage, one can obtain the following equation for the RMS voltage for a given power level in dBm:
PdBm V PR 10 10 mWR [5.5] rms
The voltages predicted by Equation [5.5] are root mean squared (RMS) averages. Peak voltages, a value that impacts diode “turn on,” can be obtained by multiplying the RMS voltage by the 2 if the input power is sinusoidal. Table 5-B shows the peak voltages for a given power level. 102
Table 5-B: Peak Voltage for a Given Sinusoidal Power Level
Peak Voltage for a Given Power Level 50 Ohm Peak Voltage (in mV) Power (in dBm) Measured Power (in mW) 50 Ω 377 Ω 175 Ω 0 1.0000 316 868 592 -1 0.7943 282 774 527 -2 0.6310 251 690 470 -3 0.5012 224 615 419 -4 0.3981 200 548 373 -5 0.3162 178 488 333 -6 0.2512 158 435 297 -7 0.1995 141 388 264 -8 0.1585 126 346 236 -9 0.1259 112 308 210 -10 0.1000 100 275 187 -11 0.0794 89 245 167 -12 0.0631 79 218 149 -13 0.0501 71 194 132 -14 0.0398 63 173 118 -15 0.0316 56 154 105 -16 0.0251 50 138 94 -17 0.0200 45 123 84 -18 0.0158 40 109 74 -19 0.0126 35 97 66 -20 0.0100 32 87 59 -21 0.0079 28 77 53 -22 0.0063 25 69 47 -23 0.0050 22 61 42 -24 0.0040 20 55 37 -25 0.0032 18 49 33 -26 0.0025 16 44 30 -27 0.0020 14 39 26 -28 0.0016 13 35 24 -29 0.0013 11 31 21 -30 0.0010 10 27 19 -35 0.0003 6 15 11
For a spectrum power level of +0 dBm the associate RMS voltages are 0.224 V at 50 Ω and
0.614 V at 377 Ω. The peak voltages are 0.317 V and 0.868 V respectively, as can be seen in Table 5-B. These levels are above the voltage threshold for many Schottky diodes. 103
Rectifier efficiency for a full-wave rectifier is computed using the RMS input voltage and threshold voltage for the diode. Sometimes the peak voltage is used instead of the RMS voltage since the peaks exceeding the threshold voltages generates current. The half- wave rectifier is half of the efficiency of the full-wave rectifier. As an example, the equation for the theoretical efficiency of a full-wave rectifier, using the voltage drop (0.15
V) of the HSMS-282x series of diode and the 0.224 Vrms for the measured 1 mW of power at 26.3 GHz, is as follows:
1 1 59.9% [5.6] V 0.15V 1 T 1 V 0.224V rms
Where VT is the turn-on voltage and Vrms is the rms voltage of the input source.
5.1.3 Line Width Impacts on Impedances for Microstrip PCBs
The dielectric permittivity and the dimensions of microstrip PCBs determine the conductor line widths needed to achieve specific circuit impedances. A simple microstrip board consists of three layers: a metal circuit layer, a dielectric layer, and a metal ground plane layer. The widths (W) of the conductor lines at a given impedance are directly related to the distance (d) between the top layer conductor and the bottom layer ground plane, i.e. the dielectric thickness. The thickness (t) of the conductors also impacts the impedance and therefore line widths. 104
Rogers RO4003 PCB laminate stock was used in this dissertation. The dielectric permittivity (εr) for RO4003 is 3.38. It comes in standard distances (d) of 8, 20, 32, and 60 mils. The standard board stock used in this dissertation was 12” x 18”, and the standard copper cladding was 1 once (t = 35µm). Individual rectifiers were arrayed or paneled on the standard board stock.
The formula and process for determining the width (W) of microstrip lines can be computed using well known techniques [46]. Table 5-C summarizes the results for Rogers
RO4003. The standard design impedance for most microstrip circuits is 50 Ω. A higher
175 Ω impedance is included for comparison purposes since higher impedance lines are often used in filters. Higher impedances are created by using narrower lines. Many fabrication processes have a line size minimum of 3 mils. At the minimum width of 3 mil, however, small fabrication variations around this minimum can have large impedance impacts. As can be seen in Table 5-C, only the 60 mil variation of the Rogers RO4003 stock is “safely” outside the fabrication minimum for the 175 Ω impedance. The distance of 32 mil is on the cusp of the fabrication minimum for the 175 Ω impedance.
Table 5-C: Line Widths for Various Impedances of RO4003 Microstrip Boards
Distance (d) Width (W) (in mils) (in mils) 50 Ω 175 Ω 8 19 0.775 20 47 1.925 32 75 3.075 60 140 5.750
105
Five different rectifier designs were fabricated on Roger’s microstrip boards during this dissertation research. The “Version 1” rectifier used 60 mil stock, and the “Version 2” rectifier used 8 mil stock. The “Version 3” rectifier used 20 mil, the “Version 4” rectifier used 32 mil, and the “Version 5” rectifier used 32 mil.
Three rectennas were fabricated. The “Version 1” Rectenna used 32 mil, the “Version 2
R0” Rectenna used 60 mil, and the “Version 2 R1” Rectenna used 60 mil.
5.1.4 Diode Basics
Diodes are passive devices that allow one-way current flow within an operating range of voltages and frequencies. Current flows through a diode when a positive voltage exceeds the device’s forward or turn-on voltage. Current in the reverse direction is blocked until a negative voltage, depending upon each diode type, exceeds a reverse voltage. This reverse voltage is also known as the reverse breakdown voltage.
This basic “on” and “off” behavior, depending upon the applied voltage, allows alternating current to be converted to direct current. This process is called rectification.
Alternating current electricity oscillates between positive and negative voltages in sine- wave cycles. Current flows through the diode when the voltage is positive and stops when the voltage is negative. This one-sided rectification is called half-wave rectification. Full- wave rectification occurs when both sides of the alternating voltages are captured as DC current using multiple diodes. By applying the rectified current flow to charge a capacitor one can engineer a relatively stable DC voltage. 106
Figure 5.2 provides the measured I-V diode curve for NXP’s BAT86113 diode. This curve provides the “turn on” characteristics for the diode, and this curve of the current and voltage relationships is typical of diodes in general. As the positive voltage increases for this diode, current begins to flow around 0.2 V and climbs to 10 mA around 0.85 V. Other diodes have different “turn on” voltages and current ramps. The voltage threshold is 0.2
V for this diode, and any voltage from a source above this threshold yields a current. Of course, the frequency of the voltage source must be below the cut-off frequency of the diode for this to occur. This I-V curve was measured in the laboratory using an actual diode with axial leads. For higher frequency Schottky diodes such testing requires the fabrication of test circuits. Manufacturers provide these curves, but the quality is often poor. These diodes can often be purchased for less than 50 cents each, and the applications do not result in the manufacturers providing higher quality graphs.
Fabrication costs are high enough that separate I-V test circuits are rarely merited. For applications such as signal detection or rectification, it is easier to infer these behaviors from actual circuits and SPICE parameters. 107
Figure 5.2: I-V Diode Curve for NXP's BAT86113 Diode
Semiconductors are commonly used to create diodes by creating a PN junction where a
P-doped semiconductor is placed adjacent to an N-type semiconductor. PN semiconductor diodes are effective for rectifying 50 Hz and 60 Hz AC electricity. As the frequency rises, however, the effectiveness of the PN diode decreases because of the 108 reverse recovery time. This is the amount of time out of every half cycle where the electrons in the PN material are reversing direction from allowing to blocking current flow.
As the reverse recovery time becomes an increasing part of each half-cycle, there is a point of diminishing effectiveness which is commonly known as the frequency cut-off.
There is a trade-off between higher breakdown voltages and higher frequencies. Putting more material in the current path of PN diodes to “resist” voltage breakdown results in longer electron transit times yielding larger reverse recovery times and lower cut-off frequencies. Voltage drops of 0.6 to 0.7 volts are commonly seen for silicon-based semiconductors. For 60 Hz AC electricity the breakdown voltage is typically engineered to be above 110 and 220 V, and the 60 Hz frequency of commercial power is engineered to be below the cut-off frequency of PN diodes. For microwave frequencies, however, PN devices are ineffective for applications such as rectification where the high frequency and relatively high voltage drops can consume much of the available power. 109
5.2 RECTIFIER DESIGN OBJECTIVES AND CHOICES
The 1 mW (+0 dBm) power level was selected as a design point for energy harvesting in this dissertation research. The spectrum analyzer measurements were -5.677 dBm for a
5 MHz resolution bandwidth (RBW) segment at 26.3 GHz. Increasing the RBW to 20 MHz segments (+6 dB) through bandwidth aggregation indicated that the +0 dBm objective was reasonable.
The theoretical efficiency of a full-wave rectifier was the key factor in the choice of +0 dBm. A theoretical efficiency of 59.9% using HSMS-282x diodes was computed using
Equation [5.6]. Power plants with steam or natural gas turbine systems have typical efficiencies of 33% to 50% respectively. When compared to the efficiencies of these power plants, rectification of heat radiation could be a significant improvement. This efficiency is even more significant given the “free” nature of the heat energy provide by the sun. Using rectifier circuits engineered for 50 Ω impedances, as much as 59% of the free space power is reflected into free space by the disparate impedance boundaries. If a rectenna (the rectifying circuit including the antenna) is engineered closer to the free space impedance of 377 Ω, e.g. a level such as 175 Ω, more power reaches the rectifier raising the efficiency towards 80%. 110
The measurement of the power spectrum in 5 MHz segments at room temperatures, using the FieldFox spectrum analyzer, identified two areas with power approaching +0 dBm:
1. +18.8 dBm at 0 Hz, and
2. -5.677 dBm at 26.3 GHz and higher.
For each of the measured power levels, two diode characteristics needed to be satisfied from a design point of view:
1. The diode needs to effectively operate at the desired frequency, and
2. The diode must have a voltage threshold (turn-on or forward voltage) lower than
the peak voltage of the power source.
An engineering design, using discrete components and a bread board, was initially pursued because of the ease of testing and the quick implementation time. Fabricating circuits from silicon materials have large, one time, fabrication costs and turnaround durations measured in weeks to months. Although the frequency cut-off equation indicated that several Schottky diodes, could in theory operate at 26.3 GHz, application notes from manufacturers and engineering caution steered the circuit design for this dissertation away from the 26.3 GHz and beyond power spectrum. Secondarily, the microwave signal generator (MSG) available in the lab at that time had a maximum frequency limit of 3 GHz. This MSG was inadequate to test and debug in the 26.3 GHz frequency range. Given this test equipment limitation, testing a 26.3 GHz rectifier was 111 impeded, and as a result a 26.3 GHz rectifier was not initially pursued. The BAT86113 and
HSMS2826 diodes also easily addressed the 0 Hz peak (and 5,000 kHz shoulder). The
HSMS2826 diode possibly could have addressed in theory the power in the 26 GHz range for powers greater than -20 dBm.
The lab wall measurements showed +18.8 dBm (76 mW and 1.95 Vrms) of power at 0 Hz.
This power level was chosen as the design objective for the early rectifier circuits. This objective was easily addressable by discrete components using breadboard and PCB fabrication on microstrip technology. Most of the previous research projects with rectennas had focused on microwave frequencies for rectification. Further, the circuit designs that were commonly used unintentionally filtered out or blocked any 0 Hz power from being received [47].
5.3 SUFFICIENT VOLTAGE FROM THE POWER SOURCE IS KEY TO RECTIFICATION
The key to sustained rectification is to have a RMS voltage that exceeds the turn-on voltage of a diode. Table 5-D shows the RMS voltages associated with a measured power level (in dBm) at a 50 Ω impedance. If -22 dBm (18 mV RMS) of measured power is available at a 50 Ω impedance, then a diode that turns-on at 10 to 12 mV is needed to generate 6 to 7 mV of DC voltage. Clearly, a power of +18.8 dBm (1.95 Vrms) would comfortably exceed the turn-on voltages for many silicon-based diodes (0.6 to 0.7 Vrms).
The RMS voltages at 377 Ω and 175 Ω impedances are included for convenience when considering alternative designs. 112
Table 5-D: RMS Voltage Associated with a Given Power Level
RMS Voltage for a Given Power Level 50 Ohm RMS Voltage (in mV) Power (in dBm) Measured Power (in mW) 50 Ω 377 Ω 175 Ω 0 1.0000 224 614 418 -1 0.7943 199 547 373 -2 0.6310 178 488 332 -3 0.5012 158 435 296 -4 0.3981 141 387 264 -5 0.3162 126 345 235 -6 0.2512 112 308 210 -7 0.1995 100 274 187 -8 0.1585 89 244 167 -9 0.1259 79 218 148 -10 0.1000 71 194 132 -11 0.0794 63 173 118 -12 0.0631 56 154 105 -13 0.0501 50 137 94 -14 0.0398 45 123 83 -15 0.0316 40 109 74 -16 0.0251 35 97 66 -17 0.0200 32 87 59 -18 0.0158 28 77 53 -19 0.0126 25 69 47 -20 0.0100 22 61 42 -21 0.0079 20 55 37 -22 0.0063 18 49 33 -23 0.0050 16 43 30 -24 0.0040 14 39 26 -25 0.0032 13 35 24 -30 0.0010 7 19 13 -35 0.0003 4 11 7
113
This dissertation created multiple rectifiers in the pursuit of one that would harvest the power that the measurements and theory indicated was available. Table 5-E identifies the key characteristics for the diodes that were used in the rectifiers fabricated in this dissertation. The differences between the BAT24-02LS and the SMS7621-060 illustrate the trade-offs that often occur in diode selection. As can be seen, the BAT24 diode has a lower frequency cut-off but a higher reverse breakdown voltage than the SMS7621 diode.
A higher reverse breakdown voltage was preferred for the “Version 4” and “Version 5”
Rectifiers.
Table 5-E: Characteristics of Schottky Diodes Used in Rectifiers in this Dissertation
Manufacturer Diode Model Rectifier C (in pF) R Computed VF (in VF max T s Positioning Version fc (in GHz) mV) (in mV) VB (in V) Bread BAT86113 8.00 380 900 50.0 Board HSMS282 V1 1.00 12.0 13 340 500 15.0 Up to 4 GHz MA4E1317 V2 & V3 0.05 7.0 455 600 700 7.0 Up to 80 GHz, High Barrier BAT15-03W 0.26 5.5 111 230 410 4.0 Up to 12 GHz BAT24-02LS V4 & V5 0.20 8.0 99 230 410 4.0 Up to 26 GHz, Low Barrier SMS7621-060 0.13 10.3 119 260 320 2.0 Above 26 GHz, Low Barrier
The “Bread Board” rectifier was a low cost, easily implemented circuit. It was a voltage doubler, and it was a success at doubling the output voltage. The BAT86 diodes used in this rectifier have axial leads suitable for insertion into the holes of a lab bread board.
When driven by a microwave signal generator (MSG) across a range of low frequencies, it successfully generated DC voltages as expected. When connected to antennas, however, rectifying the measured power around 0 Hz proved elusive. 114
The “Version 1” rectifier was the first venture into fabricating a microstrip circuit on a PCB board. Each rectifier that was fabricated by an outside vendor averaged $5,500 for the fabrication, parts, and assembly. The price was slightly dependent on the quantity of boards produced, but it was dominated by one-time fabrication costs. The “Version 1” through “Version 5” diodes used surface mount technology (SMT) with dimensions that are hard to see and harder to accurately place on the solder paste of PCB’s.
Key Sight’s ADS software was used to design and simulate the “Version 1” circuit. The
ADS software generated the Gerber format instructions for placement of metal, mask, solder paste, via holes, coax connectors, and SMT components. The Gerber format is an industry standard for fabrication. The HSMS282 diodes chosen for the “Version 1” rectifier had been successfully demonstrated in the literature for the 2.45 GHz spectrum
[48-49]. When driven by a MSG across a range of low frequencies, this rectifier successfully generated DC voltages as expected. When it was connected to antennas, however, it failed to harvest even though the diodes were rated to generate current for powers greater than -20 dBm (22 mV RMS) and for frequencies under 4.0 GHz. Power at
0 Hz and the 5,000 kHz shoulder was not present.
The “Version 2” rectifier was the first effort to address the harvesting at 26.3 GHz and beyond. The “Version 2” rectifier changed the Schottky diode to the M/A-COM
MA4E1317 diode, incorporated filtering, allowed a large 1.5 GHz span of spectrum, and added voltage doubling. The MA4E1317 diodes, used in the “Version 2” rectifier, were also successfully used in the literature [49]. Unfortunately, the physical dimensions of the 115 diodes were significantly smaller than those used in “Version 1” rectifier greatly complicating the assembly where the SMT diodes are soldered to the board. During the assembly, the diodes shifted positions literally floating on the solder balls. Bandpass filtering was introduced to limit the aggregate power that was expected from a frequency span of multiple GHz. This filtering brought insertion losses, but the aggregate power from 300 segments of 5 MHz per segment was expected to offset the losses. Keysight’s
Genesys software was used to design the filters and the circuit, simulate the circuit, and generate the Gerber output. Unfortunately, the line widths in the filters pushed the 3 mil minimums of the fabrication process. Sadly, the resultant “Version 2” board failed to rectify using both the microwave signal generator as well as the WR-187 and WR-340 waveguide antennas.
The “Version 3” rectifier was a simplification and an effort to eliminate anything that could have gone wrong. The MA4E1317 Schottky diode was retained. Since the “Version
2” rectifier introduced multiple changes, there was limited ability to determine what went wrong. In the “Version 3” rectifier the bandpass filtering was removed along with its borderline line widths. Because the expected power below 20 GHz was naturally low, the bandpass filter and its insertion losses were deemed unnecessary. A low pass filter with a cut-off frequency around 50 GHz was substituted to limit the frequency span entering the rectifier to roughly 30 GHz and to prevent the losses to higher harmonics. The voltage doubling function was also removed. The board thickness was increased from 8 mil to 20 mil to improve the board stability during assembly (the placement of the SMT diodes). 116
The fabricator made numerous recommendations to address the assembly of the SMT diodes onto the board. This iterative process resulted in seven revisions in the design while interacting with the fabricator before the rectifier was released to the floor for fabrication.
An Anritsu 69067 Synthesized Continuous Wave Generator (MSG) with a frequency range from 10 MHz to 40 GHz was acquired. The “Version 3” rectifier successfully generated DC voltage when it was driven by the 40 GHz MSG at multiple power levels and multiple frequencies. When the “Version 3” rectifier was connected to the antennas, however, it failed to produce DC voltages. Since the bandpass filter removal failed to deliver the expected increase in voltages from the serial aggregation of each 5 MHz segment [50], the assumption that heat noise was a collection of voltage sources in series was challenged. A few mV per each 5 MHz segment should have generated a large voltage across a span of 30 GHz. The idea began to form that the heat noise was in some way related to individual voltage sources. Since the DC voltage output from the “Version 3” rectifier when driven by the MSG was much closer to a single 5 MHz voltage source, maybe individual 5 MHz segments were failing to clear the turn on voltages and as a result aggregation was somehow impeded. This resulted in an assessment that low barrier or zero barrier diodes should be used so that individual voltage sources without bandwidth aggregation could clear the turn-on voltages of the rectifying diodes.
The character and results for the “Bread Board” through “Version 5” rectifiers are explained in the following sections. 117
6 MEASUREMENTS, EXPERIMENTAL RESULTS, AND DISCUSSION
6.1 HARVESTING 0 HZ POWER
6.1.1 Voltage Doubler Rectifier Using NXP BAT86113 Diode
Current engineering literature did not reveal any research on the harvesting of “thermal noise” power from heat sources at room temperature. Commercial rectifiers are commonly designed to operate in the U.S. at commercial power frequencies of 60 Hz and
AC voltages of 110 and 220 V. A custom circuit needed to be built as a result. Breadboard circuits using discrete components are used to quickly design, debug, and test electronic circuits with discrete components. Because of the expected low power levels for
“thermal noise,” a voltage doubler circuit was chosen to literally double the output voltage for a rectifier. This more complex circuit for rectification was chosen early in this dissertation. This allowed an early test of the rectification alternatives.
Figure 6.1 illustrates the circuit schematic for a voltage doubler circuit. This circuit used
4.7 µF capacitors, a 10 kΩ resistor, and Schottky diodes. The Schottky diodes were
BAT86113 diodes from NXP. These were among the best discrete component diodes available in the market with axial leads that can be plugged into a circuit breadboard. The specification sheet for these diodes quotes a combined (RS CJ) product of 4 ns yielding a 118 theoretical frequency cut-off of 40 MHz. This cut-off frequency was good enough for 0
Hz power harvesting.
Figure 6.1: Circuit Schematic for Voltage Doubler Rectifier
Figure 6.2 is a photograph of the breadboard circuit used to test this rectification circuit.
An Agilent N9310A RF Signal Generator was used as a power source providing manually selectable frequencies up to 3 GHz and power levels ranging from -30 to +20 dBm. A digital volt meter was used to measure the DC voltage across a load resistor. 119
Figure 6.2: Photograph of the Breadboard Circuit Voltage Doubler
Figure 6.3 plots the DC output voltages from the voltage doubler rectifier across a frequency range up to 200 MHz. Two configurations were tested: one using 4.7 µF capacitors and one using 10 µF capacitors. This test confirmed the conservation of power where the higher voltage of a voltage doubler circuit yields less current. The voltage across the two values of capacitance are the same, and they can only be such for different currents flowing through the diodes. Two power levels were also tested: +0 dBm (0.224
Vrms) and +15 dBm (1.57 Vrms). This graph is somewhat deceptive since both axes are logarithmic. At the +0 dBm power level the output voltage rapidly drops to 31 mV or so around 100 MHz from the high of roughly 1350 mV at 45 MHz. These results comport with the theoretical cut-off frequency of 40 MHz. The performance curves for this diode show forward current of 0.1 mA at a turn-on voltage around 180 mV. At +0 dBm power 120 levels the peak sinusoidal voltage is 316 mV from Table 5-B on page 102. This translates to a rectifier efficiency using Equation [5.6] of 64%.
Figure 6.3: Voltage Output from Breadboard Rectifier across Frequency Range
6.1.2 Version 1 Rectifier
Advanced Design System (ADS) from Agilent, now Keysight Technologies, was chosen to design a full wave rectifier using microstrip technology. A key capability of this software system is the ability to generate the machine instructions in Gerber format for printed circuit boards (PCB) allowing an external vendor to fabricate the printed circuit board including the placement of surface mounted technology (SMT) components such as the diodes and capacitors. The surface mounted Avago HSMS2824 Schottky diodes were 121 selected given the numerous papers where comparable data was available on rectifier performance for various frequencies and power levels [51]. Given the 2.7 mm x 3.1 mm dimensions of the diodes, these dimensions require the automated placement of the diodes using robotics to properly solder the diodes to the circuit pads on the PCB.
Figure 6.4 shows the Gerber formatted output from ADS for the eventual design. Each diode package, the yellow colored SMT’s in Figure 6.4, consists of two diodes in parallel.
To achieve full wave rectification two diode ladders of six packages each were created: one ladder for each half (positive and negative voltages) of the input sine wave. The resultant 12 diodes in parallel for each half of the input sine wave provides maximum current for a given source voltage. While the rectifiers in the literature use single diodes, this design confirmed that diodes can be used in parallel wherever single diodes are used within rectifiers in the literature. A 15 µF SMT capacitor was used to collect the current from the diodes. The circuit was designed for a 10 kΩ SMT resistor, but this resistor was left off at the time of fabrication because the resistor was not yet available from the manufacturer. The resistor SMT’s were sent by the manufacturer nearly six months later.
The coax cable from the antenna or the microwave signal generator was attached to the port (Port 1) on the left. The DC output voltage was available at the port (Port 2) on the right. 122
Figure 6.4: Board Layout for Discrete Components from ADS
Using a Gerber file, this design was fabricated by Advanced Circuits (www.4pcb.com) at their Aurora, Colorado location. The circuit was fabricated on Rogers 4003C with the relative permittivity (εr) of 3.38 and a dielectric layer height of 1.524 mm (60 mil). The board dimensions were 4.8125” (12.224 cm) x 2.500” (6.35 cm) as shown in a photograph in Figure 6.5. 123
Figure 6.5: Photograph of Full Wave Rectifier Implemented as a PCB
6.1.3 “Version 1” vs Breadboard Rectifier Measurements
Both rectifiers were tested using an Agilent N9310A RF microwave signal generator (MSG) for input and a digital voltmeter to measure the DC output. The DC voltage was measured 124 across a load resistor. Figure 6.6 is a plot of output voltages from the two rectifiers tested using the microwave signal generator. The MSG fed +10 dBm (0.707 Vrms) of power to each rectifier. The voltage doubler rectifier implemented on a breadboard generated 3.0 to 5.2 V DC across the operating range of 10 kHz through 70 MHz. The frequency cutoff is quite visible as the frequencies rise above 70 MHz for the “Bread Board” rectifier. The
“Version 1” rectifier implemented on the microstrip generated 2.8 to 1.8 V DC across the operating range of 10 kHz through 100 MHz. A frequency cutoff for the “Version 1” rectifier is suggested in the measurements above 1 GHz. Based upon the manufacturer guidance from Avago, however, there could have been a final cutoff around 4 GHz which is beyond the frequency range of the MSG used to test this rectifier. Often in subsequent testing driven by a MSG with a range up to 40 GHz, a rectifier output would attenuate and then resurge at higher frequencies.
The voltage turn-on for the Avago diode is .01 mA at 90 mV. For a peak input voltage of
316 mV, the rectifier efficiency using Equation [5.6] was 78%. 125
Figure 6.6: Measurements from the Version 1 PCB and Breadboard Rectifiers
When both rectifiers were connected to antennas, the measured DC voltages for both rectifiers was 0 V DC. The operating frequency ranges for the diodes in both the breadboard and PCB rectifiers were below 100 MHz and 4 GHZ for the breadboard and microstrip rectifiers respectively. The threshold voltages of both diodes were below the measured powers. The measured power from the FieldFox meter (Spectrum Analyzer application) showed +18.83 dBm at 0 Hz and + 14.31 dBm at 5,000 KHz. Since power measurements are within the operating ranges of both rectifiers, the rectifier should have worked when connected to the waveguides. Since they did not, these 0 Hz and 5,000 kHz power measurements must have been artifacts of the FFT method for computing the power of the spectrum measured by the FieldFox meter. 126
6.2 HARVESTING IN THE 26 TO 50 GHZ RANGE
6.2.1 Design Considerations for Harvesting at 26 GHz and Beyond
Designing a rectifier to harvest “thermal noise” power at frequencies of 26 GHz and beyond involves uncertainties. Using the Spectrum Analyzer (SA) application on the
FieldFox meter, the power in the 5 MHz segments around each measurement frequency in the 26.3 GHz range was measured as -5.677 dBm. The turn “on” threshold voltages for many detector diodes are close to the source voltages associated with this measured power. The average DC voltage that can be produced by each of these larger frequency segments could be a few mV per segment.
The design considerations can be summarized as follows:
Computed RMS voltages per 5 MHz segment vary from a few to 20 mV,
Computed RMS voltages per 80 MHz segment climb to 112 mV,
Breakdown voltages for many high frequency diodes are around 2-4 V,
Aggregate voltages across each 1 GHz of spectrum could quickly and easily reach
2 V using a voltages sources “in series” model,
Voltage multiplier circuits can raise the output voltages,
Circuits engineered for the intrinsic free space impedance capture more power,
and
Frequency cutoffs for Schottky diodes may be lower than predicted. 127
The DC voltages that can be produced from each 5 MHz segment vary widely depending on the turn “on” voltage of the diode and the actual voltage presented at the diode by the “thermal noise”. Actual currents, albeit small, often flow at voltages below the threshold voltage. The actual DC voltage produced thus becomes an exercise in probabilities that also varies with the temperature of the diode. A diode becomes hotter as it experiences recurring voltage breakdowns and surges. More current flows when the diode heats up.
The power for a + 0 dBm and 5 MHz segment is a peak power. It is also an average of measurements. The average of the power peak floats within a range that makes each measurement significantly different. The FieldFox meter measures the power in 5 MHz segments averaging multiple samples around the measurement frequency. These segments aggregate across the spectrum such that the expected peak voltage using a series equivalent model can be represented as a summation of the peak powers (and indirectly the peak voltages) for each 5 MHz segment. This results in 200 such segments per GHz. A few mV for a given frequency segment aggregates to a larger voltage source across a frequency span. For 19 mV per segment, 200 5 MHz segments in a 1 GHz span could yield 269 mV. Actual efficiencies for rectification can vary, however. If 19 mV of voltage was harvested, the following computation shows how to estimate the potential voltage source from 1 GHz of bandwidth in the 26.3 GHz range:
200 2 V V 200 V 19 mV [6.1] S i unknown i 1 128
The average of peak voltages per 5 MHz segment that yields this unknown voltage is 1.34 mV. A rectifier with this level of measured performance would be losing over 91% of the potential voltage.
If the RMS average were 19 mV, the peak voltages for a sinusoidal source are roughly 27 mV. Using an average voltage of 19 mV from an average power of -21 dBm across a frequency span of 1 GHz in bandwidth yields 269 mV, and a 30 GHz span yields 1.472 V
RMS and 2.081 V peak. In an area where -21.3 dBm might be the average of the peak powers or the average of the powers, there is an exposure to burning out diodes due to nomenclature confusions. For a 30 GHz span of frequencies, a 2.081 V peak is quite different from 19 mV. If the reverse breakdown voltage of the diode is 4 V, the diode is close to reverse breakdown (2 V peak to -2 V peak) in a voltage doubler circuit. This could lead to repeated breakdown voltages with the recurring peaks. Since the manufacturing tolerances for individual diodes produce small variations in the manufacturing of individual diodes, repeated breakdowns are even further likely for some boards.
To compensate for the aggregation of multiple 5 MHz segments one can limit the total power and the associated voltage by using filters to limit the frequency span presented to the rectifier. Determining the span of the filtering depends on the power per 5 MHz segment, the design impedance, and the circuit used.
Most circuits in microwave systems are engineered for 50 Ω impedances to avoid power reflections at dissimilar impedance boundaries within an overall system. Many off-board antennas are engineered for 50 Ω connections via coax cable. Antennas receive 377 Ω 129 signals from free space producing 50 Ω output. The 50 Ω output from an antenna, when connected to a downstream device via 50 Ω cables, encounters minimal reflections before entering a downstream device. If a power meter, engineered internally at 50 Ω impedances, measures +0 dBm in power, the actual power before entering the antenna from free space (377 Ω) is + 3.8 dB higher. Engineering at a higher impedance for the rectifier circuit requires moving the antenna on to the rectifier circuit board. A rectenna with an onboard antenna and rectifier, if designed for a 120 Ω impedance, nearly doubles the power that could be captured from free space for a total of 1.8 mW versus 1 mW captured at 50 Ω.
6.2.2 Thermal Noise Modeling
The power measurements from the FieldFox meter showed -5.677 dBm (0.24 Vrms) at 26.3
GHz for a 5 MHz segment. For a 10 MHz segment it showed a + 3 dB higher power, and it showed an additional +3 dB for 20 MHz segments. The Planck’s law predictions in Figure
1.6 on page 21 shows the noise floor from Planck radiation. It also suggests that +60 dB of engineering gains could raise the powers to roughly + 20 dBm (2.2 Vrms) at 100 GHz and
+ 60 dBm (223.6 Vrms) at 1 THz for each 5 MHz segment. Using a “voltage sources in series” model for a rectifier designed to operate in the 26 to 100 GHz range, there should be enough power to generate RMS voltages greater than the threshold voltages of current
Schottky diodes. Given the increased powers and voltages with larger frequency segments and spans, it is logically essential to limit the bandwidth selected by the rectifier. 130
If the aggregate voltage exceeds the breakdown voltage of the diode, the circuit will likely suffer reverse breakdowns and eventually burn out.
Diodes allow the one-way passage of electric charges. Without this selectivity the average of the random voltages of the thermal noise would be 0 V, the middle of the – Vpk to + Vpk.
Thermal noise is an aggregation of individual emission events creating a batch of photons.
Since the diodes turn on when the random voltage exceeds the voltage threshold, the voltages for an aggregate emission event ranges from 0 to Vpk with the average being Vrms per “batch of photons.” A key question is whether this “batch of photons” behavior occurs for specific frequencies or a narrow range of frequencies.
Measurement parameters such as resolution bandwidths, channel power, and averaging implies that aggregation occurs in some way. The Fourier Transform theory posits that any signal can be represented as the sum of its Fourier frequencies. The FieldFox meter measures power in the time domain and maps it into the frequency domain using Fast
Fourier Transforms (FFT). If the behavior of thermal noise is frequency insensitive for a limited range, one would expect that the concurrent emissions of different frequencies would aggregate like the addition of the amplitudes of two “ai cos (ωit)” signals. Both
the Fourier representation of signals and the kbTB equation reinforce this belief. This would imply that the voltage output from each frequency within a segment should aggregate. If 10 mV (-27 dBm) RMS was the measured result of a 5 MHz segment, then the 200 segments in a 1 GHz span should have aggregated to 141 mV (-4 dBm) RMS. From 131 an equivalent circuit modelling perspective, this would suggest that thermal noise could be represented as “voltage sources connected in series”, one for each 5 MHz segment.
This expected result did not happen in the “Version 4” rectifier. This rectifier allowed a
30 GHz frequency span to enter the diodes. The manufacturer’s S12 curves for the diodes look like a bandpass filter with a frequency span of 30 GHz. Even if the power was -60 dBm (224 µV) per 5 MHz, the frequency span of 30 GHz would have aggregated to 17 mV
RMS3. For the measured channel power of -21.3 dBm (19.2 mV RMS) the frequency span of 30 GHz should have produced 1.378 V RMS.
The actual peak voltage output of the “Version 4” rectifier was measured as 7 mV. This was not anywhere close to the possible 1.4 V RMS. Either the rectifier sharply attenuated the inputted power, noise power does not aggregate as multiple voltage sources (one each for each 5 MHz segment) in series as expected, or the voltage peak and averages are not sinusoidally related. While theory suggested voltage sources in series, for reasons unknown at the time the measurements did not support this expectation. With experimental hindsight the rectifier attenuated the input power and voltage (0.1 mV vs. the theoretical 19.3 mV per 5 MHz segment), and noise was not even close to sinusoidal.
3 -60 dBm is equivalent to 1 nW in each 5 MHz segment. There are 6000 segments of 5 MHz in 30 GHz. This yields 6 µW (17.3 mV). 132
6.2.3 V2 Rectifier
The “Version 2” rectifier was the first design in pursuit of the 26 GHz and beyond power.
KeySight’s Genesys software was used to design and simulate the filters and the circuit.
Rogers RO4003 board stock was used. The damage from exceeding the power limit with the Agilent N1911A power meter and the automatic 5 dB attenuations inserted by the
FieldFox meter during measurements were fresh experiences at that point. Consequently, band pass filters were deemed necessary to limit the bandwidth to 1.5 GHz and to limit the associated power entering the rectifying diodes. The success of the voltage doubler sub-circuit used in the “Bread Board” rectifier encouraged the adoption of the voltage doubler sub-circuit into the “Version 2” rectifier. This sub-circuit made low pass filters a necessity to prevent microwave inbound power from shunting to ground. Given the narrow bandwidth needed for the bandpass filter, the design drove the depth of the board stock to 8 mil. It also pushed the minimum line widths achievable by the fabrication process for both the bandpass and low pass filters. Figure 6.7 shows the resultant Gerber image generated by the Genesys software. Figure 6.8 shows a photograph of the finished microstrip PCB. 133
Figure 6.7: Gerber Output for the Version 2 Rectifier
Figure 6.8: Photograph of Version 2 Rectifier
The fabrication of the “Version 2” rectifier was an arduous process. The thin 8 mil stock created substantial stability difficulties for the assembly (placement) of the SMT components. The MA4E1317 diodes were particularly difficult. Being 17 mil x 31 mil
(0.431 mm x 0.787 mm) in size, they require optical magnification to see and to manually 134 place. Automated robots could have been used, but the tape feeds come in upwards of
7000 diodes per reel. The MA4E1317 diodes also come in a tube which require manual placement. The fabricator chose diodes in a tube. The manufacturer recommended solder pads were too small, and the solder mask boundaries resulted in solder balls during heating. The manual placement on the solder paste was imprecise and was aggravated by the board stability. Further, the heating process to melt the solder paste resulted in random floating of the diodes on the solder balls. The smallest 32 mil, coax, end- connectors were too big for the stock of 8 mil. This required additional manual attention to solder bridge the top lead to the circuit line. Finally, as can be seen in Figure 6.9, the placement of the lines could have resulted in shorts with the coax connectors. The fabricator prevented this issue by snipping off one side of each of the coax connectors.
When the finished Version 2 rectifier was tested using the 3 GHz MSG to drive it, the rectifier failed to produce a DC output across the two output coax connectors. The causation was never determined. S12 measurement subsequently with the FieldFox confirmed that signal was passing into the circuit up through 26.5 GHz. The signal was most likely not passing through the diodes since there was no output DC voltage. Figure
6.10 shows the power measured from the waveguide antenna. The connection to the waveguide antenna also failed to generate any DC voltage. The “Version 2” rectifier was an unmitigated disaster otherwise known as a “learning experience.” 135
Figure 6.9: Version 2 Rectifier Design Error Example
136
Figure 6.10: Measured Power from Antenna for Version 2 Rectifier
The benefit of the Version 2 rectifier was that it revealed the limitations of diagnosing performance difficulties in the 26 GHz and above frequencies. It motivated the acquisition of additional testing equipment. It also suggested that circuit simplification was wise and that iterative improvements across rectifier versions was prudent. 137
6.2.4 V3 Rectifier
An Aritsu 69067B Synthesized CW Generator was acquired during the design and fabrication of the “Version 3” rectifier. This microwave signal generator has a frequency range up to 40 GHz, and it can generate signal powers ranging from -35 dBm to +16 dBm.
Even though this MSG was lab certified, it was tested using the FieldFox meter. Figure
6.11 shows the result of this testing for various power levels: 0, +10, and +20 (+16) dBm for up to 26.5 GHz of the 40 GHz frequency span (limited to 26.5 GHz by the FieldFox).
The MSG did not generate the same power across the frequencies even though it was set at a specific power level. It is only effective for testing for a specific frequency, such as
26.3 GHz. The Schottky diode used in the “Version 3” rectifier has a turn-on voltage of
480 mV. For 26.3 GHz the MSG failed to generate enough voltage to activate the diode turn-on voltage for +0 dBm (0.224 Vrms) and +10 dBm (0.707 Vrms). At +16 dBm power levels the MSG was validated for testing the “Version 3” rectifier. 138
Figure 6.11: Output from 40 GHz MSG As Measured by FieldFox Meter
Figure 6.12 shows a photograph of the “Version 3” rectifier. This rectifier generated DC voltage when driven by the MSG, as is shown in Figure 6.13. It failed to generate DC voltage when connected to the WR-187 waveguide pointed at the laboratory wall. This rectifier’s performance prompted the Channel Power measurements that indicated that power per 5 MHZ segment could be 15 dB lower than expected. It also challenged the modeling of noise as aggregate voltage sources in series. It led to the conclusion that low barrier diodes were required. 139
Figure 6.12: Photograph of Version 3 Rectifier
Figure 6.13: DC Output Voltage from V3 Rectifier
140
6.2.5 V4 Rectifier
The “Version 4” rectifier is a simplified variant of the “Version 3” rectifier where Infineon
BAT24-02LS Schottky diodes have replaced the MA4E1317 diodes used in the “Version 3” rectifier. The BAT24 diodes are low barrier diodes that turn-on at a few millivolts. Figure
6.14 shows the manufacturer I-V curves for the two diodes. Where the MA4E1317 diode has a relatively high turn-on voltage of 480 mV, the BAT24 diode turns-on with very little voltage. It was hypothesized that thermal noise generates so little voltage per frequency segment that lots of photons were reaching the MA4E1317 diodes, but not enough of them were present to clear the turn-on threshold. The FieldFox Spectrum Analyzer and
Channel Power applications suggested much lower powers were entering the rectifier.
Given the uncertainty of how much power was reaching the diodes, the BAT24 diodes offered a significant margin for error. With the lower voltage threshold of the BAT24 diodes, the lowest measured channel power of -21.3 dBm (19 mV RMS) in each 5 MHz segment would be enough to turn-on the diodes.
141
Figure 6.14: I-V Curves for Schottky Diodes Used in Version 3 and 4 Rectifiers
The Version 4 rectifier used the Rogers RO4003 microstrip laminate. The distance (d) between the top and the bottom conductors was 32 mil. The dimensions of each rectifier were 1.4” x 1.2” (L x W). The SMT capacitor was moved off board to a measurement circuit. The low pass filter was retained. Figure 6.15 shows a photograph of the resultant rectifier.
142
Figure 6.15: Photograph of Version 4 Rectifier
Figure 6.16 shows the DC Voltages generated from the “Version 4” rectifier when driven by the Aritsu microwave signal generator. For the 25 to 40 GHz range the measured DC voltage outputted by the rectifier was under 1 mV. Since the FieldFox measurement of the Aritsu MSG at 26.3 GHz was 120 mV or so for a +0 dBm setting, as can be seen in
Figure 6.11, the under 1 mV output in Figure 6.16 raises questions regarding the actual power being generated by the Anritsu MSG. Alternatively, very little of the 120 mV is reaching the diodes. If the diodes turn on at 11 mV, then the 1 mV output suggests that only 12 mV (10%) of the 120 mV from the MSG is reaching the diodes. The impedance mismatch between the low pass filters and the diodes accounts for an attenuation to 21% 143 of the measured MSG voltage output. The cause for the further reduction to 10% is unknown. The key result of the MSG testing, however, is that the “Version 4” rectifier works for very low power levels.
Figure 6.16: Version 4 DC Output (in mV) Using Aritsu Microwave Signal Generator
The WR-187 waveguide was used as an antenna, and it was pointed perpendicularly 1 m from the laboratory wall. When the “Version 4” rectifier was connected to the WR-187 waveguide via coax cable, the rectifier charged the capacitor of the measurement circuit.
The digital voltmeter measured a peak voltage on the charged capacitor of 7 mV. Given the low turn-on threshold for the diode per the diode manufacturer, this suggests a peak 144 voltage of 17-18 mV was received from the waveguide. Using Table 5-B on Page 102, this peak voltage corresponds to a power level around -25 dBm.
Table 6-A analyzes the power measurement which is highlighted in yellow. The rest of the table is computed from these values. The FieldFox meter (Channel Power application) measured -21.3 dBm (19.3 mVrms) at 26.3 GHz for a 5 MHz segment. The actual peak voltage that was harvested was -28.9 dBv (8 mVpk). One possible explanation for this difference could have been the absence of impedance matching between the rectifier’s low pass filter (50 Ω) and the diodes (6 Ω). Nearly 83% of the power was lost due most likely to the impedance mismatch. Given the differences in the predicted diode impedances, it is likely that much of the difference in the measured versus predicted results can be explained by the reflections.
Table 6-A: Measurements and Comparisons for Version 4 Rectifier
Meaurement Power Power Vpeak (in dBm) (in µW) (in mV)
WR-187 to V4 Rectifier WR-187 with FieldFox Channel Power -21.3 7.4 19.3 V4 DC Output 7.0 Turn On 1.0 WR-187 implied Input to V4 Diodes -28.9 1.3 8.0
WR-187 to V4 Losses -7.6 82.7% 58.4%
A natural question arising from the measured 7 mV is “what was harvested?” Was the power harvested thermal noise or ambient RF? Most ambient RF in a residential environment is less than 3 GHz. Higher frequency radars, air navigation aids, and military 145 sources are limited in the Reno NV area, and the distances to the laboratory from such sources are on the order of 15 km and greater. Path losses for 15 km are on the order of
-130 dB for 5 GHz frequencies. Path losses are even greater for higher frequencies. The
FieldFox Spectrum Analyzer of the area around the laboratory shows no sources outside the thermal noise floor in the 26 GHz frequencies. Free space path losses are substantial at Wi-Fi microwave frequencies (-60 dB at 10 m, -66 dB at 20 m, and -80 dB at 100 m).
Losses are even greater when passing through walls with metal rebar. Interior ranges for
Wi-Fi at 2.4 GHz are commonly 20 m or less. The WR-187 is highly directional and was pointed away from the interior Wi-Fi sources. This would likely result in at least a 30 dB attenuation of this out of beam signal. The likely nearest transmitter within the WR-187 primary lobe is at least 50 m away. Additionally, the frequency cut-off for the WR-187 waveguide is 3.156 GHz. Frequencies below the cut-off are reflected from the waveguide
(e.g. Wi-Fi 2.4 GHz), and frequencies up to 3.8 GHz (+20% of the cut-off) are significantly reduced. Cell phones do not pick-up the Wi-Fi networks from the possible transmitters on the WR-187 directional path. There is substantial intervening walls and metal. Further,
Figure 6.17 shows the S12 frequency behavior of the Schottky diode used in the “Version
4” rectifier. The Wi-Fi frequency of 2.4 GHz experiences a -12 dB power attenuation per the S12 curve, and the power attenuation is – 5 dB at 5 GHz. It is very unlikely that the rectified power source was Wi-Fi or any other ambient RF. 146
Figure 6.17: Manufacturer’s S12 Curve for BAT-24 Diode Used in Version 4
Figure 6.18 shows the power range for the measured peak voltages. The FieldFox meter
(Channel Power application) measured -21.3 dBm (19.3 mVrms) of power at 26.3 GHz. If the diode turned-on at 0 mV then the measured net voltage of 7 mV corresponds to -30 dBm. The rectifier captured the 7 mV net voltage, a power corresponding to roughly -25 dBm. A power of -25 dBm is roughly midway between the power ranges shown in Figure
6.18. 147
Figure 6.18: Power Range for Measured Voltages
Figure 6.19 poses two possible variants for a noise equivalent model. Are noise sources parallel sources of voltage for a small frequency span? Or should they be modeled as voltage sources in series for a frequency span? Resolution bandwidth measurements suggest that noise aggregates as voltage sources in series. The results from the “Version
3” and “Version 4” rectifiers suggest that the voltages do not appear to aggregate as a
“noise sources in series” view would suggest. Interestingly, in an experiment a 12 inch wire aligned vertically to the floor was connected to an oscilloscope. The time domain plot of the multiple signals captured from the air showed an average of 3-4 mV peaks.
For a spectrum active with ambient, lower frequency RF and thermal noise, why does the 148 oscilloscope show such small voltages? Thermal noise is considered somewhat flat across the spectrum. This suggests the parallel model might also be in some way applicable.
Figure 6.19: Noise Equivalent Model
6.2.6 V5 Rectifier
The “Version 5” rectifier is a simplified variant of the “Version 4” rectifier where impedance matching was introduced between the low pass filter and the diodes. This matching was achieved by three transmission line segments in front of each of the diodes.
The optimizer feature of Genesys was used to iteratively determine the optimal length and width dimensions of the six transmission line segments. The three segments in front 149 of the positive half diode ended up with different dimensions than the path in front of the negative half diode.
Figure 6.20 shows the microstrip board layout for the V5R1 rectifier.
Figure 6.20: Genesys Layout for the V5R1 Rectifier
Figure 6.21 shows the V5 Rectifier’s performance compared to the V4 Rectifier when driven by the MSG. The voltage harvested by the V5 Rectifier for a given frequency substantially improved. 150
Figure 6.21: V5 and V4 Rectifiers Driven by MSG
Figure 6.22 shows the measured performances of the V5 vs V4 rectifiers. The V5 rectifier harvested 19.0 mV of the theoretical 19.3 mV reaching the diodes. The harvested power corresponding to this voltage was 7 µW and the computed amperage was 0.4 mA. 151
LadyBug Patch V4 Rectifier V5 Rectifier
Operating Frequency (in GHz) 10.0 26.3 26.3
Planck's Law (dBm per m2) -68.5 -60.1 -60.1
Difference Between Planck's Law and Average Power 36.9 13.8 13.8
Measured Average Power (dBm) -31.6 -46.3 -46.3
Difference Between Average and Peak Power 27.2 25.0 25.0
Measured Peak Power (dBm) -4.4 -21.3 -21.3
Theoretical Voltage (in mV) 19.3 19.3 Measured Voltage (in mV) 7 19.0 Effective Rectification 36.4% 98.7%
Power (in mW) at Measured Power (in dBm) 0.007 0.007 Voltage (in V) 0.007 0.019 Current (in mA) 1.1 0.4
Power Harvested (in mW) 0.001 0.007
Figure 6.22: Measurements of V5 vs V4 Rectifiers
6.3 HARVESTING IN THE 75 GHZ RANGE
6.3.1 V1 Rectenna
The waveguide antennas and coax connections to test equipment and rectifier circuits allowed easy measurement and testing. This configuration was crucial to confirming that there was enough ambient power to be useful. The natural next step was to move the antenna and rectifier onto the same PCB board creating a rectenna. There were several 152 benefits to be derived. First, a section of 22-inch waveguide is bulky and awkward to use in testing. Patch antennas can easily be implemented on microstrip PCB laminate. For higher frequencies the dimensions of patch antennas fit into the millimeter range.
Secondly, higher frequencies allow the combined rectenna to be smaller. Thirdly, Planck radiation increases at higher frequencies. At 26.3 GHz the Planck floor for a 5 MHz frequency span is -60 dBm (1 nW). At 75 GHz the Planck floor for a 5 MHz frequency span is -51 dBm (7.9 nW). Fourthly, a patch antenna with a 3% bandwidth at 26.3 GHz yields
+22.0 dB of bandwidth gains while the same antenna type at 75 GHz yields +26.5 dB of bandwidth gains. Additionally, the impedance between the patch antenna and the rectifying diodes can be increased and the coax connectors can be eliminated. These improvements reduced power losses by 8.7 dB increasing the amount of free space power that reaches the diodes.
The first rectenna, V1R0 Rectenna, was implemented on Rogers 4003C 32 mil laminate.
This was the same laminate used in the V4 and V5 Rectifiers. As can be seen in Figure
6.23, multiple changes between the two designs were made. To provide as much antenna gain continuity as possible, a quad patch antenna was implemented with a predicted gain of +15 dB. The waveguide antenna in the V5 Rectifier configuration provided a predicted gain of +20.3 dB. By moving to 176 Ω transmission line connections between the antenna and diodes, the board impedance losses were reduced providing an improvement of +3.2 dB. The 5.5 dB of connector losses were also eliminated. Evaluating the net gains and losses between the two designs, rough parity was achieved. 153
Known Attenuations and Gains V5 Rectifier V1 Rectenna
Board Impedance (in Ohm) 50 176 Gains Wall Area 6.1 6.1 Wall 6.0 6.0 Antenna 20.3 15.0
Attenuations Polarity -3.0 -3.0 Impedance Losses (377 to Board) -3.8 -0.6 Measured Connectors -5.5
S21 Losses (LPF and Diodes at fo) -7.0 -7.8 Impedance Mismatch (9 to 54 Ohm) -2.9 Net Gain (Loss) from Planck's Law 13.1 12.8
Figure 6.23: Predictive Differences between V5 Rectifier and V1 Rectenna
The quad patch antenna was simulated with Genesys, and the S11 resonance and antenna bandwidth are shown in Figure 6.24. The maximum resonance was predicted at 74.4 GHz, and the bandwidth (S11 below -10 dB) spanned from 74.3 to 75.5 GHz (1.2 GHz) for a predicted bandwidth gain of +23.8 dB.
Figure 6.24: Simulated Resonance and Bandwidth of V1R0 Rectenna
154
Figure 6.25 shows the Genesys layout of the microstrip board for the V1R0 Rectenna with dimensions of (4” x 1”). The quad patch antenna sub-circuits were arrayed into four rectennas connected in series. Three segment impedance matching was included between each quad antenna and the rectifying diode. Unfortunately, the real impedance
(9 Ω) rather than the complex impedance (54 Ω) of the diode at 75 GHz was used for the impedance match. An impedance mismatch of -2.9 dB was introduced as a result.
Figure 6.25: Genesys Microstrip Board Layout for the V1R0 Rectenna
The copper pads at the top of the board allow the testing of the boards performance by attaching the measurement equipment to the board with alligator clip connections. The pads associated with the negative terminals of each sub-circuit are connected to the via pads. This let electrons escape from the negative half of the rectifier lowering the overall performance.
The measurement results for the V1 Rectenna in comparison to V5 Rectifier are shown in
Figure 6.26. The measured peak power for the V1 Rectenna was -18.7 dBm (13.5 µW), an improvement of +2.6 dB over the V5 Rectifier. The measured voltage that was harvested was 5.5 mV. The impedance mismatch and the connection to the via pad reduced the 155 effective rectification to 20.3%. The difference between average and peak power corresponds to bandwidth gain of +19.2 dB even though the Genesys simulation suggested +23.8 dB would occur.
V5 Rectifier V1 Rectenna
Operating Frequency (in GHz) 26.3 75.0
Planck's Law (dBm per m2) -60.1 -51.0
Difference Between Planck's Law and Average Power 13.8 13.1
Measured Average Power (dBm) -46.3 -37.9
Difference Between Average and Peak Power 25.0 19.2
Measured Peak Power (dBm) -21.3 -18.7
Theoretical Voltage (in mV) 19.3 27.1 Measured Voltage (in mV) 19.0 5.5 Effective Rectification 98.7% 20.3%
Figure 6.26: V1 Rectenna Performance Compare to the V5 Rectifier
6.3.2 V2 Rectenna
The second rectenna, V2R0 Rectenna, was implemented on Rogers 4003C 60 mil laminate.
As can be seen in Figure 6.27, multiple changes between the two Rectenna designs were made. By changing from a rectangular to square patch with a corner feed (Figure 6.28), the rectenna achieves dual polarity removing the polarity loss. By moving to 202 Ω transmission line connections between the antenna and diodes, the board impedance 156 losses were reduced. The impedance mismatch between the quad patch antennas and the diodes was eliminated.
Known Attenuations and Gains V5 Rectifier V1 Rectenna V2 Rectenna
Board Impedance (in Ohm) 50 176 202 Gains Wall Area 6.1 6.1 6.1 Wall 6.0 6.0 6.0 Antenna 20.3 15.0 15.0
Attenuations Polarity -3.0 -3.0 0.0 Impedance Losses (377 to Board) -3.8 -0.6 -0.4 Measured Connectors -5.5
S21 Losses (LPF and Diodes at fo) -7.0 -7.8 -7.8 Impedance Mismatch (9 to 54 Ohm) -2.9 Net Gain (Loss) from Planck's Law 13.1 12.8 18.9
Figure 6.27: V2R0 vs V1R0 Improvements
Figure 6.28: Rectangular vs Square Patch Antennas
Figure 6.29 shows the Genesys layout of the microstrip board for the V2R0 Rectenna with dimensions of (3” x 1”). The quad patch antenna sub-circuits continued to be arrayed into four rectennas connected in series. Each of the patch antennas is square in shape with a corner edge connection. On board capacitors were introduced between each of the sub- 157 circuits. Three segment impedance matching was included between each quad antenna and the rectifying diode.
Figure 6.29: Genesys Layout of the V2R0 Rectenna
Figure 6.30 shows the measured performance of the V2R0 Rectenna. While the average power level improved to -31.8 dBm, the measured peak performance improved only to -
18.2 dBm. The bandwidth of the quad antenna decreased giving up the gains from the design changes. The measured voltage came in at 8.8 mV. 158
V1 Rectenna V2R0 Rectenna
Operating Frequency (in GHz) 75.0 75.0
Planck's Law (dBm per m2) -51.0 -51.0
Difference Between Planck's Law and Average Power 13.1 19.2
Measured Average Power (dBm) -37.9 -31.8
Difference Between Average and Peak Power 19.2 13.6
Measured Peak Power (dBm) -18.7 -18.2 Theoretical Voltage per Cell (in mV) 27.1 28.7 Measured Voltage per Cell (in mV) 5.5 8.8
Figure 6.30: Performance of V2R0 Rectenna
Figure 6.31 shows the Genesys layout of the microstrip board for the V2R1 Rectenna. The big changes included increasing the number of rectenna sub-circuits from 4 to 5. The measured voltage did not improve as expected for each rectenna sub-circuit for the V2R0
Rectenna. The voltage doubler sub-circuit is a charge pump. V2R0 did not include blocking capacitance between the antennas and the diodes. As a result, electrons returned to the antenna and the ground plane much like a water pump without seals behaves. V2R1 sought to fix this issue by introducing a current blocking capacitance and an additional, third diode to prevent 75 GHz power on the negative half from shunting to ground through the capacitors. 159
Figure 6.31: Genesys Microstrip Board Layout for the V2R1 Rectenna
Figure 6.32 shows the improvement per sub-circuit to 20.5 mV. The five sub-circuits in series generate a combined voltage of 102 mV. The negative half cycle does not appear to be contributing to the voltage of each sub-circuit as desired, and the board yield is impacted by sub-circuits that randomly fail from board to board to generate current/voltage. This yield problem appears to be related to floating diodes during the solder melting stage of the board assembly. The tolerances for solder mask shields do not appear to be as tight as they need to be. The bandwidth aggregation gain remains the same between the R0 and R1 revisions. 160
V2R0 Rectenna V2R1 Rectenna
Operating Frequency (in GHz) 75.0 75.0
Planck's Law (dBm per m2) -51.0 -51.0
Difference Between Planck's Law and Average Power 19.2 19.2
Measured Average Power (dBm) -31.8 -31.8
Difference Between Average and Peak Power 13.6 13.6
Measured Peak Power (dBm) -18.2 -18.2
Theoretical Voltage (in mV) 28.7 28.7 Measured Voltage (in mV) 8.8 20.4 Effective Rectification 30.7% 71.2%
Power (in mW) at Measured Power (in dBm) 0.076 0.076 Voltage (in V) 0.102 0.102 Current (in mA) 0.7 0.7
Power Harvested (in mW) 0.013 0.069
Figure 6.32: Performance for V2 R1 Rectenna
6.4 NATURAL VERSUS MANMADE RADIATION
Theory associated with quantum physics posits that radiating electromagnetic waves are quantized into photons that have h·f energies where h is Planck’s constant and f is the frequency of the photons. Planck’s Law predicts the power that will spontaneously emit from a surface of matter at a given frequency and for a given temperature. These emissions are natural and appear as noise in most communication and radar signals. 161
Photons do not come with tags that identify each photon as being man-made or natural.
As a result, determining the origin of a photon requires observations, deductive reasoning, and specific testing to exclude man-made from natural emissions. This deductive process requires ruling out increasingly improbable sources to improve the likelihood of an emission being from a natural source. For example, much of man-made EM waves are below 3 GHz in frequency. A WR187 waveguide has a cutoff frequency of 3.15 GHz. Using a WR187 waveguide as an antenna effectively eliminates the likelihood of capturing man- made emissions below 3 GHz. Similarly, a patch antenna designed for 75 GHz eliminates man-made radiation below this frequency. Further, much of man-made EM waves propagate parallel to the earth’s surface. Pointing the waveguide aperture towards the ceiling of a room decreases the odds of capturing man-made, terrestrial emissions.
Higher frequency EM waves are also highly directive. The power from a man-made source will be greater in the direction of the source. Pointing a highly directive antenna in incremental, radial directions will quickly identify man-made sources. This technique is used in Radio Direction Finding to find radio transmitter and cell phone locations. Higher frequency signals also rapidly attenuate for distances of 100 feet or so. Transmitting antennas and electronics can often be seen at this distance. Additionally, manmade signals tend to be sinusoidal with predictable peaks while natural sources tend to be highly random with highly variable peaks. Unfortunately, ruling out other sources does not prove that the source is Planck radiation and therefore natural. 162
Antennas convert irradiating photons to electron movements that aggregate to electric currents. Absent an electrical circuit connected to the antenna, radiation that is absorbed by an antenna reemits after a temporal delay related to the resonant length of the antenna. If the electrical path to ground from an antenna is superior to the reemission path, however, the power that is transmitted to a circuit can be greater than the power that is reemitted by an antenna. If that circuit path includes an energy storage device, such as a battery or a capacitor, then the energy can be stored by the device and does not return, as a result, to the antenna for reemission. Consequently, the absorption of EM radiation does not always equal emission as might be deduced by the thermal equilibrium condition commonly used in thermodynamics. The “antenna noise temperature” that drives noise absorption is not the same as the surface temperature of the antenna that drives thermal emissions. Additionally, transmission through a material affects the absorption, reflection, and emission balance at a boundary for EM waves. As a result, absorptions that transform photons to electron energies look like transmissions via a different path that happens to be electrical.
Further, temperature differences are quite common in actual environments. Everyone recognizes that hot air rises, and, as a result, the ceiling of a room is often hotter than the floor. Uneven air currents in a room also alter the temperatures within a room creating temperature strata. Small temperature differences have disproportionate impacts on radiated power given the temperature to the fourth power relationship. Anechoic chambers can isolate electronics under test from external, man-made emissions, but 163 thermal radiation emissions will still be created by the temperatures of the matter within the chambers. Planck radiation also rises rapidly as a function of frequency to the fourth power, so this type of radiation emission is far greater in magnitude at higher frequencies.
6.4.1 Anechoic Chamber Testing
The V4R1 Rectifier connected to the WR-187 was tested inside the anechoic chamber at
UNR. When the voltage from the V4R1 Rectifier was measured in the anechoic chamber, a DC voltage of 5.4 mV (77% of the voltage measured outside the chamber) was observed.
The power associated with the 5.4 mV corresponds to 292 nW (-35.4 dBm) for the full- wave rectifier.
Since power transfer for heat radiation requires a temperature differential, this power should theoretically match the predicted Planck powers associated with this temperature difference when adjusted using the known factors technique. Using the known factors technique, measurements of average power for the WR-187 waveguide showed a delta of +13.8 dB between the theoretical Planck floor and the average power.
There was limited space between the absorbent cones on the floor in the chamber to place a stand and a horizontal WR-187 waveguide. Resultantly, the WR-187 was serendipitously stood on its end with the aperture pointing to the ceiling of the chamber.
The WR-187 was thermally and electrically grounded by the metal floor of the chamber.
This prompted the stand-off measurement of the ceiling temperature with an IR thermometer. The temperature in the chamber at the level of the aperture was 71.8oF
(22.1oC), and the temperature at the ceiling of the chamber was measured as 78oF 164
(25.6oC). Since thermodynamics prohibits heat transfer without a temperature differential, this difference in temperature between the ceiling and waveguide aperture theoretically allowed heat transfer into the waveguide. The waveguide was further grounded to the metal floor. In theory this provided a path to the earth outside the chamber and its unknown temperature. Depending upon the depth of the earthen ground, earth temperatures in April are often around 60oF in Northern Nevada.
The predicted Planck power density at 78oF for 26.3 GHz and 1.5 GHz of bandwidth corresponds to 298.585 nW per m2. The predicted Planck power density at 60oF for 26.3
GHz and 1.5 GHz of bandwidth corresponds to 288.568 nW per m2. The power density delta between the two temperatures is 10.017 nW per m2. This power density delta when adjusted by the delta of +13.8 dB between the Planck floor and the average power results in a power difference of 240.3 nW (-36.2 dBm). The power of -35.4 dBm associated with the measured voltage of 5.4 mV is relatively close to the predicted power of -36.2 dBm associated with the temperature difference. The relative closeness of this analysis suggests that energy and power was conserved.
Only three electronic devices were in the chamber: a handheld digital voltmeter, a handheld stand-off IR thermometer, and the FieldFox power meter. These devices were place on the floor and were below and behind the aperture of the waveguide. As a result, contaminating emanations from these devices were unlikely. Any emanations that did enter the antenna as reflections would have been attenuated and deflected by the absorbent and angled cones in the anechoic chamber. 165
Given the electromagnetic isolation of the anechoic chamber and the absence of active electronics that might emit EMF at 26.3 GHz, common sources of man-made, ambient radiation were eliminated. This strongly suggests that the measured EM radiation originated in the anechoic chamber. The metal walls of the chamber were covered by the angled, absorbent cones. This further suggests that radiation came largely from the air in the chamber in addition to what might have been emitted from the metal walls that were covered by the pyramidal cones. Given the isolation provided by the anechoic chamber, it is unlikely that the power came from man-made EM sources. While man-made radiation can be largely excluded, the hypothesis that this radiation was Planck radiation could not be absolutely proven by the anechoic chamber testing.
6.4.2 Hot Pot Testing
A “hot pot” test was also performed in the control room of UNR’s Anechoic Chamber using the apparatus shown in Figure 6.33. A black, iron, 10-inch pot was placed on a hot plate with a rheostat control for the plate’s temperature. The aperture of the WR-187 was pointed at the pot. There was a distance of 8 inches between the pot and the antenna aperture. The interior of the pot was empty. The temperature of hot plate was varied in increments of 5-10 minutes while recording the pot’s temperature and the measured
Channel Power from the Field-Fox meter. 166
Figure 6.33: Apparatus for Hot Pot Test
The control room by design was isolated from outside RF. The WR-187 waveguide, pot, and hot plate were placed on a table in the control room. The temperature of the pot was raised and lowered by a rotary switch on the hot plate. The voltage output of the rectifier was measured.
Figure 6.34 shows the measurement results. The left most data-point around 50oF came from a winter measurement of a “cold” pot. It was included to provide a broader temperature range for comparisons. The balance of the data-points on the right side of 167 the graph were obtained in the control room. The +14 dB increase in output voltage corresponded to a 168oF increase in temperature. If this were heat radiation, then
Planck’s law predicts a + 9.5 dB increase in output voltage. Given the 0.1 mV precision of the voltage measurements, this correlation between the measured and predicted results roughly supports the hypothesis that Planck radiation was measured. Given the distance of 8 inches between the WR187 aperture and the kitchen pot, the EM radiation entering the waveguide was dominated by Planck radiation. It is unlikely that external man-made
EM radiation materially impacted the “hot pot” test.
Figure 6.34: Rectifier V4R1 Output from Hot Pot Test
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6.4.3 Logical Exclusions of Manmade Sources
The WR-187 waveguide antenna and rectifiers captured ambient EM radiation above 3
GHz. Pointing the waveguide section towards the ceiling substantially excluded the EM radiation being directly received from terrestrial man-made sources. Further, the beam width of the WR-187 inside the control room of the anechoic chamber was dominated by the surface area of the kitchen pot. The hot pot testing confirmed that radiation was being received that temporally tracked with the changes in the temperature controls of the hot plate.
While other sources of EM radiation could not be completely ruled out, testing in an anechoic chamber substantially eliminated external, man-made, EM radiation as a possible source. The experimental testing showed that 26.3 GHz EM radiation with powers levels around -20 dBm was received and rectified inside the anechoic chamber during the testing. Through the process of the elimination of the alternatives this fact indicates that the measured EM radiation may be Planck radiation. The ambient EM radiation inside of the anechoic chamber was successfully rectified using the V4 rectifier.
169
6.5 EXPERIMENT INCONSISTENCIES
Much of this dissertation research was spent resolving lab experiment inconsistencies and anomalies. Thomas Edison famously stated in his authorized biography that he discovered the successful incandescent light bulb after a thousand failed experiments [52].
The actual statement was:
“Walter S. Mallory said: 'Isn't it a shame that with the tremendous
amount of work you have done you haven't been able to get any results?'
Edison turned on me like a flash, and with a smile replied: 'Results! Why,
man, I have gotten lots of results! I know several thousand things that
won't work!'".
This dissertation research helped reinforce the observation that research discovery is paved with successful, “failed” experiments.
6.5.1 Equipment and Fabrication Limits
Planck’s equation suggests that there is enough power for rectification with currently available Schottky diodes. While heat radiation spans from microwave to visible light wave lengths, the 20 to 100 GHz range looks most promising for energy harvesting with current commercial technology. Diode technology used in rectification becomes quite small as the frequencies rise. This complicates microstrip PCB assembly pushing the capabilities of the leading fabricator used in this research. Measurement and testing equipment also become increasingly expensive as the frequencies rise. Equipment 170 limitations guided the research to “easier” solutions that over time proved to be fruitless.
While aggregation of power did not materialize as expected in several of the rectifier versions, its potential impact had to be included in the circuit designs. A power sensor on one meter was burned out when connected to antennas, and another meter inserted automatic attenuation in two 5 dB increments above a fixed attenuator of 30 dB.
Consequently, microstrip filters in the rectifier were deemed necessary to limit the potential voltages. The filtering led to many simulation iterations that pushed the fabrication limits in line widths. When the power measurements distinctly identified the average and peak power levels as separated by +25 dB, it became obvious that the ambient radiation was not sinusoidal. This insight led to further design simplification of the rectifying circuits.
6.5.2 Measurement Inconsistencies
The FieldFox meter has two power measurement tools that presented a difference in power magnitudes of +15 dB. The meter also reported power around 0 Hz. While this 0
Hz was undoubtedly a mathematical artifact in hindsight, the time domain sampling was real. The Fast Fourier Transform is well proven, and the 0 Hz prediction suggests that there is lower frequency content in the time domain samples. The engineering of the energy harvesting solution was complicated by these measurement inconsistencies, while at the same time the power potential was reinforced.
Between the periods using the LadyBug and the FieldFox meters, the Agilent N1911A power meter was acquired and used to measure the “thermal noise” power being emitted 171 from the laboratory wall. The testing circuit did not include the 30 dB attenuator between the antennas and the meter. The power sensor for the meter was not protected from the potential of excessive power as a result. The automated program, using LABVIEW, stepped through the 10 kHz to 40 GHz frequency span taking power measurements.
While the LABVIEW program could have had errors, the manual operation of the measurements validated the automated measurements. The measurements yielded a flat line of power measurements across the frequency range, as can be seen in Figure 6.35.
This anomaly occurred equally when the meter was connected and disconnected from the WR-340 waveguide. This suggests that the power sensor for the meter was damaged by the power received. The meter that was “damaged” has a maximum limit for input signal power of +23 dBm. A frequency span of 40 GHz has 8000 (+39 dB) segments of 5
MHz. If the power in a segment of 5 MHz exceeded -16 dBm, then the +39 dB of segments would have yielded enough power to damage the power sensor (-16 dBm + 39 dB = + 23 dBm). The only frequency range subsequently identified by the FieldFox meter with power greater than +0 dBm was the phantom 0 Hz spike. The only other possible source of +23 dBm plus power was the potential of serial aggregation of voltage (power) sources.
The possibility that the aggregate power “fried” the power sensor for a $9,000 meter engendered significant caution and analysis in subsequent design activities during this dissertation research. Perversely, it did offer encouragement that there was significant power that could be harvested. 172
Figure 6.35: Power Measurements Using the Agilent N1911A Power Meter
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6.5.3 Aggregation: The Missing Power
How to model the power spectrum was a key engineering unknown throughout the dissertation research. Prevailing theory and practice treat thermal noise as voltage sources in series. When modeled as multiple, frequency-dependent, voltage sources in series, the potential for over voltage conditions were substantial. To avoid burn-outs diode selection was driven to higher barrier diodes with higher breakdown voltages and to filtering that limited aggregate frequency spans. The absence of impedance matching within the rectifier circuit reduced the power entering the diodes. When the engineering along the serial line did not generate the possible DC voltages, it spawned a different line of thinking. Maybe each segment of resolution bandwidth needed to clear the voltage thresholds of the diodes used in the rectifier. The result was the use of low barrier, detector diodes with low breakdown voltages. 174
7 CONCLUSIONS AND NEXT STEPS
7.1 SUMMARY
The hypothesis of this dissertation research was that energy from heat radiation could be directly harvested to produce electricity. A simple engineering design was formulated modelling after traditional communication systems where a transmitter sends electromagnetic waves through free space to a receiver. The electromagnetic waves of heat radiation transfer energy in the microwave and infrared frequencies. For an electric generator using heat radiation, the transmitter is a material surface such as a wall, and the receiver is a rectenna tuned to microwave frequencies.
Physics and electrical engineering theories left questions regarding the magnitude of heat energy generated by a material surface. Well known equations predicted disparate power densities being emitted from a material surface at ambient temperatures. To engineer a rectifier design, multiple power meters were used to measure the power being received through various antennas. As can be expected, the multiple power meters introduced additional variants and data differences regarding the potential power magnitude that might enter a rectifier.
The power measurements and theory indicated that large amounts of power should be available for harvesting. Since heat radiation is emitted across a broad range of frequencies, representing its behavior using circuit theory became a core engineering design question. Prevailing theory represents “thermal noise” power as a Thevenin 175 equivalent voltage (power) source. Measurements showed the power magnitude for a resolution bandwidth (RBW). Since “thermal noise” spans microwave through light frequencies, there are multiple measurement RBW’s within a frequency span of hundreds of GHz. The basic dilemma was: Are the voltage (power) sources that are frequency dependent best represented as circuit elements in series or in some other way? Most of engineering thought supports an “in series” view. If one chose the “in series” view, the rectifier design had to protect against excess power from large frequency spans burning out the electronic components. The absence of aggregated power in some of the rectifier measurements for unknown reasons challenged the “in series” view while at the same time plausible alternatives could explain the absence of the expected aggregation.
Given the uncertainty, the design of the rectifiers had to be flexible enough to support multiple possibilities. Multiple rectifiers were designed and fabricated using different
Schottky diodes and techniques to limit the aggregate bandwidth into a rectifier. Since excess power could have damaged the diodes in the rectifier, this was a continuing design consideration.
After four versions of rectifiers, a fifth rectifier using low-barrier detector diodes successfully harvested electricity, albeit a small 7 mV peak. Unfortunately, photons entering an antenna do not come labelled as “thermal radiation noise,” “experiment contamination,” or “ambient RF.” Fortunately, the antenna and rectifier system under test consisted of completely passive components, and the potential sources for the EM radiation were high quality laboratory instruments. This makes “experiment 176 contamination” a less likely source. “Ambient RF” is always a possibility when antennas are used. The WR-187 waveguides used as antennas have high frequency cutoffs that reject RF signals below 3.0 to 3.7 GHz. The patch antennas designed for 75 GHz also reject
EM signals below 75 GHz further eliminating manmade radiation. The Schottky diodes used in the rectifier inherently attenuate RF below 5 GHz by 5 to 12 dB. The Reno area has limited RF above 5 GHz, and path losses are substantial at these frequencies and above. Most manmade radiation propagates horizontally to the earth’s surface. Pointing the highly directive waveguides vertically greatly reduces the reception of manmade radiation. Most manmade radiation is sinusoidal with predictable peaks that are 1.5 dB greater than the average powers. The radiation being harvested shows peaks that are
+25 dB greater than the average powers. The harvested energy that was measured across multiple power meters might be “thermal noise” radiation. The experiments in the anechoic chamber at UNR further reinforced the view that the harvested power was potentially “thermal noise.”
7.2 NEXT STEPS
Two steps are natural in the further improvements in harvesting ambient radiation in pursuit of heat radiation:
1. Create An Improved Quad Rectangular Patch Rectenna. Combine the success in impedance matching from the V2R1 Rectenna with the greater bandwidth results from the V1R0 Rectenna. Implement the quad rectangular patch antenna from the V1R0 Rectenna using Rogers 4003 60 mil laminate. 177
2. Scale through An Array of Rectennas. Create an array of rectennas from step 1. Scale to create a power source with an output voltage in the range of 1 to 3 V.
7.2.1 Step 1: Create an Improved Quad Rectangular Patch Rectenna
The three rectennas fabricated during this dissertation use quad antenna arrays to achieve increasing antenna gains at the expense of antenna bandwidths. A simple patch antenna can achieve gains of +9 dB or so and bandwidths around 3% of the operating frequency. The quad array of patch antennas raised the antenna gains to +15 dB, an improvement of +6 dB over single patch antennas. The rectangular patch antenna used in the V1R0 Rectenna captured a single polarity. The square patch antenna with a corner feed sought to capture dual polarities. The bandwidth dropped even though the simulations indicated comparable performance between the rectangular and square antennas. The bandwidths that were harvested dropped from +25 dB for the WR-187, to
+19.2 dB for V1R0 Rectenna, and finally to +13.6 dB for the V2R1 Rectenna. While seeking the dual polarity gains of +3 dB with the square patch, the bandwidth aggregation dropped by 6 dB. By moving the V1R0 design to 60 mil laminate the bandwidth should increase from the V1R0 results. At 75 GHz 3% bandwidths using the laminate with 60 mil translates to a bandwidth gain of + 26.5 dB.
7.2.2 Step 2: Scale through An Array of Rectangular Patch Rectennas
Each quad antenna and rectifier represent a cell comparable to a battery cell. By connecting multiple cells in series higher voltages can be created. The next iteration of rectenna with dimensions of (3” x 1”) should include multiple cells. The capacitance 178 blocking and three diode design from the V2R1 Rectenna should yield the higher voltages that the V2R1 Rectenna produced.
7.3 ADDITIONAL EXPERIMENTS TO FURTHER CONFIRM SOURCE AS HEAT RADIATION
The focus of the dissertation was to harvest ambient radiation that might be heat radiation through improvements in microstrip rectennas to achieve even greater power generation. While the experiments to date indicate that heat radiation may be the source of the ambient power being harvested, it also has not confirmed it. Non-radiative sources of electricity, such as static electricity, are possible although measurements show large variations (+25 dB) in the measured voltages that are more characteristic of noise than static buildup. The power computations using radiometry techniques and the kTB formula also suggest that the expected power magnitudes should be less than what has been measured with multiple lab instruments, multiple voltmeters, and multiple circuits.
Given the disparate predictions that traditional techniques have generated, the measurement and known factors technique was used for engineering rectenna improvements. While this technique has been productive for engineering, better predictive tools with more rigorous foundations in theory are needed. Additional experiments are also merited to better understand the phenomenon being measured.
Additional experiments of improved rectennas could include the measurement of the improved rectennas:
. Inside a metal box (a simple anechoic chamber), 179
. Inside a freezer (a colder anechoic chamber),
. Encased in plexiglass (an electrically insulated environment),
. Immersed in water (an electrically isolated environment), and
. Cooled by dry ice (an even colder environment).
Given that power transfer via radiation requires differentials in temperature, testing in thermally stable and isolated environments might be productive. Without the serendipitous thermal and electrical grounding inside the anechoic chamber, the chamber test might have failed to generate electricity. Finding a way to interrupt the generation of electricity by the rectennas might help to better understand the underlying science that drives it.
7.4 CONCLUSIONS
The Planck’s Law was used as the foundation to predict magnitudes of potential power from heat radiation. Its utility over the kTB methodology was in large measure validated by this dissertation research. The theoretical predictions suggest that there is power available for energy harvesting. Future circuits are anticipated to scale the power magnitudes harvested and to better resolve the differences in expected versus actual power. This dissertation research confirmed the feasibility of harvesting ambient radiation that looks like heat radiation. 180
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