and Measurement Agenda Page 2 Transmission Lines S-Parameters - PowerPoint PPT Presentation

Network Characteristics, Analysis and Measurement

Agenda Page 2 – Transmission Lines – S-Parameters – The Smith Chart – Network Analyzer Block Diagram – Network Analysis Measurements – Calibration and Error Correction

RF Energy Transmission Incident Transmitted Reflected Lightwave DUT RF Page 3

Transmission Line Basics _ + I Low frequencies – Wavelengths >> wire length – Current (I) travels down wires easily for efficient power transmission – Measured voltage and current not dependent on position along wire High frequencies – Wavelength » or << length of transmission medium – Need transmission lines for efficient power transmission – Matching to characteristic impedance (Zo) is very important for low reflection and maximum power transfer – Measured envelope voltage dependent on position along line Page 4

Transmission line Z o – Z o determines relationship between voltage and current waves – Z o is a function of physical dimensions and  r – Z o is usually a real impedance (e.g. 50 or 75 ohms) Page 5

Power Transfer Efficiency R S For complex impedances, maximum power transfer occurs when Z L = Z S * R L (conjugate match) Rs +jX 1.2 -jX 1 Load Power (normalized) 0.8 R L 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 9 10 R L / R S Maximum power is transferred when R L = R S Page 6

Transmission Line Terminated with Zo Zo = characteristic impedance Zs = Zo of transmission line Zo V inc V reflect = 0! (all the incident power is transferred to and absorbed in the load) For reflection, a transmission line terminated in Zo behaves like an infinitely long transmission line Page 7

Transmission Line Terminated with Short, Open Zs = Zo V inc In-phase (0 o ) for open, V reflect out-of-phase (180 o ) for short For reflection, a transmission line terminated in a short or open reflects all power back to source Page 8

Transmission Line Terminated with 25 Ohms Zs = Zo Z L = 25 W V inc V reflect Standing wave pattern does not go to zero as with short or open Page 9

Reflection Parameters V Z L - Z o G = r F reflected = = = Reflection Coefficient [S11] V incident Z L + Z o r G Return loss = -20 log( r ), = Voltage Standing Wave Ratio V max 1 + r V max V min VSWR = = 1 - r V min Full reflection No reflection (ZL = open, short) (ZL = Zo) 1 0 r  dB 0 dB RL  1 VSWR Page 10

Transmission Parameters V Incident V Transmitted Port 1 DUT Port 2 V Transmitted =  Transmission Coefficient [S21] = T = V Incident V Trans = - 20 Log(  ) Insertion Loss (dB) = -20 Log V Inc V Trans = 20 Log(  ) Gain (dB) = 20 Log V Inc Page 11

Demonstration: Page 12

Agenda Page 13 – Transmission Lines – S-Parameters – The Smith Chart – Network Analyzer Block Diagram – Network Analysis Measurements – Calibration and Error Correction

High-Frequency Device Characterization Incident Transmitted R B Reflected A TRANSMISSION REFLECTION B Transmitted A Reflected = = R Incident R Incident VSWR Group Delay Return Loss Gain / Loss Insertion S-Parameters Impedance, S-Parameters S 11 , S 22 Phase Reflection Admittance Transmission S 21 , S 12 Coefficient R+jX, G+jB Coefficient G, r T, t Page 14

Characterizing Unknown Devices Using parameters (H, Y, Z, S) to characterize devices: – Gives linear behavioral model of our device – Measure parameters (e.g. voltage and current) versus frequency under various source and load conditions (e.g. short and open circuits) – Compute device parameters from measured data – Predict circuit performance under any source and load conditions H-parameters Y-parameters Z-parameters V 1 = h 11 I 1 + h 12 V 2 I 1 = y 11 V 1 + y 12 V 2 V 1 = z 11 I 1 + z 12 I 2 I 2 = h 21 I 1 + h 22 V 2 I 2 = y 21 V 1 + y 22 V 2 V 2 = z 21 I 1 + z 22 I 2 h 11 = V 1 I 1 (requires short circuit) V 2 =0 h 12 = V 1 V 2 (requires open circuit) I 1 =0 Page 15

Why Use Scattering, S-Parameters? – Relatively easy to obtain at high frequencies • Measure voltage traveling waves with a vector network analyzer • Don't need shorts/opens (can cause active devices to oscillate or self-destruct) – Relate to familiar measurements (gain, loss, reflection coefficient ...) – Can cascade S-parameters of multiple devices to predict system performance – Can compute H-, Y-, or Z-parameters from S-parameters if desired – Can easily import and use S-parameter files in electronic-simulation tools S 21 Incident Transmitted a 1 b 2 S 11 DUT Reflected S 22 Port 2 Port 1 Reflected b 1 a 2 Incident S 12 Transmitted b 1 = S 11 a 1 + S 12 a 2 b 2 = S 21 a 1 + S 22 a 2 Page 16

Measuring S-Parameters b 2 S 21 Incident Transmitted a 1 Z 0 S 11 Load Forward Reflected DUT b a 2 = 0 1 b 2 b 1 Reflected Reflected S 22 S 11 = = = = a 1 a 2 a 1 = 0 a 2 = 0 Incident Incident b 1 b 2 Transmitted Transmitted S 12 S 21 = = = = a 1 = 0 a 2 = 0 a 2 a 1 Incident Incident a 1 = 0 b 2 S 22 Z 0 DUT Reverse Reflected Load a 2 S 12 b Transmitted Incident 1 Page 17

Equating S-Parameters With Common Measurement Terms Port 1 DUT Port 2 S 11 = forward reflection coefficient (input match) S 22 = reverse reflection coefficient (output match) S 21 = forward transmission coefficient (gain or loss) S 12 = reverse transmission coefficient (isolation) Page 18

Demonstration 4 S-Parameters with Correction Off Page 19

Demonstration 4 S-Parameters with Correction On Page 20

Agenda Page 21 – Transmission Lines – S-Parameters – The Smith Chart – Network Analyzer Block Diagram – Network Analysis Measurements – Calibration and Error Correction

Smith Chart Review o Polar plane 90 +jX 1.0 .8 .6 .4 + o 0 o .2 180   0 +R -  0 -jX -90 o Rectilinear impedance plane Inductive Constant X Constant R Z = Z o L G = 0 Smith Chart maps rectilinear (open) Z = (short) Z = 0 impedance plane onto L L G G O = 0 1 O = 1 ±180 polar plane Capacitive Smith Chart Page 22

Demonstration: Smith Chart Short, and Open, and a Matched Impedance Page 23

Agenda Page 24 – Transmission Lines – S-Parameters – The Smith Chart – Network Analyzer Block Diagram – Network Analysis Measurements – Calibration and Error Correction

Generalized Network Analyzer Block Diagram (Forward Measurements Shown) Incident Transmitted DUT Reflected SOURCE SIGNAL SEPARATION INCIDENT REFLECTED TRANSMITTED (R) (A) (B) RECEIVER / DETECTOR PROCESSOR / DISPLAY Page 25

Source Incident Transmitted DUT Reflected SOURCE SIGNAL SEPARATION REFLECTED TRANSMITTED INCIDENT (R) (A) (B) RECEIVER / DETECTOR – Supplies stimulus for system PROCESSOR / DISPLAY – Can sweep frequency or power – Traditionally NAs had one signal source – Modern NAs have the option for a second internal source and/or the ability to control external source Can control an external source as a local  oscillator (LO) signal for mixers and converters Useful for mixer measurements like  conversion loss, group delay Page 26

Signal Separation Incident Transmitted DUT Reflected – Measure incident signal for reference SOURCE SIGNAL SEPARATION – Separate incident and reflected signals REFLECTED TRANSMITTED INCIDENT (R) (A) (B) RECEIVER / DETECTOR PROCESSOR / DISPLAY splitter bridge Detector directional coupler Test Port Page 27

Directional Coupler undesired reverse leakage desired coupled signal desired through signal Page 28

Directivity Directivity is a measure of how well a directional coupler or bridge can separate signals moving in opposite directions (undesired leakage (desired reflected signal) signal) leakage desired I C result Test port L Directional Coupler Directivity = Isolation (I) - Fwd Coupling (C) - Main Arm Loss (L) Page 29

Interaction of Directivity with the DUT (Without Error Correction) 0 Data max DUT RL = 40 dB Directivity Add in-phase Return Loss 30 Device 60 Frequency Directivity Data min Device Device Data = vector sum Directivity Add out-of-phase (cancellation) Page 30

Detector Incident Transmitted DUT Reflected SOURCE SIGNAL Tuned Receiver SEPARATION REFLECTED TRANSMITTED INCIDENT (R) (A) (B) RF IF = F  F RF LO RECEIVER / DETECTOR ADC / DSP PROCESSOR / DISPLAY IF Filter LO Vector narrowband (magnitude and phase) Page 31

Detector: Narrowband Detection - Tuned Receiver RF ADC / DSP IF Filter – Best sensitivity / dynamic range – Provides harmonic / spurious signal rejection LO – Improve dynamic range by increasing power, decreasing IF bandwidth, or averaging – Trade off noise floor and measurement speed 10 MHz 26.5 GHz Page 32

Dynamic Range and Accuracy Error Due to Interfering Signal 100 - 10 + phase error Error (dB, deg) Dynamic range is 1 very important for magn error measurement 0.1 accuracy! 0.01 0.001 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50 -55 -60 -65 -70 Interfering signal or noise (dB) RF Back to Basics Page 33

Demonstration VNA - 2 port Block Diagram Page Page VNA Block Diagrams 34