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Waveguides and Waveguide Measurements 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”.
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