1ECE 435Microwave Cavity MeasurementLatest revision: November 1999IntroductionThe basic objectives of this experiment are to make the following measurements and observationsregarding the characteristics of microwave cavities:1. Become familiar with techniques for measuring the resonant frequency and Q of amicrowave cavity; in particular, the TM010 and TE111 circular cylinder cavity modes as wellas the TE10p rectangular cavity modes.2. Observe the dependence of the cavity resonant frequency and Q upon the size, shape,mode type, wall conductor, and dielectric loading of the cavity resonator.3. Measure the complex microwave permittivity (dielectric constant) of a dielectric materialby using cavity perturbation techniques.4. Observe the effect of cavity coupling on the shape of the cavity Q-curve and the resonantfrequency of the microwave cavity.The cavities to be studied in this experiment have resonant frequencies in the X-band (8.2 – 12.4 GHz)microwave frequency range.The theoretical Q for TM010 cavity is given by( )da12405.2Q+πδλ=where δ is the skin depth of the cavity walls, λ is the wavelength in the cavity, a is the radius of thecavity, and d is the height of the cavity.The complex permittivity of a dielectric rod can be determined by measuring the resonant frequencyand cavity Q for the cases of no rod (unperturbed case) and with the rod fully inserted into the cavity(perturbed case). The equations relating the real part ()ε′ and imaginary part ()ε′′ of the complexpermittivity are()()()( )+−ε′−=ωω−ω405.2Jab405.2Jab405.2Jab21212120200()()( )+ε′′=−405.2Jab405.2Jab405.2JabQ1Q1212120202where 0ω and Q0 are the values for the unperturbed case.Procedure1. Connect the HP8620C Sweep Oscillator, the Digitizing Oscilloscope, and the TM101 cavity (drumcavity) as shown in Figure 1. Set the Sweep Oscillator to sweep between 9.2 and 9.4 GHz.2. Tune the detector for maximum output (e.g. set the standing wave in the shorted cavity so that thepeak is at the detector).3. Using the cavity data (a = 1.23 cm, air-filled), show that the theoretical resonant frequency is 9.3GHz. Note that the actual measured frequency is slightly lower due the skin effect and the holes inthe cavity walls.4. Adjust the sweep oscillator frequency range so that only one cavity Q curve is displayed on theoscilloscope.5. Using the cavity wavemeter, measure the resonant frequency and Q of the empty cavity whereBfQ0= and B is the 3-dB bandwidth of the Q-curve. Use the program Progs/BenchLinkprogram to capture the oscilloscope display and print it.6. The cavity wavemeter is a resonant cavity connected to the X-band waveguide. The mode ofoscillation utilized is the TE111 mode. Use the wavemeter pip to determine the resonant frequencyand bandwidth of the Q-curve. Read the frequency from the wavemeter.7. Insert a pyrex glass rod into the cavity parallel to its axis. Be very careful, since the rod will breakquite easily. Locate the new resonant frequency (somewhere around 8.8 GHz) and measure itsfrequency and the Q of the loaded cavity.8. Construct an aperture-coupled TE10p mode rectangular cavity by connecting an adjustable short-circuit to the directional coupler with one of the brass circular aperture plates (the one marked 5mm) placed between the short and the coupler connecting flanges. You now have formed arectangular cavity of adjustable length. Adjust the Sweep Oscillator frequency to 9.5 GHz andvary the length of the cavity until the resonance is observed on the oscilloscope. Adjust the cavityattached to the detector to again establish a standing wave peak at the detector location. WhichTE10p mode are you observing? Print the Q-curve.9. Insert various apertures and print the oscilloscope display of the resulting cavity Q-curve.3Sweep OscillatorSweep SignalRF OutLoadisolatorVariableattenuatorWave-meterDirectional couplerAmpl.detectorExp. cavityChannel 4Channel 1Digitizing OscilloscopeFigure 1. Experimental setup.ReportIn you report, you should minimally address the following questions.1. Compare the theoretical Q to the measured Q.2. Calculate the complex permittivity of the pyrex glass rod based on the unperturbed and perturbedresonant frequency and Q measurements. Note, a very careful measurement of the rod diameter isimportant for reasonable and accurate results. A small error in this dimension greatly alters theresults obtained. Also note the conductivity of brass us 1.57 x107 mhos/meter.3. Why does the insertion of a glass rod perturb the cavity’s resonant frequency and Q?4. What is the Q of the rectangular cavities with the 2.5mm, 5.0mm, and 10mm feed apertures?5. Why does the feed aperture diameter affect the performance of the