# Experiment 7: Familiarization with the Network Analyzer

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1 Experiment 7: Familiarization with the Network Analyzer Measurements to characterize networks at high frequencies (RF and microwave frequencies) are usually done in terms of scattering parameters (S parameters). This is because practical network characterization can no longer be done in terms of simply open- or short-circuit measurements that lead to impedance and admittance parameters. Practical measurement of S parameters is often performed using a network analyzer. Network analyzers typically function in the 9 khz to 110 GHz range. First let us consider how S parameters are defined. S Parameters S parameters are descriptors that permit us to define the input-output relations of a network in terms of incident and reflected power waves. In Figure 1 an is the incident normalized power wave and bn is the reflected normalized power wave, defined as follows where the index n refers to the port number 1 or 2. Here, Vn and In are the peak voltage and current values at the nth port (n=1,2) and impedance Zo is the characteristic impedance of the connecting lines at each port. a1 a2 b1 b2 The physical meaning of (1) and (2) become clear when it is noted that the net power flowing into the nth port is The S parameters for a two-port network are now defined as

2 Equations (4) and (5) can be written in matrix form as The meaning of each S parameter is as follows Impedance, admittance, hybrid, and ABCD parameters can be determined for a network, once S parameters are known. This can be done in the following way. Impedance parameters can be obtained from S parameters as follows. Note: The S parameters used in (11) are typically complex and require both amplitude and phase information versus frequency. The table on the next page can be used to obtain the other traditional network parameters. Network Analyzers Network analyzers measure S parameters for two port networks. The measurement of S parameters requires reflection and transmission evaluations of traveling waves at both ports. There are two types of network analyzers: scalar and vector network analyzers. Scalar network analyzers evaluate only amplitudes of these signals. Vector network analyzers measure both amplitude and phase of these signals. Usually analyzers have an output port that provides the RF signal from either an external or internal signal generator, and three measured channels, which are denoted as R, A, and B (see Figure 2).

3 The RF source is usually swept over a specified frequency range. The measurement channel R is employed for measuring the incident wave. Channel R also serves as a reference port. Channels A and B usually measure the reflected and transmitted waves. As shown in Figure 2, S11 and S21 can be measured. S11 can be obtained by evaluating the ratio A/R and S21 through computing B/R. S12 and S22 can be evaluated for the DUT (device under test) by reversing the DUT ports in this configuration. It is apparent that a practical test arrangement is more complicated when compared to the ideal S parameter measurement concept that employs perfectly matched transmission lines and ideal directional couplers with perfect isolation and impedance match. Network Analyzer Calibration To overcome the effect of these non-ideal elements in the S parameter measurement process, a calibration procedure must be performed. The main goal of the calibration procedure is to characterize the non-ideal elements, provide this

4 information to a computer internal to the network analyzer to evaluate the errorfree S parameters of the actual DUT relative to a desired reference plane for phase measurements. Calibration involves using known standards. Convenient standards are perfect shorts, opens, loads, and a zero length transmission line (connecting the input to the Figure 2 Measurement system for S11 and S21 parameters using a network analyzer output with no DUT). Such standards have simple reflection and transmission coefficients, namely: A short circuit at the reference plane gives = -1 A load at the reference plane gives An open circuit at the reference plane gives Connecting input to the output gives S21 = S12 = 1 Connecting a load at the input and output gives S21 = S12 = 0 After making these measurements, the network analyzer can compute some correction values to produce the expected answer. For answers that are supposed to be zero, the analyzer can subtract the residual. For non-zero values, the analyzer could calculate complex factors that will compensate for both phase and amplitude

5 errors. It is not easy to make ideal standards. Network analyzers will account for imperfections in standards. 1 A calibration using a mechanical calibration kit may take a significant amount of time. Not only must the operator sweep through all the frequencies of interest, but also the operator must disconnect and reconnect the various standards. To avoid that work, network analyzers can employ automated calibration standards. The operator connects one box to the network analyzer. The box contains a set of standards and switches that have already been characterized. The network analyzer can read the characterization and control the configuration using a digital bus such as USB. Agilent calls such boxes used with their network analyzers ECal (electronic calibration) modules. Laboratory Procedure 1. Calibrate the vector network analyzer over the 1 GHz to 6 GHz frequency range. A new calibration procedure should be performed each time the cables and/or type of connectors (e.g. N-type or SMA) feeding the device under test are changed. 2. Over the 1 to 6 GHz range, measure and record all appropriate S parameters for each of the following devices after the calibration procedure is completed: a. An open circuit b. A short circuit c. A 50 ohm termination d. The input connected directly to the output (or connected to each other using a type adapter, if necessary) Make sure that data is taken at enough frequencies to record the major features of the S parameters versus frequency behavior. For example, data taken at intervals of 100 MHz is probably reasonable. 3. Measure and record all appropriate S parameters (both amplitude and phase data at each frequency for all four S parameters) for both the commercially available 10 db directional coupler and the quadrature hybrids over the frequency ranges stipulated on the pertinent specification sheet. Remember, these are inherently 4- port devices. Measure amplitude of the signal reflected from the input port. Also, measure the amplitude and phase of the coupled and the transmitted signal ports. Measure the amplitude of the signal emerging from the isolated port. 4. Over the 1 to 6 GHz frequency range, measure and record all appropriate S parameters for a straight-through microstrip transmission line on a PCB. Make the length of this line as close as practical to the length of the line to be constructed in part 5. Describe and photograph the resulting straight line geometry for use in the lab report. (S parameters here will be compared to those obtained in the part 5.)

6 5. Over the 1 to 6 GHz frequency range, measure and record all appropriate S parameters for the right-angle microstrip bend on a PCB. You will create a right angle microstrip bend by attaching and trimming two pieces of conducting tape of the appropriate width. Experiment with modifications to the sharp corner in this bend to obtain the optimum performance in terms of impedance match and insertion loss through the bend. Do your best to sketch and photograph the resulting bend geometry for use in the lab report. Compare the performance of this line to that of part 4.

7 6. Lab Report a. For the 1 to 6 GHz frequency range show plots of the appropriate S parameters from experimental parts 2a through 2d. For part 2d, convert the S21 parameter values at each frequency to Z parameters using equation (11) and then to ABCD parameters. The ratio of V2/V1 = 1/A. For part 2d, plot the amplitude and phase of V2/V1 and reflection coefficient versus frequency for the 1 to 6 GHz frequency range. Discuss how these values correlate with what is expected based upon the calibration of the equipment. b. For the appropriate frequency bands show plots for the directional coupler and quadrature hybrids of the coupled signal, transmitted signal, isolated signal, and VSWR versus frequency. Note that Be aware that the network analyzer in the laboratory can read VSWR directly. On one graph for each of these devices, plot the phase of the coupled and transmitted signals. Compare and discuss how well these characteristics agree with the manufacturer provided specifications and with what would be expected for an ideal coupler. Also, calculate the amount of (power in db) dissipated in each type of coupler at its midband frequency. This can be determined by adding up the power reflected from the input port, the power emerging from the transmitted, coupled, and isolated ports and subtracting this sum from the total input power. c. For the frequency range from 1 to 6 GHz show plots of transmission loss and reflection coefficient for the straight-through transmission line. d. For the frequency range from 1 to 6 GHz show plots of transmission loss and reflection coefficient for the right-angle microstrip bend. Look in the literature for technical papers on how to mitre (shape) the corner for a 90 o microstrip bend. Show the optimum shape you found in the lab and compare it to what the paper describes for such a bend. Compare performance with that obtained in part c. References 1. R. Ludwig and P. Bretchko, RF Circuit Evaluation, Theory and Application, Prentice-Hall, Upper Saddle River, NY, 2000,

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