1S-PARAMETER MEASUREMENT TECHNIQUEThe vector voltmeter measures the magnitude of a reference and test voltage and thedifference in phase between the voltages. Because it can measure phase, it allows us to directlymeasure the S-parameters of a circuit. Unfortunately, the use of directional couplers and test cablesconnecting the measuring system to the vector voltmeter introduces unknown attenuation and phaseshift into the measurements. These can be compensated for by making additional "calibration"measurements.A) Reflection measurements: obtain S11 or S22Set up the experimental arrangement shown in Figure 1. It is seen that the voltage atchannel A of the vector voltmeter ()DA is proportional to the amplitude of the voltage waveentering the device under test (DUT) ()D1a . Similarly, the voltage at channel B ()DB isproportional to the amplitude of the voltage wave reflected from the DUT ()D1b . Thus, wecan writewhere KA and KB are constants that depend on the connecting cables. Since aD2 is zerobecause of the matched load at port 2, S11 is given byTo find KA and KB it is necessary to make a second measurement with a known DUT. This is called a "calibration" measurement. If the DUT in Figure 1 is removed and replacedby a short circuit, the voltages at channel A ()SA and channel B ()SB are given bywhere aS1 is the amplitude of the voltage wave entering the short and bS1 is the amplitude ofthe voltage wave reflected from the short. However, for a short circuit the ratio of theseb K = Ba K = AD1BDD1AD(1)K/AK/B = ab = SADBDD1D111(2)b K = Ba K = AS1BSS1AS(3)2amplitudes is -1 (reflection coefficient of a short). ThusThusFinally, substituting this into (2) gives the formula for S11Note that since the vector voltmeter displays quantities in terms of magnitude and phase, (6)can be written more conveniently aswhereNOTE: The HP 8508A vector voltmeter can perform the calibration calculation (6)automatically (manual sheets available in the lab).1- = K/AK/B = abASBSS1S1(4)AB- = KKSSAB(5)ABAB- = SSSDD11(6))--( = SSDSD11πφφ∠ΓΓ (7)φ∠Γφ∠ΓSSSSDDDD = AB = AB(8)3B) Transmission measurements: obtain S12 or S21.Set up the arrangement shown in Figure 2 with the DUT connected directly between twodirectional couplers. In this case the voltage at channel A of the vector voltmeter isproportional to the amplitude of the voltage wave incident on the DUT while the voltage atchannel B of the vector voltmeter is proportional to the amplitude of the voltage wavetransmitted through the DUT. ThusS21 is thenTo find the constants a calibration measurement must be made. Remove the DUT andconnect the two directional couplers directly together. The known DUT in this case is just azero-length guide with a transmission coefficient of unity. The measured voltages are thuswhereThusSubstituting this into (10) then gives the formula for S21b K = Ba K = AD2BDD1AD(9)K/AK/B = ab = SADBDD1D221(10)b K = Ba K = AE2BEE1AE(11)1 = K/AK/B = abAEBEE1E2(12)AB = KKEEAB(13)4orwhereABAB = SEEDD21(14))-(TT = SEDED21θθ∠ (15)θ∠θ∠EEEEDDDDT = ABT = AB(16)5Figure 1. Experimental setup for measuring S11.Figure 2. Setup for measuring