EE 3323 Electromagnetics Laboratory

Experiment #1

Waveguides and Waveguide Measurements

1. Objective

The objective of Experiment #1 is to investigate waveguides and their use in microwave systems. You will use a precision benchtop microwave system to investigate various microwave measurement techniques. Among the waveguide parameters which are measured are the source frequency, the waveguide wavelength, the standing wave ratio and signal power. In addition, the characteristics of square law detectors in the measurement of microwave signals are investigated.

2. Introduction

Waveguides are typically used to transmit microwave signals between a source and load in an application which requires low loss and high power. Microwave signals lie within the frequency range of 300 MHz to 300 GHz with corresponding wavelengths ranging from 1 m down to 1 mm. The most commonly used waveguide shape is the rectangular waveguide shown in Figure 1. The two types of modes which can propagate in the rectangular waveguide are designated as transverse electric (TE) and transverse magnetic (TM). There are an infinite number of discrete propagating TE and TM modes which may be excited in the rectangular waveguide. These discrete modes are denoted with integer subscripts m and n as TEmn and TMmn. The propagating modes within the rectangular waveguide can only be excited by a source operating above the cutoff frequency for that mode. The cutoff frequencies for both TE and TM modes in the rectangular waveguide are Figure 1. Rectangular waveguide. given by

(1)

where c is the speed of light, ìrr and å are the relative permeability and permittivity, repsectively, of the material within the waveguide. For the TE modes, the case of m = n = 0 is not allowed. In most applications, the waveguide is designed to operate such that only one propagating mode is excited within the waveguide. The waveguide modes which do not propagate (excited at frequencies below their cutoff) are called evanescent modes and decay rapidly away from the source. The wavelengths of the propagating modes (TE or TM) in the rectangular waveguide are given by

(2)

When waveguides are used to connect a microwave source with a load, mismatches between the waveguide and the load can cause reflections just as with transmission lines. These reflected waves set up standing wave patterns along the waveguide. The standing wave ratio (s) for a waveguide is defined in basically the same way as for a transmission line. Rather than using circuit quantities (voltage and current), which are easily defined on a transmission line, the standing wave ratio for a waveguide is defined in terms of field quantities such that

(3) where Emax and Emin are the maximum and minimum electric field magnitudes along the waveguide. If the electric field is probed with a diode detector at low power levels, the diode detector will obey a square law. That is, the current measured in the diode detector will be proportional to the square of the electric field being probed so that

(4)

where k is a constant of proportionality. Using Equation (4) to relate Emax and Emin to Imax and Imin in conjunction with Equation (3) yields

(5)

The corresponding waveguide reflection coefficient is

(6)

where Einc is the electric field associated with the forward-traveling incident wave and Eref is the electric field associated with the reverse-traveling reflected wave. The power associated with the

incident wave (Pir) and the reflected wave (P ) are proportional to the square of the respective electric field. Thus, squaring both side of Equation (6) yields

(7)

The waveguide return loss (in dB) is defined as (8)

When measuring the power associated with a microwave signal, a bolometer is commonly employed. A thermistor-type bolometer is a sensitive resistive element made from semiconductor whose resistance decreases with an increase in temperature. Thus, when the incident microwave power is absorbed by the thermistor, it is converted to heat and the resistance of the thermistor decreases. The power of the microwave signal may be determined through the precise measurement the bolometer resistance. The bolometer resistance can be accurately determined by placing the bolometer in a Wheatstone bridge circuit as shown in Figure 2. The principle of the measurement method is to measure the bridge DC balancing current with the microwave source off and with it on. The difference in the DC power dissipated in the bolometer for these two cases yields the microwave power level. With the microwave source off, the bridge is brought into balance by adjusting RS. Remember that the resistance of the bolometer (RB) changes as the bolometer current changes. The bridge is brought into balance when the bolometer resistance equals 1 kÙ. The corresponding DC power dissipated in the bolometer is

(9) since IB1 = ½ IT1 when the bridge is in balance. If the microwave source is now turned on such that the bolometer is now absorbing microwave power, the bridge becomes unbalanced. The bridge is brought back into balance by Figure 2. Wheatstone bridge circuit. again adjusting RS which changes the bolometer current until the bolometer resistance is again 1 kÙ. Note that there is DC power and microwave power being dissipated in the bolometer for this case. The DC power dissipated in the bolometer is

(10)

Yet, the total power dissipated in the bolometer for these two cases is the same (RBo = R = 1 kÙ in both cases). Thus, we may write

(11) where PRF is the microwave power dissipated in the bolometer. Solving Equation (11) for the microwave power and using Equations (10) and (11) yields

(12)

When using a diode detector, the square-law relationship defined in Equation (4) can be verified experimentally. Given a short-circuited waveguide, the resulting electric field amplitude along the waveguide is given by

(13) where l is the distance away from the short circuit. If we assume that the rectified current in the diode detector is related to the electric field by I = kEn, then

(14)

By taking the natural logarithm of both sides of Equation (14), we find

(15)

Differentiating both sides of Equation (15) with respect to ln (sin âl) gives

(16)

Thus, the slope of a ln I vs. ln(sinâl) plot should equal the order n of the detector current-electric field relationship.

3. Equipment List

Feedback MWT530 Microwave Trainer

4. Procedure

The Feedback MWT530 Microwave Trainer

The Feedback MWT530 Microwave Trainer is a benchtop system designed to enable students to familiarize themselves with the basic waveguide components of microwave systems. The trainer is comprised of a set of waveguide components along with a console which contains the microwave source power supply along with bridge and amplifier circuits used to measure microwave power and signal strength. The MWT530 components are standard WR-90 waveguide components (rectangular waveguide, 0.9"×0.4" internal dimensions) designed for operation in the X-band (8.2-12.4 GHz) which is an important band for applications such as microwave radio, satellite communications and radar. The MWT530 source operates at a fixed frequency of 10.687 GHz. Each of the MWT530 system components are identified by a letter designation for convenience (see Table 1). Quantity Part Description

2 A Variable attenuators (max. attenuation at 0oo = 36 dB, minimum attenuation at 90 less than 1 dB)

1 B Slotted line (to sample waveguide electric field pattern, used with diode-probe detector to measure the guide wavelength, standing wave ratio and impedance)

1 C Slotted line-probe tuner (used as an impedance matching device)

1 D Cavity wavemeter (adjustable cylindrical resonant cavity used to measure frequency)

1 E H-plane or shunt Tee waveguide junction (acts as a power divider in the plane containing H)

1 F Directional coupler (used to monitor power and measure standing wave ratio)

1 G E-plane or series Tee waveguide junction (acts as a power divider in the plane containing E)

1 H Hybrid Tee or ”magic Tee” (superposition of a shunt and a series Tee junction)

2 J Waveguide-to-coaxial transformer

1 K Resistive termination (a waveguide section containing a taper of lossy material which ideally absorbs all of the incident energy thus acting as a matched load)

1 L Thermistor type bolometer (a temperature-sensitive resistor mounted in a waveguide used to measure microwave power)

1 M Diode detector in waveguide mount (used to rectify microwave signals for their detection)

2 N Horn antenna (matches the waveguide impedance to the surrounding air)

1 P X-band CW Gunn oscillator source, f =10.687 GHz (fixed), output power = 10 mW typical, 5 mW min.

2 R Short circuit termination (used to short circuit the waveguide section)

2 S Probe detector (diode detector mounted in a coaxial section, used to detect microwave signals)

Table 1. Feedback MWT530 Component Designations and Descriptions.

Warning: Although the microwave power levels generated by this equipment are below 10mW and not normally dangerous, the human eye can suffer damage by exposure to direct microwave radiation. NEVER look directly into an energized waveguide.

1. Source Frequency Measurement. Connect the microwave system shown in Figure 3 with the following settings on the control console: power (off) amplifier/detector sensitivity control (mid-position) meter switch (detector output) supply for the X-band oscillator - left switch (internal keying), right switch (off) Set the micrometer position of the cavity wavemeter fully out to a reading of greater than 21 mm (maximum length cavity). Set the angular position of the resistive vane for both attenuators at approximately 20o. These attenuator settings provide about 10 dB of combined attenuation in order to avoid overloading the detector and display meter when the system is turned on. Turn on the console power switch and then turn the X-band oscillator switch to “on”. Adjust the vane penetration of the detector attenuator to give a meter reading of 4 mA. Turn the wavemeter micrometer thimble very slowly to move the plunger downward such that the cavity length is reduced. Observe the meter reading and search for a position where a sharp dip in the current reading is obtained. This dip in the detected current corresponds to the cavity resonance at which significant power is coupled into the cavity. Record the micrometer reading and determine the frequency of the microwave source using the

calibration curve shown in Figure 4 (Use the curve labeled E011 mode).

Figure 3. Source frequency measurement setup.

2. Guide Wavelength Measurement. Connect the microwave system shown in Figure 5 with the following settings on the control console: power (off) meter switch (detector output) supply for the X-band oscillator - left switch (internal keying), right switch (off) The slotted line probe position should be set to a penetration depth of somewhere between 1 and 2 mm. Switch on the console power and the oscillator and adjust the attenuators (and the sensitivity control, if necessary) to obtain a detector reading. Move the slotted line probe to obtain a position of maximum field and re-adjust the sensitivity control and/or attenuators to obtain a meter reading of 4 mA. Move the slotted line probe such that the scale on the side of the slotted line reads “zero”. Carefully move the slotted line along the waveguide section to locate and record the positions of electric field nulls. It should be possible to Figure 4. Calibration curves for cavity wavemeter. Figure 5. Guide wavelength measurement setup.

locate three consecutive nulls using the slotted line. Determine the wavelength within the waveguide according to your measurements. Compare the measured waveguide wavelength to the theoretical waveguide wavelength. 3. Waveguide Standing Wave Ratio Measurement. Connect the microwave system shown in Figure 6 with the following settings on the control console: power (off) amplifier/detector sensitivity control (mid-position) meter switch (detector output) supply for the X-band oscillator - left switch (internal keying), right switch (off) Set the attenuator vane position at approximately 25o. Turn on the console power and the then the X-band oscillator. Move the slotted line probe along the waveguide to locate a position of maximum electric field. Adjust the detector sensitivity and, if necessary, the attenuator setting to obtain a detector current which is close to full scale. Record the value

of the detector current (Imax). Move the slotted line probe to locate the adjacent position of

minimum electric field. Record the detector current at this location (Imin). From these measurements, determine the standing wave ratio, the reflection coefficient, the percentage of power reflected and the return loss in dB. Remove the resistive load termination and

connect one of the horn antennas. Using the same procedure, determine Imax and Imin for the horn antenna and determine the standing wave ratio, the reflection coefficient, the percentage of power reflected and the return loss in dB. Repeat with the second horn antenna. Discuss Figure 6. Standing wave ratio measurement setup.

and compare the results of the three “loads”. 4. Microwave Power Measurement. Connect the microwave system shown in Figure 7 with the console supply on but with the X-band oscillator switched off. Switch the meter switch to the bridge current position. Turn the thermistor bridge control fully counterclockwise to

minimize the bridge current (maximum Rss). With R at its maximum value, the bridge

balance meter reads approximately 40 units to the right of balance. Reduce Rs slowly thereby

increasing the total bridge current IT. The bridge balance first deflects further to the right,

reaches a peak and the deflection decreases. Adjust Rs so that the thermistor bridge needle

is centered on zero. Record the value of IT and calculate the DC power dissipated in the thermistor. Set the attenuator to its 0o position (maximum attenuation). Set the left switch of the supply for the X-band oscillator to the “full power” position and turn on the oscillator o with the right switch. Measure the balanced bridge current IT for attenuator settings of 0 , 10o, 20ooo, 30 , 40 and 50o. Compute the DC power in the thermistor and the microwave power for each case. Put your results in a table in your report. 5. Microwave Diode Detector. Connect the microwave system shown in Figure 8 with the following settings on the control console: power (off) meter switch (detector output) Figure 7. Microwave power measurement setup.

supply for the X-band oscillator - left switch (internal keying), right switch (off) Set the angle of the variable attenuator to 0o and the depth of penetration for the detector probe between 1 and 2 mm. Switch the console power on and turn on the oscillator using the right hand switch. Gradually reduce the attenuation by moving the vane from the 0o position until a deflection is observed on the meter. Move the probe along the slotted line and locate a position of maximum electric field as indicated by the detector current reading. Adjust the attenuator and , if necessary, the detector sensitivity control to provide a near full- scale meter reading. Move the probe along the slotted line and accurately locate the position of an electric field null. Record the position of this null (lo) as indicated on the slotted line scale. Using this point as a reference, move away from the short circuit end and take a series of detector current readings at a number of points up to the position of a field maximum. Record the following values in a table in your report: probe position on the slotted line scale ! (l in mm), probe position relative to the electric field null (l lo in mm), and the diode detector current (I in mA) at that position. Measure the guide wavelength using the ! procedure given in part (2). Include the following values in a table in your report: l lo (mm), âl, sin(âl), ln[sin(âl)], I and ln(I). Plot ln(I) vs. ln[sin(âl)] and draw a “best-fit” line through your data. Determine the slope of the best-fit line and discuss how this illustrates the square-law relationship. Figure 8. Diode detector measurement setup.

5. Additional Question

1. Determine all TEmn and TMmn modes which have cutoff frequencies of 20 GHz or less for the

WR-90 waveguide. From your results, show that only the TE10 propagates in the waveguide of the MWT530 based on the measured source frequency.