RF Basics - Part 1
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Radiometry and the Friis Transmission Equation Joseph A
Radiometry and the Friis transmission equation Joseph A. Shaw Citation: Am. J. Phys. 81, 33 (2013); doi: 10.1119/1.4755780 View online: http://dx.doi.org/10.1119/1.4755780 View Table of Contents: http://ajp.aapt.org/resource/1/AJPIAS/v81/i1 Published by the American Association of Physics Teachers Related Articles The reciprocal relation of mutual inductance in a coupled circuit system Am. J. Phys. 80, 840 (2012) Teaching solar cell I-V characteristics using SPICE Am. J. Phys. 79, 1232 (2011) A digital oscilloscope setup for the measurement of a transistor’s characteristic curves Am. J. Phys. 78, 1425 (2010) A low cost, modular, and physiologically inspired electronic neuron Am. J. Phys. 78, 1297 (2010) Spreadsheet lock-in amplifier Am. J. Phys. 78, 1227 (2010) Additional information on Am. J. Phys. Journal Homepage: http://ajp.aapt.org/ Journal Information: http://ajp.aapt.org/about/about_the_journal Top downloads: http://ajp.aapt.org/most_downloaded Information for Authors: http://ajp.dickinson.edu/Contributors/contGenInfo.html Downloaded 07 Jan 2013 to 153.90.120.11. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission Radiometry and the Friis transmission equation Joseph A. Shaw Department of Electrical & Computer Engineering, Montana State University, Bozeman, Montana 59717 (Received 1 July 2011; accepted 13 September 2012) To more effectively tailor courses involving antennas, wireless communications, optics, and applied electromagnetics to a mixed audience of engineering and physics students, the Friis transmission equation—which quantifies the power received in a free-space communication link—is developed from principles of optical radiometry and scalar diffraction. -
25. Antennas II
25. Antennas II Radiation patterns Beyond the Hertzian dipole - superposition Directivity and antenna gain More complicated antennas Impedance matching Reminder: Hertzian dipole The Hertzian dipole is a linear d << antenna which is much shorter than the free-space wavelength: V(t) Far field: jk0 r j t 00Id e ˆ Er,, t j sin 4 r Radiation resistance: 2 d 2 RZ rad 3 0 2 where Z 000 377 is the impedance of free space. R Radiation efficiency: rad (typically is small because d << ) RRrad Ohmic Radiation patterns Antennas do not radiate power equally in all directions. For a linear dipole, no power is radiated along the antenna’s axis ( = 0). 222 2 I 00Idsin 0 ˆ 330 30 Sr, 22 32 cr 0 300 60 We’ve seen this picture before… 270 90 Such polar plots of far-field power vs. angle 240 120 210 150 are known as ‘radiation patterns’. 180 Note that this picture is only a 2D slice of a 3D pattern. E-plane pattern: the 2D slice displaying the plane which contains the electric field vectors. H-plane pattern: the 2D slice displaying the plane which contains the magnetic field vectors. Radiation patterns – Hertzian dipole z y E-plane radiation pattern y x 3D cutaway view H-plane radiation pattern Beyond the Hertzian dipole: longer antennas All of the results we’ve derived so far apply only in the situation where the antenna is short, i.e., d << . That assumption allowed us to say that the current in the antenna was independent of position along the antenna, depending only on time: I(t) = I0 cos(t) no z dependence! For longer antennas, this is no longer true. -
Design and Application of a New Planar Balun
DESIGN AND APPLICATION OF A NEW PLANAR BALUN Younes Mohamed Thesis Prepared for the Degree of MASTER OF SCIENCE UNIVERSITY OF NORTH TEXAS May 2014 APPROVED: Shengli Fu, Major Professor and Interim Chair of the Department of Electrical Engineering Hualiang Zhang, Co-Major Professor Hyoung Soo Kim, Committee Member Costas Tsatsoulis, Dean of the College of Engineering Mark Wardell, Dean of the Toulouse Graduate School Mohamed, Younes. Design and Application of a New Planar Balun. Master of Science (Electrical Engineering), May 2014, 41 pp., 2 tables, 29 figures, references, 21 titles. The baluns are the key components in balanced circuits such balanced mixers, frequency multipliers, push–pull amplifiers, and antennas. Most of these applications have become more integrated which demands the baluns to be in compact size and low cost. In this thesis, a new approach about the design of planar balun is presented where the 4-port symmetrical network with one port terminated by open circuit is first analyzed by using even- and odd-mode excitations. With full design equations, the proposed balun presents perfect balanced output and good input matching and the measurement results make a good agreement with the simulations. Second, Yagi-Uda antenna is also introduced as an entry to fully understand the quasi-Yagi antenna. Both of the antennas have the same design requirements and present the radiation properties. The arrangement of the antenna’s elements and the end-fire radiation property of the antenna have been presented. Finally, the quasi-Yagi antenna is used as an application of the balun where the proposed balun is employed to feed a quasi-Yagi antenna. -
ECE 255, MOSFET Basic Configurations
ECE 255, MOSFET Basic Configurations 8 March 2018 In this lecture, we will go back to Section 7.3, and the basic configurations of MOSFET amplifiers will be studied similar to that of BJT. Previously, it has been shown that with the transistor DC biased at the appropriate point (Q point or operating point), linear relations can be derived between the small voltage signal and current signal. We will continue this analysis with MOSFETs, starting with the common-source amplifier. 1 Common-Source (CS) Amplifier The common-source (CS) amplifier for MOSFET is the analogue of the common- emitter amplifier for BJT. Its popularity arises from its high gain, and that by cascading a number of them, larger amplification of the signal can be achieved. 1.1 Chararacteristic Parameters of the CS Amplifier Figure 1(a) shows the small-signal model for the common-source amplifier. Here, RD is considered part of the amplifier and is the resistance that one measures between the drain and the ground. The small-signal model can be replaced by its hybrid-π model as shown in Figure 1(b). Then the current induced in the output port is i = −gmvgs as indicated by the current source. Thus vo = −gmvgsRD (1.1) By inspection, one sees that Rin = 1; vi = vsig; vgs = vi (1.2) Thus the open-circuit voltage gain is vo Avo = = −gmRD (1.3) vi Printed on March 14, 2018 at 10 : 48: W.C. Chew and S.K. Gupta. 1 One can replace a linear circuit driven by a source by its Th´evenin equivalence. -
INA106: Precision Gain = 10 Differential Amplifier Datasheet
INA106 IN A1 06 IN A106 SBOS152A – AUGUST 1987 – REVISED OCTOBER 2003 Precision Gain = 10 DIFFERENTIAL AMPLIFIER FEATURES APPLICATIONS ● ACCURATE GAIN: ±0.025% max ● G = 10 DIFFERENTIAL AMPLIFIER ● HIGH COMMON-MODE REJECTION: 86dB min ● G = +10 AMPLIFIER ● NONLINEARITY: 0.001% max ● G = –10 AMPLIFIER ● EASY TO USE ● G = +11 AMPLIFIER ● PLASTIC 8-PIN DIP, SO-8 SOIC ● INSTRUMENTATION AMPLIFIER PACKAGES DESCRIPTION R1 R2 10kΩ 100kΩ 2 5 The INA106 is a monolithic Gain = 10 differential amplifier –In Sense consisting of a precision op amp and on-chip metal film 7 resistors. The resistors are laser trimmed for accurate gain V+ and high common-mode rejection. Excellent TCR tracking 6 of the resistors maintains gain accuracy and common-mode Output rejection over temperature. 4 V– The differential amplifier is the foundation of many com- R3 R4 10kΩ 100kΩ monly used circuits. The INA106 provides this precision 3 1 circuit function without using an expensive resistor network. +In Reference The INA106 is available in 8-pin plastic DIP and SO-8 surface-mount packages. Please be aware that an important notice concerning availability, standard warranty, and use in critical applications of Texas Instruments semiconductor products and disclaimers thereto appears at the end of this data sheet. All trademarks are the property of their respective owners. PRODUCTION DATA information is current as of publication date. Copyright © 1987-2003, Texas Instruments Incorporated Products conform to specifications per the terms of Texas Instruments standard warranty. Production processing does not necessarily include testing of all parameters. www.ti.com SPECIFICATIONS ELECTRICAL ° ± At +25 C, VS = 15V, unless otherwise specified. -
Transistor Basics
Transistor Basics: Collector The schematic representation of a transistor is shown to the left. Note the arrow pointing down towards the emitter. This signifies it's an NPN transistor (current flows in the direction of the arrow). See the Q1 datasheet at: www.fairchildsemi.com. Base 2N3904 A transistor is basically a current amplifier. Say we let 1mA flow into the base. We may get 100mA flowing into the collector. Note: The Emitter currents flowing into the base and collector exit through the emitter (the sum off all currents entering or leaving a node must equal zero). The gain of the transistor will be listed in the datasheet as either βDC or Hfe. The gain won't be identical even in transistors with the same part number. The gain also varies with the collector current and temperature. Because of this we will add a safety margin to all our base current calculations (i.e. if we think we need 2mA to turn on the switch we'll use 4mA just to make sure). Sample circuit and calculations (NPN transistor): Let's say we want to heat a block of metal. One way to do that is to connect a power resistor to the block and run current through the resistor. The resistor heats up and transfers some of the heat to the block of metal. We will use a transistor as a switch to control when the resistor is heating up and when it's cooling off (i.e. no current flowing in the resistor). In the circuit below R1 is the power resistor that is connected to the object to be heated. -
S-Parameter Techniques – HP Application Note 95-1
H Test & Measurement Application Note 95-1 S-Parameter Techniques Contents 1. Foreword and Introduction 2. Two-Port Network Theory 3. Using S-Parameters 4. Network Calculations with Scattering Parameters 5. Amplifier Design using Scattering Parameters 6. Measurement of S-Parameters 7. Narrow-Band Amplifier Design 8. Broadband Amplifier Design 9. Stability Considerations and the Design of Reflection Amplifiers and Oscillators Appendix A. Additional Reading on S-Parameters Appendix B. Scattering Parameter Relationships Appendix C. The Software Revolution Relevant Products, Education and Information Contacting Hewlett-Packard © Copyright Hewlett-Packard Company, 1997. 3000 Hanover Street, Palo Alto California, USA. H Test & Measurement Application Note 95-1 S-Parameter Techniques Foreword HEWLETT-PACKARD JOURNAL This application note is based on an article written for the February 1967 issue of the Hewlett-Packard Journal, yet its content remains important today. S-parameters are an Cover: A NEW MICROWAVE INSTRUMENT SWEEP essential part of high-frequency design, though much else MEASURES GAIN, PHASE IMPEDANCE WITH SCOPE OR METER READOUT; page 2 See Also:THE MICROWAVE ANALYZER IN THE has changed during the past 30 years. During that time, FUTURE; page 11 S-PARAMETERS THEORY AND HP has continuously forged ahead to help create today's APPLICATIONS; page 13 leading test and measurement environment. We continuously apply our capabilities in measurement, communication, and computation to produce innovations that help you to improve your business results. In wireless communications, for example, we estimate that 85 percent of the world’s GSM (Groupe Speciale Mobile) telephones are tested with HP instruments. Our accomplishments 30 years hence may exceed our boldest conjectures. -
Fully-Differential Amplifiers
Application Report S Fully-Differential Amplifiers James Karki AAP Precision Analog ABSTRACT Differential signaling has been commonly used in audio, data transmission, and telephone systems for many years because of its inherent resistance to external noise sources. Today, differential signaling is becoming popular in high-speed data acquisition, where the ADC’s inputs are differential and a differential amplifier is needed to properly drive them. Two other advantages of differential signaling are reduced even-order harmonics and increased dynamic range. This report focuses on integrated, fully-differential amplifiers, their inherent advantages, and their proper use. It is presented in three parts: 1) Fully-differential amplifier architecture and the similarities and differences from standard operational amplifiers, their voltage definitions, and basic signal conditioning circuits; 2) Circuit analysis (including noise analysis), provides a deeper understanding of circuit operation, enabling the designer to go beyond the basics; 3) Various application circuits for interfacing to differential ADC inputs, antialias filtering, and driving transmission lines. Contents 1 Introduction . 3 2 What Is an Integrated, Fully-Differential Amplifier? . 3 3 Voltage Definitions . 5 4 Increased Noise Immunity . 5 5 Increased Output Voltage Swing . 6 6 Reduced Even-Order Harmonic Distortion . 6 7 Basic Circuits . 6 8 Circuit Analysis and Block Diagram . 8 9 Noise Analysis . 13 10 Application Circuits . 15 11 Terminating the Input Source . 15 12 Active Antialias Filtering . 20 13 VOCM and ADC Reference and Input Common-Mode Voltages . 23 14 Power Supply Bypass . 25 15 Layout Considerations . 25 16 Using Positive Feedback to Provide Active Termination . 25 17 Conclusion . 27 1 SLOA054E List of Figures 1 Integrated Fully-Differential Amplifier vs Standard Operational Amplifier. -
MOS Amplifier Basics
ECE 2C Laboratory Manual 2 MOS Amplifier Basics Overview This lab will explore the design and operation of basic single-transistor MOS amplifiers at mid-band. We will explore the common-source and common-gate configurations, as well as a CS amplifier with an active load and biasing. Table of Contents Pre-lab Preparation 2 Before Coming to the Lab 2 Parts List 2 Background Information 3 Small-Signal Amplifier Design and Biasing 3 MOSFET Design Parameters and Subthreshold Currents 5 Estimating Key Device Parameters 7 In-Lab Procedure 8 2.1 Common-Source Amplifier 8 Common-Source, no Source Resistor 8 Linearity and Waveform Distortion 8 Effect of Source and Load Impedances 9 Common-Source with Source Resistor 9 2.2 Common-Gate Amplifier 10 2.3 Amplifiers with Active Loading 11 Feedback-Bias Amplifier 11 CMOS Active-Load CS Amplifier 12 1 © Bob York 2 MOS Amplifier Basics Pre-lab Preparation Before Coming to the Lab Read through the lab experiment to familiarize yourself with the components and assembly sequence. Before coming to the lab, each group should obtain a parts kit from the ECE Shop. Parts List The ECE2 lab is stocked with resistors so do not be alarmed if you kits does not include the resistors listed below. Some of these parts may also have been provided in an earlier kit. Laboratory #2 MOS Amplifiers Qty Description 2 CD4007 CMOS pair/inverter 4 2N7000 NMOS 4 1uF capacitor (electrolytic, 25V, radial) 8 10uF capacitor (electrolytic, 25V, radial) 4 100uF capacitor (electrolytic, 25V, radial) 4 100-Ohm 1/4 Watt resistor 4 220-Ohm 1/4 Watt resistor 1 470-Ohm 1/4 Watt resistor 4 10-KOhm 1/4 Watt resistor 1 33-KOhm 1/4 Watt resistor 2 47-KOhm 1/4 Watt resistor 1 68-KOhm 1/4 Watt resistor 4 100-KOhm 1/4 Watt resistor 1 1-MOhm 1/4 Watt resistor 1 10k trimpot 2 100k trimpot © Bob York Background Information 3 Background Information Small-Signal Amplifier Design and Biasing In earlier experiments with transistors we learned how to establish a desired DC operating condition. -
ANTENNA INTRODUCTION / BASICS Rules of Thumb
ANTENNA INTRODUCTION / BASICS Rules of Thumb: 1. The Gain of an antenna with losses is given by: Where BW are the elev & az another is: 2 and N 4B0A 0 ' Efficiency beamwidths in degrees. G • Where For approximating an antenna pattern with: 2 A ' Physical aperture area ' X 0 8 G (1) A rectangle; X'41253,0 '0.7 ' BW BW typical 8 wavelength N 2 ' ' (2) An ellipsoid; X 52525,0typical 0.55 2. Gain of rectangular X-Band Aperture G = 1.4 LW Where: Length (L) and Width (W) are in cm 3. Gain of Circular X-Band Aperture 3 dB Beamwidth G = d20 Where: d = antenna diameter in cm 0 = aperture efficiency .5 power 4. Gain of an isotropic antenna radiating in a uniform spherical pattern is one (0 dB). .707 voltage 5. Antenna with a 20 degree beamwidth has a 20 dB gain. 6. 3 dB beamwidth is approximately equal to the angle from the peak of the power to Peak power Antenna the first null (see figure at right). to first null Radiation Pattern 708 7. Parabolic Antenna Beamwidth: BW ' d Where: BW = antenna beamwidth; 8 = wavelength; d = antenna diameter. The antenna equations which follow relate to Figure 1 as a typical antenna. In Figure 1, BWN is the azimuth beamwidth and BW2 is the elevation beamwidth. Beamwidth is normally measured at the half-power or -3 dB point of the main lobe unless otherwise specified. See Glossary. The gain or directivity of an antenna is the ratio of the radiation BWN BW2 intensity in a given direction to the radiation intensity averaged over Azimuth and Elevation Beamwidths all directions. -
Radiation Pattern, Gain, and Directivity James Mclean, Robert Sutton, Rob Hoffman, TDK RF Solutions
Interpreting Antenna Performance Parameters for EMC Applications: Part 2: Radiation Pattern, Gain, and Directivity James McLean, Robert Sutton, Rob Hoffman, TDK RF Solutions This article is the second in a three-part tutorial series covering antenna terminology. As noted in the first part, a great deal of effort has been made over the years to standardize antenna terminology. The de facto standard is the IEEE Standard Definitions of Terms for Antennas, published in 1983. However, the EMC community has developed its own distinct vernacular which contains terms not included in the IEEE standard. In the first part of this series, we discussed radiation efficiency and input impedance match. In the second part of this series, we will discuss antenna field regions and antenna gain and how they relate to EMC measurements. Geometrical Considerations In order to quantitatively discuss radiation from antennas, it is necessary to first specify a coordinate system for describing the antenna and the associated electromagnetic fields. The most natural coordinate system for this task is the spherical coordinate system. This is because at a sufficient distance from an antenna (or any localized source of electromagnetic radiation), the electromagnetic fields must decay inversely with radial distance from the antenna (see references 1 and 2). Traditional spherical coordinates consist of a radial distance, an elevation angle, and an azimuthal angle as shown in Figure 1. The elevation angle is taken as the angle between a line drawn from the origin to the point and the z axis. The azimuthal angle is taken as the angle between the projection of this line in the x-y plane and the x axis. -
Fully Differential Op Amps Made Easy
Application Report SLOA099 - May 2002 Fully Differential Op Amps Made Easy Bruce Carter High Performance Linear ABSTRACT Fully differential op amps may be unfamiliar to some designers. This application report gives designers the essential information to get a fully differential design up and running. Contents 1 Introduction . 2 2 What Does Fully Differential Mean?. 2 3 How Is the Second Output Used?. 3 3.1 Differential Gain Stages. 3 3.2 Single-Ended to Differential Conversion. 4 3.3 Working With Terminated Inputs. 5 4 A New Function . 7 5 Conclusions . 8 6 References . 9 List of Figures 1 Single-Ended Op Amp Schematic Symbol. 2 2 Fully Differential Op Amp Schematic Symbol. 2 3 Closing the Loop on a Single-Ended Op Amp. 3 4 Closing the Loop on a Fully Differential Op Amp. 3 5 Single Ended to Differential Conversion. 4 6 Relationship Between Vin, Vout+, and Vout– . 5 7 Fully Differential Amplifier Component Calculator. 6 8 Using a Fully Differential Op Amp to Drive an ADC. 7 9 Effect of Vocm on Vout+ and Vout– . 8 1 SLOA099 1 Introduction Fully differential op amps may be intimidating to some designers, But op amps began as fully differential components over 50 years ago. Techniques about how to use the fully differential versions have been almost lost over the decades. However, today’s fully differential op amps offer performance advantages unheard of in those first units. This report does not attempt a detailed analysis of op amp theory; reference 1 covers theory well. Instead, this report presents just the facts a designer needs to get started, and some resources for further design assistance.