ECE 5317-6351 Microwave Engineering Adapted from notes by Prof. Jeffery T. Williams Fall 2019 Prof. David R. Jackson Dept. of ECE Notes 17 S-Parameter Measurements 1 S-Parameter Measurements S-parameters are typically measured, at microwave frequencies, with a network analyzer (NA). These instruments have found wide, almost universal, application since the mid to late 1970’s. Vector* network analyzer: Magnitudes and phases of the S parameters are measured. Scalar network analyzer: Only the magnitudes of the S-parameters are measured. Most NA’s measure 2-port parameters. Some measure 4 and 6 ports. * The S parameters are really complex numbers, not vectors, but this is the customary name. There is an analogy between complex numbers and 2D vectors. 2 S-Parameter Measurements (cont.) A Vector Network Analyzer (VNA) is usually used to measure S parameters. Port 1 Device Under Test (DUT) Port 2 Note: If there are more than 2 ports, we measure different pairs of ports separately with a 2-port VNA. 3 S-Parameter Measurements (cont.) Vector Network Analyzer Port 1 Measurement plane 1 a1 Measurement Port 2 plane 2 a2 b1 b2 Device under test (DUT) Test cables 4 S-Parameter Measurements (cont.) We want to measure [S] for DUT m a 1 Port 1 b1m Error Box A Meas. plane 1 Error Box B DUT Ref. plane a2m m 2 Port 2 b Meas. plane 2 Ref. plane Error boxes contain effects of test cables, connectors, couplers,… A B C D A B C D A A B C D MEAS A B C D B 5 S-Parameter Measurements (cont.) A B C D A B C D MEAS A A B C D A B C D MEAS A A B C D B A B A B A B C D C D C D B Embedded inside measured ABCD matrix De-embedded 1 A MEAS A B B A B A B A B C D C D C D C D 1 6 S-Parameter Measurements (cont.) Measurement plane A S A S S B Error box A DUT Error box B Measurement plane B Assume error boxes are reciprocal (symmetric matrices) We need to "calibrate" to find S A and S B . If S A and S B are known we can extract S from measurements. This is called “de-embedding”. 7 Calibration “Short, open, match” calibration procedure Connect S SC L 1 L 1 Short Error box OC Open L 0 Z0 Match Calibration loads These loads are connected to the end of the cable from the VNA. S S m 11SC S 21 11 1 S22 S S m 11 OC S m 11 match S 2 2 21 11 1 S22 S11 Recall from Notes 16: 3 measurements : ( S11m , S11m , S11m SC OC match ) in S11 S21S12 L 1 L S22 3 unknowns: S , S , S 11 21 22 8 Calibration (cont.) “Thru-Reflect-Line (TRL)” calibration procedure This is an improved calibration method that involves three types of connections: 1) The “thru” connection, in which port 1 is directly connected to port 2. 2) The “reflect” connection, in which a load with an (ideally) large (but not necessarily precisely known) reflection coefficient is connected. 3) The “line” connection, in which a length of matched transmission line (with an unknown length) is connected between ports 1 and 2. The advantage of the TRL calibration is that is does not require precise short, open, and matched loads. This method is discussed in the Pozar book (pp. 193-196). 9 Discontinuities In microwave engineering, discontinuities are often represented by pi or tee networks. Sometimes the pi or tee network reduces to a singe series or shunt element. For waveguide systems, the TEN is used to represent the waveguide. 10 Discontinuities: Rectangular Waveguide Inductive iris or strip Capacitive iris or strip Resonant iris 11 Discontinuities: RWG (cont.) Z 01 Z 02 Z 01 Z 02 E plane step H plane step 12 Discontinuities: Microstrip Z0 Z0 C Cs Z0 Z 01 Z0 Z 02 Z0 Z 01 Cp Cp L L C Z0 Z 02 Note: For a good equivalent circuit, the element values are fairly stable over a wide range of frequencies. 13 Z-Parameter Extraction Assume a reciprocal and symmetrical waveguide or transmission-line discontinuity. T Examples g T Microstrip gap Waveguide post We want to find Z1 and Z2 to model the discontinuity. Note: We could also use a pi network if we wish. Z1 Z11 Z 21 Discontinuity model T T Z1 Z1 Z0 Z 2 Z 21 Z2 TEN Z0 14 Z-Parameter Extraction (cont.) T T Z1 Z1 Z0 Z0 Z2 Plane of symmetry (POS) The Z2 element is split in two: POS T T Z1 Z0 Z1 2Z 2 2Z 2 Z0 15 Z-Parameter Extraction (cont.) Assume that we place a short or an open along the plane of symmetry. T T POS Z1 Short Z0 Z1 2Z 2 Z0 2Z 2 SC ZLSC L Z1 SC ZLLSC Z POS Z1 Z1 Open 2Z 2 Z0 2Z 2 Z0 OC ZZ1122 Z 2Z 2 ZZLOC L OC OC LL ZZ Z1 Z LSC , Z 2 1 OC Z L Z LSC 2 16 Z-Parameter Extraction (cont.) The short or open can be realized by using odd-mode or even-mode excitation. 1V 1V Z0 Z0 Port 2 Port 1 Incident voltage waves 1 1 1 Odd mode excitation 1 Even mode excitation Even/odd-mode analysis is very useful in analyzing devices (e.g., using HFSS). 17 Z-Parameter Extraction (cont.) 1V 1V Z0 Z0 Port 1 Port 2 S11SC Odd mode voltage waves Z SC L 1V 1 S11SC Z0 SC 1 S11 1V Z0 Z0 Port 1 Port 2 S11OC Even mode voltage waves Z OC L 1 S11OC Z0 OC 1 S11 18 Z-Parameter Extraction (cont.) Discontinuity model T T Z1 Z1 Z0 Z2 Z0 Hence we have: 1 S11SC Z1 Z 0 SC 1 S 11 1 S11SC 1 1 S11OC Z 2 Z 0 Z0 OC SC 2 1 S11 1 S 11 19 De-embeding of a Line Length We wish the know the reflection coefficient of a 1-port device under test (DUT), but the DUT is not assessable directly – it has an extra length of transmission line connected to it (whose length may not be known). S11DUT S11m Recall : Sij Sij e i li e L j l j li l j L MEAS 11 S i j j DUT j 2 L 11 S e DUT Meas. plane Ref. plane S Replace DUT with short circuit S11DUT 1 S11DUT S11MEAS, DUT e j 2 L MEAS, SC 11 e j 2 L 1 / e j 2 L 1 S11DUT S11MEAS,DUT MEAS,SC S11 20