EEE161 Applied Electromagnetics Practical Laboratory

Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 1

Instructor: Dr. Milica Markovi´c Oﬃce: Riverside Hall 3028 Email: [email protected] Web:http://gaia.ecs.csus.edu/˜milica

California State University Sacramento EEE161 revised: 15. December, 2010 Chapter 1

Power Measurements at Microwave Frequencies

In this lab we will be learning about power measurements at high frequencies. Lohimw-frequency techniques for power measurement involve measuring current and voltage and calculating power from these basic measurements. at I and RF frequencies both voltage and current and power measurements are done. However at microwave frequencies power measurements are almost exclusively done. The methods that will be shown here are based on direct measurement of power, as it is diﬃcult to measure directly voltages and currents at high frequencies. Diﬃculties arise from:

1. voltages are not uniquely deﬁned and would depend on the length and position of measurement leads. In addition, at microwave frequencies the equipment that is used to measure voltages and currents is of the size of the wavelength. The loop that is used to ﬁnd the voltage will have a physical size that is comparable to the wavelength. The voltage will therefore vary along the loop and the accurate voltage measurement is not possible.

2. In rectangular waveguide curl of the fake out to magnetic field vector does not vanish anywhere across the waveguide, and volequal to the integral between two points. You cannot define the characteristic impedance of a rectangular waveguide. ( You can still define the wave impedance but this is not the same thing as the transmission line impedance).

3. The voltage and current definition in transmission line is meaningless without specificiation of the transmission line impedance. Power definition on the other hand (if the transmission line is terminated in a matched load) is not dependent on the tranmission line impedance).

Microwave power is often pulsed and we distinguish between average power and pulsed power. Both quantities are averaged, and the diﬀerence is the time quantities are averaged over. The power that is averaged over a single pulse is called a pulsed power. The power that is averaged over a long period of time compared to the duration of one period or pulse period is called an average power. Finally there are peak power instruments that allow measurements of peak power modulation envelopes. These instruments are used in radars, navigation systems, and modern wireless communication signals such as TDMA or CDMA signals.

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1.1 Power Units

The units for power is a Watt (W), but we will often use a the decibel (DB), deﬁned as

PW PdB = 10log (1.1) Pref

Where PW is the power we are measuring, and Pref is some known reference power level. At microwave frequencies, very often this reference power level is 1 mW, and in this case the unit is a dBm:

P P = 10log W (1.2) dBm 1mW dBs are convenient for two reasons: they are easier to write for a large span of values (for example the range between 100 dB to -100 DB corresponds to 105 to 10−5, and adding dBs, corresponds to multiplying power (because of properties of logarithms)/ This is useful in cascaded systems with for example, several stages of ampliﬁers. For each ampliﬁer stage, the overall gain is equal to the sum of individual gains in DB.

1.2 Power Measurmenent

At microwave frequencies there are several ways to measure power. they are converting my current power to heat, which aﬀects resistance of an element, for example a thermocouple and a bolometer. Two most important bolometers are the barretter and the thermistor. Another way to measure microwave power is to convert the microwave power into a DC signal or low-frequency signal using diode detectors (also called crystal detectors).

1.2.1 Bolometers: Thermistors and Barreters The barretter is a short wire mounting on terminals of the transmission line. Barretters have positive thermal coefficient on the resistance, which is typical of metals. The barretters are very fragile and easily burn out. The equivalent circuit of a baretter is a parallel RL circuit in series with a voltage source (DC and AC source if there is bias and RF power). The thermistor consists of a semiconductor bead installed in a small glass capsule. The equivalent circuit of a thermistor is a series RC circuit and a voltage source. Thermistor have negative thermal coefficient of the resistance, typically -5%/C. Thermistors are more rugged than barretters. Barretters and thermistors are very sensitive power detectors and can detect few microwatts of power. The microwave power in bolometer’s is used by placing a bolometer as one arm of a Wheatstone bridge. Initially Wheatstone bridge is in balance. When the microwave power is applied, the resistance of that branch will change. Instead of changing the resistance of that branch the bridge will adjust its self bias to a different bias point effectively showing the RF power applied.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 4

Figure 1.1: Thermistor bead enclosed in glass. From MIT RadLab Series: Technique of Microwave Measurements, Vol. 11

Figure 1.2: Cross-section of a thermistor bead waveguide mount. From HP Journal, July 1954, Vol 5, No 11

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 5

Figure 1.3: Thermistor resistance vs. RF power incident on thermistor. From MIT RadLab Series: Technique of Microwave Measurements, Vol. 11

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 6

1.2.2 Measuring Microwave Power Using Bolometers - Wheatstone Bridge Several different bridge circuits have been used to measure microwave power. A simple circuit using a Wheatstone bridge is shown in Figure 1.4. Wheatstone bridge is used to measure unknown impedances. Two resistors R1 and R2 in the bridge circuit are set to a constant value. Unknown resistance is labeled as Rt in Figure 1.4 has the same value as R3 when R3 is adjusted so that the current through the ammeter in the bridge is equal to zero. When the current through the ammeter is zero, the current that flows through the resistor R1 is equal to the current that flows through the resistor R3 and the current on the right side of the bridge through the resistor R2 is equal to the current that flows through the resistor Rt. When there’s no current through the ammeter, the points a and b on the Wheatstone bridge are on the same potential, therefore R3i3 = itRt and R1i1 = R2i2. R3 Rt Finally by using the above equations we can see that ratio of the resistors is = . If resistors R1 R1 R2 and R2 are set to be equal, then R3 = Rt. In microwave measurements, resistor Rt is substituted by the thermistor mounted on a coaxial cable or a waveguide. In this lab, we will first find the resistance of the thermistor as a function of applied DC bias voltage on the bridge. When DC voltage source is applied to the Wheatstone bridge, thermistor is heated due to the DC current flowing through it. We will measure the resistance of the thermistor by adjusting the resistor R4 to apply different DC voltages on the bridge. For each applied voltage, we will measure thermistor’s resistance (by balancing the bridge) using resistor R3. when the bridge is balanced resisters are free and RTR the same. From this measurement we will calculate the value of the incident power on the thermistor. Using Matlab, we will plot thermistor’s resistance as a funciton of the applied DC bias, and therefore applied DC power. When RF power is applied, the resistance of thermistor RT will decrease and therefore the current through the ammeter will start flowing again because the resistance is RT and R3 are not equal anymore. to find out how much RF power has been applied to the thermistor, we will decrease the amount of DC power applied, for the amount of RF power applied, so that we see the balance in the bridge again. By calculating the difference between the DC power applied before and after RF power on the thermistor we can calculate the amount of RF power applied. The RF power is measured ”by substitution”, as it is assumed that the heating effect of the DC power is the same as the heating effect of an equivalent amount of RF power. This method is used in older HP power meters that we have in the lab (with additional sophisticated circuits) to accurately measure the RF power. In this lab we will measure both DC and RF properties of a thermistor mounted in an X-band waveguide. We will use manual bridge balancing, which was the way people originally measured microwave power. The main problem with this measurement is that the changes in ambient temperature will not be taken into account during power measurements. However, we will perform calibration of a thermistor to correct for frequency response, temperature effects, substitution errors from RF to DC and heating effects using an HP power meter.

1.3 HP Power Meter with Thermistor

HP power meter consists of the power meter and a power sensor, see Figure ??. The main parts of a power meter are RF Wheatstone bridge, temperature compensation Wheatstone bridge, Opamp, and analog circuitry for signal processing and zeroing. Two identical thermistors are used in Wheatstone

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 7

Bridge. HP power meter has ambient temperature compentsation, as shown in Figure 1.5. When there is no RF power, the gain of the op amp is set to such value to maintain the resistance of a thermistor at a certain value, for example 200 ohms. When RF power is applied to thermistor, its resistance decreases. Since the thermistor resistance is in the feedback branch of the opamp, the output voltage of the opamp will decrease, as the gain of the amplifier will decrease. This in turn will cause the voltage on the bridge to decrease to maintain the resistance of the thermistor to 200 ohms. This change in output op amp voltage represents the applied RF power on the thermistor. A power sensor’s block diagram, used with this power meter is shown in Figure 1.6. thermistors are represented with resistances RD and the incident power is applied through the coupling capacitor cc. The bias is applied to the bridge through RF bridge bias. If both thermistors are biased to 100 ohms, the RF power will see two resistors in parallel, and the equivalent load impedance for RF power will be equal to 50 ohms. On the other hand RF bridge bias will see 200 ohms impedance, because tourist sisters are connected in series looking from the bridge bias. No RF power will flow into the bridge bias, because of the capacitor CB, and no DC bias will flow into RF power circuit because of the coupling capacitor cc.

Figure 1.4: Manual Wheatstone bridge for measuring RF power using waveguide mounted thermistor.

1.3.1 Commercially Available Power Meters Power meters consist of two parts power meter, and the power sensor. 1. Power meters available in our lab employ either thermistor sensors which are HP models 430, 431 and 432. Power meters with thermocouples that were developed in early 1970s are HP 435, 436, 437, and 438. All of these power meters measure average power. There are also peak power meters, that are used to measure powers of the signals that have signiﬁcant peak to average ratios, such as modern communication signals. Power meter will capture all power whether it’s desirable power that we want to measure or noise power that has coupled into the system. 2. Power sensor (aka Power Head) contains the sensing element: thermistor or a diode, see Figure 1.7. Power sensor attached between the power meter and the device under test. In Agilent 478 a and 8478B thermistor sensors measure power from 10 MHz to 10 and 18 GHz respectively. A sensor circuit 447 a coaxial sensor is shown in Figure 1.7. You will be using HPXXXXX sweeper, HP 436 power meter with HP XXXX sensor for calibration and the waveguide mounted thermistor and a diode detector.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 8

Figure 1.5: Block-diagram of Agilent/HP power meter using thermistor sensor. From: Agilent Application Note 1449-2.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 9

Figure 1.6: Block-diagram of Agilent/HP thermistor power sensor. From: Agilent Application Note 1449-2.

1.3.2 Thermocouples 1.3.3 Diode Detectors Detectors that were used in the ﬁrst radios were diodes made of galena crystal (semiconductor) and cat’s whisker (thin piece of wire). These ﬁrst diodes were to slow to work at microwave frequencies. Later in 1970s people developed diodes that were fast enough to to be used at microwave frequencies these are low barrier Schottky diodes and planar-doped-barrier diodes. The major advantage of diodes over bolometers and thermocouples is that diodes have much wider dynamic range sometimes of the order of 90 dB, and diodes directly convert input power to output DC voltage, making them a lot faster than thermal sensors, and a lot more useful when measuring peak power. Diode detectors have three regions of operation: square law region, linear region, and the saturation region. The current through the diode is given by the following formula and graphically shown in Figure 1.12.

nvD V iD = Is e T − 1 (1.3)

Where vD = V + v is total voltage (V DC and v AC) on the diode, IS is the saturation current, n = 1.1 is the correction constant for power-sensing devices, and VT = 25 mV is the thermal voltage at room temperature. If we use the Taylor’s formula

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 10

Figure 1.7: Two power meters: Agilent/HP 430 (top left), Agilent/HP 435 and power heads: coaxial thermistor mount (sensor) HP 478A (top right) and diode mounts.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 11

Figure 1.8: Agilent/HP 436A power meter.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 12

Figure 1.9: Agilent/HP 438A power meter..

di 1 d2i i = I + v D + v2 D + ... (1.4) D 0 2 dvD vD=V 2 dvD vD=V The ﬁrst derivative and second derivative of the current at the DC bias point are

nvD di ne VT n 1 D = = (IS + I) = GD = (1.5) dvD vD=V VT VT RD nvD 2 2 V d i n e T n n 0 D = = (I + I) = G = G (1.6) 2 2 S D D dvD vD=V VT VT VT

Where I is the DC current through the diode, RD is the junction resitance of the diode and GD is dynamic conductance of teh diode. The total current is now:

1 0 i = I + G v + G v2 + ... (1.7) D D 2 D We see that the current through the diode has several terms. The ﬁrst term is linearly proportional to the voltage across the diode. The second term is proportional to the voltage squared, or linearly proportional to the power applied to the diode. For small-signals, only the ﬁrst two terms are

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 13

Figure 1.10: Agilent/HP 435 power meter using thermocouple.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 14

Figure 1.11: Block-diagram of Agilent/HP power meter and thermocouple sensor. From: Agilent Application Note 1449-2.

Figure 1.12: I-V curve of a diode.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Marković Applied Electromagnetics Laboratory page 15 significant. This is called a square-law region of diode operation. Average packaged diode works in this region from the noise floor to about -20dBm. When input voltage gets higher than this, diode enters transition region (until about 0dBm), and for very high input voltages (over 20dBm), saturation, aka linear region. In saturation output voltage is proportional to input voltage. This equation shows that the small-signal model of a diode is

Figure 1.13: Small-signal model of a diode.

If the voltage incident on the diode is sinusoidal, as it is usually in rectiﬁer applications, and we will use a sinusoidal signal for proof-of-concept detector measurements.

v = v0cosω0t (1.8) and if we use the Equation 1.7 the current through the diode will be of the form

1 0 i = I + G v cosω t + G (cosω t)2 (1.9) D D 0 0 2 D 0 2 2 v 0 v 0 i = I + 0 G + G v cosω t + 0 G cos2ω t (1.10) D 4 D D 0 0 4 D 0

were ω0 is the RF carrier frequency. The output DC current is proportional to the square of the magnitude of the input RF voltage, or proportional to the input RF power. To get the output current, and therefore voltage proportional to the input power, we have to remove sinusoidal components of the current by using a low-pass ﬁlter. This equation shows that the small-signal model of a diode is a resistance. In addition to this resistance there will be a small-signal capacitance that models junction capacitance.

California State University Sacramento EEE161 revised: 15. December, 2010 Chapter 2

Power Measurement Experiment

You will need the following equipment

1. Part I - DC power measurements with Thermistor Part Number Equipment Quantity None decade resistor boxes 5 XXXX DC Power Supply 1 XXXX Waveguide-mount Thermistor 1 XXXX Waveguide-mount Diode Detector 1 2. Part II RF power measurements with Thermistor Part Number Equipment Quantity None decade resistor boxes 5 XXXX DC Power Supply 1 XXXX Waveguide-mount Thermistor 1 XXXX Waveguide-mount Diode Detector 1 3. Part III RF power measurements with Diode Detector Part Number Equipment Quantity None decade resistor boxes 5 XXXX DC Power Supply 1 XXXX Waveguide-mount Thermistor 1 XXXX Waveguide-mount Diode Detector 1

2.1 DC Power Measurements with Thermistor

Objective: Calculate the DC power characteristics of the thermistor as a function of the voltage on the bridge. First you will measure the DC properties of the thermistor mounted in an X-band waveguide. You will do this using a manual bridge shown in Figure 2.1,

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Figure 2.1: Manual Wheatstone bridge for measuring RF power using waveguide mounted thermistor.

2.1.1 Question 1

Calculate the value of the resistor R3 if R1 = R2 = Rt = 200Ω so that the bridge is balanced.

2.1.2 Question 2 Calculate the DC power on the thermistor if the resistance of the thermistor is as the one above, the bridge is balanced, and you set the voltage on the bridge at 10V.

2.1.3 Measurement 1 There are two ways to achieve balance of the bridge:

1. One way is to change the resistance R3 until it matches the resistance of a termistor for a speciﬁed voltage on the bridge.

2. Instead adjusting R3 we can adjust the DC voltage on the bridge, eﬀectively changing the resistance of the thermistor until it becomes equal to R3.

Obtain the DC voltage vs. Thermistor resistance table and graph by doing the following measurements:

1. Set the resistance R3 = 1000Ω

2. Change the DC voltage on the bridge by adjusting R4 until the bridge is in balance

3. Note the value of the resistance R3 and the voltage on the bridge. From the voltage on the bridge, and resistance of the thermistor calculate the DC power incident on the thermistor. Write all and save in an excell ﬁle.

4. Set the resistance R3 = 900Ω. Continue with step 1, until you get to 100Ω. 5. Plot the resistance of the thermistor as a function of bridge’s voltage and resistance of the thermistor as a function of DC power.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 18

2.2 Measuring microwave power with thermistor

Objective: Compare the readings of the manual bridge with waveguide thermistor mount and HP Power Meter with XXX power head. Connect the circuit in Figure 2.2. The block diagram consists of an RF Generator, isolator, attenuator, waveguide magic-T, HP power meter with power sensor, waveguide thermistor mount and the manual bridge. Isolator is an circuit element that transmits RF power only in one direction, for example from port 1 to port 2. No power can be transmitted from port 2 to port 1. Isolator is used to protect high-power sources from RF power reﬂecting back from an open or short circuit to the input of the RF generator and destroying it. Attenuator attenuates the power presented at the input to a lower power at the output. Magic-T is a power-splitter that divides the power presented at one port to two ports. The fourth port has to be matched. This circuit will take the power from the RF Generator and divide it equally between the waveguide thermistor mount and the HP power meter. This will allow us to compare the RF power measurements between our manual bridge and an actual HP power meter.

Figure 2.2: Block diagram of measurement setup for RF power measurement using thermistor.

1. Make sure the RF Generator output power is turned oﬀ.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 19

2. Set the attenuator to the maximum attenuation 30db or more.

3. Zero the HP power meter. This step assures that power meter ”knows” there is no input RF power incident on it.

4. Set the resistor R3 = 100Ω and leave it at 100Ω throughout this part of the experiment. 5. Turn the RF Generator power on. Set the power to 10dBm.

6. Change the voltage on the manual bridge to balance it using resistor R4. Record the voltage on the bridge for which the bridge is balanced.

7. Record the power indicated by the power-meter.

8. Decrease the attenuation for 3db. Repeat steps 1-7 until the attenuator is 0db.

9. Calculate the RF power on the waveguide thermistor mount from the DC voltage measurements and the resistance of the thermistor.

10. Plot the power on the thermistor bridge vs. power on HP power meter.

2.2.1 Question 3 In this measurement you have both RF and DC power incident of the thermistor. How can you ﬁnd the RF power incident on the thermistor?

2.3 Measuring Microwave Power with Diode Detector

Replace waveguide thermistor mount with a diode detector. Connect the circuit as in Figure ??. Connect the other side of the diode detector to a voltmeter.

1. Make sure the RF Generator output power is turned oﬀ.

2. Set the attenuator to the maximum attenuation 30db or more.

3. Zero the HP power meter. This step assures that power meter ”knows” there is no input RF power incident on it.

4. Turn the RF Generator power on. Set the power to 10dBm.

5. Record the voltage indicated by the diode detector.

6. Decrease the attenuation for 3db. Repeat steps 1-7 until the attenuator is 0db.

7. Calculate the RF power on the diode detector as 10 log V.

8. Plot the power on the thermistor bridge vs. power on HP power meter.

California State University Sacramento EEE161 revised: 15. December, 2010 Dr. Milica Markovi´c Applied Electromagnetics Laboratory page 20

Conclusion Write what you have learned. Do not write an essay, just in a few sentences write what you have done in each problem, and speciﬁcally what you have learned from the work done. Due Date Submit the printout of the lab work and the conclusion by NEXT FRIDAY. LAB IS DUE BY noon (stamped) next Friday in the main oﬃce. No late labs. Do not bring previous lab writeup for the next Lab session.

California State University Sacramento EEE161 revised: 15. December, 2010