Network Analysis 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 _ + Low frequencies I – 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 Zo
– Zo determines relationship between voltage and current waves
– Zo is a function of physical dimensions and r
– Zo is usually a real impedance (e.g. 50 or 75 ohms)
Page 5 Power Transfer Efficiency
RS For complex impedances, maximum
RL power transfer occurs when ZL = ZS* (conjugate match) Rs +jX
1.2 1 -jX 0.8 0.6 RL
0.4 Load Power Power Load (normalized) 0.2 0 0 1 2 3 4 5 6 7 8 9 10
RL / RS
Maximum power is transferred when RL = RS
Page 6 Transmission Line Terminated with Zo
Zo = characteristic impedance Zs = Zo of transmission line
Zo
Vinc
Vreflect = 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
Vinc
In-phase (0o) for open, Vreflect out-of-phase (180o) 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
ZL = 25 W
Vinc
Vreflect
Standing wave pattern does not go to zero as with short or open
Page 9 Reflection Parameters
Vreflected ZL - Zo Reflection Coefficient [S11] = G = = r F = Vincident ZL + Zo Return loss = -20 log(r ), r = G Voltage Standing Wave Ratio Vmax Vmax 1 + r Vmin VSWR = = Vmin 1 - r No reflection Full reflection (ZL = Zo) (ZL = open, short)
0 r 1 dB RL 0 dB 1 VSWR
Page 10 Transmission Parameters
V Incident V Transmitted Port 1 DUT Port 2
VTransmitted Transmission Coefficient [S21] = T = = V Incident
VTrans Insertion Loss (dB) = -20 Log = -20 Log() V Inc
V Trans Gain (dB) = 20 Log = 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
REFLECTION TRANSMISSION
Reflected A Transmitted B = = Incident R Incident R
VSWR Group Delay Return Loss Gain / Loss S-Parameters Impedance, Insertion S , S Reflection Admittance S-Parameters Phase 11 22 Transmission Coefficient R+jX, G+jB S21, S12 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 V1 = h11I1 + h12V2 I1 = y11V1 + y12V2 V1 = z11I1 + z12I2 I2 = h21I1 + h22V2 I2 = y21V1 + y22V2 V2 = z21I1 + z22I2
V1 h11 = I1 V2=0 (requires short circuit)
V1 h12 = V2 I1=0 (requires open circuit)
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
Incident S 21 Transmitted a1 S 11 b2 DUT Reflected S 22 Port 1 Port 2 Reflected b1 a 2 Transmitted S 12 Incident
b1 = S 11a1 + S 12 a 2
b2 = S 21 a1 + S 22 a 2 Page 16 Measuring S-Parameters
b Incident S 21 Transmitted 2 a 1 Z 0 S 11 Forward Reflected DUT Load b 1 a 2 = 0
Reflected b 1 Reflected b 2 S 11 = = S 22 = = Incident a 1 a 2 = 0 Incident a 2 a 1 = 0 b b Transmitted 2 Transmitted 1 S 21 = = S 12 = = Incident a 1 a 2 = 0 Incident a 2 a 1 = 0
a 1 = 0 b 2 S 22 Z 0 DUT Load Reflected Reverse a 2 S 12 b 1 Transmitted Incident
Page 17 Equating S-Parameters With Common Measurement Terms
Port 1 DUT Port 2
S11 = forward reflection coefficient (input match)
S22 = reverse reflection coefficient (output match)
S21 = forward transmission coefficient (gain or loss)
S12 = 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 .2 o 0 +R - 180 0
0
-jX -90 o Rectilinear impedance plane Inductive Constant X
o Constant R Z L= Z G = 0 Smith Chart maps rectilinear Z = 0 (short) Z L = (open) impedance plane onto L O polar plane G = 1 ±180 O G = 1 0
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
directional Detector
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 I C desired 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 30 Device Return Loss Return
60 Frequency Directivity Data min Data = vector sum Device Device Add out-of-phase (cancellation) Directivity
Page 30 Detector Incident Transmitted DUT
Reflected SOURCE
SIGNAL Tuned Receiver SEPARATION
REFLECTED TRANSMITTED INCIDENT (R) (A) (B) RF IF = F LO F RF 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 1 Dynamic range is very important for magn error measurement 0.1 Error (dB, deg) (dB, Error 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 VNA Block Diagrams Page 34 Processor / Display
Incident Transmitted DUT
Reflected SOURCE
SIGNAL SEPARATION
REFLECTED TRANSMITTED INCIDENT (R) (A) (B)
RECEIVER / DETECTOR
PROCESSOR / DISPLAY
– Markers – Limit lines – Pass/fail indicators – Linear/log formats – Grid/polar/Smith charts – Time-domain transform – Trace math
Page 35 Agenda Page 36
– Transmission Lines
– S-Parameters
– The Smith Chart
– Network Analyzer Block Diagram
– Network Analysis Measurements
– Calibration and Error Correction Why Do We Need to Test Components?
– Verify specifications of “building blocks” for more complex RF systems
– Ensure distortion-free transmission of communications signals • Linear: constant amplitude, linear phase / constant group delay • Nonlinear: harmonics, intermodulation, compression, X-parameters
– Ensure good match when absorbing power (e.g., an antenna)
KPWR FM 97
Page 37 The Need for Both Magnitude and Phase
S21 1. Complete characterization S S of linear networks 11 22
S12 4. Time-domain characterization 2. Complex impedance needed to design Mag matching circuits
Time 3. Complex values 5. Vector-error correction needed for device Error modeling
Measured Actual
6. X-parameter (nonlinear) characterization
Page 38 Linear Versus Nonlinear Behavior
o A * Sin 360 * f (t - to) A Linear behavior: Time to Input and output frequencies are the same (no additional frequencies Sin 360o * f * t A phase shift = created) to * 360o * f Output frequency only undergoes Time f Frequency magnitude and phase change 1 Input DUT Output
Nonlinear behavior:
f Frequency Output frequency may 1 Time undergo frequency shift (e.g. with mixers) Additional frequencies created (harmonics, intermodulation) f 1 Frequency
Page 39 Phase Variation with Frequency
F(t) = sin wt + 1 /3 sin 3wt + 1 /5 sin 5wt
Linear Network
Time Time Magnitude
Frequency 0° Frequency Frequency -180° -360°
Page 40 Deviation from Linear Phase
Use electrical delay to remove linear portion of phase response
Linear electrical Deviation from linear RF filter response length added phase (Electrical delay function) o o + = Phase 45 /Div Phase Phase 1 /Div Phase
Frequency Frequency Frequency
Low resolution High resolution
Page 41 Group Delay
Group delay ripple Frequency (w) t g Dw Phase t o
Average delay D
Frequency Group Delay =(tg) -d -1 d = o d w 360 * d f Group-delay ripple indicates phase distortion in radians Average delay indicates electrical length of DUT w in radians/sec Aperture (Dw) of measurement is very important in degrees f in Hertz (w = 2 p f)
Page 42 Why Measure Group Delay? Phase Phase
f f -d -d d w d w Group Group Delay Group Group Delay
f f Same peak-peak phase ripple can result in different group delay
Page 43 Why the Time Domain?
RF Back to Basics Page 44
44 Frequency Domain S11 Response of Semirigid Coax Cable
r Upper Limit
Frequency
RF Back to Basics Page 45
45 Time Domain S11 Response of Semirigid Coax Cable
r
Time
RF Back to Basics Page 46
46 Gain Compression
DUT − Parameter to define the transition between the linear and nonlinear region of an active device. − The compression point is observed as x dB drop in the gain with VNA’s power sweep. Output Power (dBm) Gain (S21)
Sufficient power level to drive DUT Linear region Power is not high enough Compression to compress DUT. (nonlinear) region
Input Power (dBm) Input Power (dBm)
Enough margin of source power capability is needed for analyzers.
Page 48 Gain Compression Measurement Example
Ch 1 (vs. Input power): Tr 1: Gain Compresssion vs. Pin Tr 2: Pout vs. Pin
Ch 2 (vs. Frequency): Tr 1: Pin @ P1dB vs. Freq Tr 2: Pout @ P1dB vs. Freq
RF Back to Basics Page 49 Multiport Measurement
Application Examples Tx Antenna Rx Antenna SW • RF front end modules / antenna switch modules SW hmn : : • Channel measurements of MIMO antennas • Interconnects (ex. cables, connectors) • General-purpose multiport devices
Page 50 Agenda Page 51
– Transmission Lines
– S-Parameters
– The Smith Chart
– Network Analysis Measurements
– Calibration and Error Correction The Need For Calibration
– Why do we have to calibrate? • It is impossible to make perfect hardware • It would be extremely difficult and expensive to make hardware good enough to entirely eliminate the need for error correction
– How do we get accuracy? • With vector-error-corrected calibration • Not the same as the yearly instrument calibration
– What does calibration do for us? • Removes the largest contributor to measurement uncertainty: systematic errors Systematic error • Provides best picture of true performance of DUT
Page 52 Measurement Error Modeling
– Systematic errors • Due to imperfections in the analyzer and test setup • Assumed to be time invariant (predictable) • Generally, are largest sources or error – Random errors • Vary with time in random fashion (unpredictable) • Main contributors: instrument noise, switch and connector repeatability – Drift errors • Due to system performance changing after a calibration has been done Errors: • Primarily caused by SYSTEMATIC Measured Unknown temperature variation Data RANDOM Device DRIFT
Page 53 Systematic Measurement Errors
R A B Directivity Crosstalk
DUT
Frequency response Reflection tracking (A/R) Source Load Transmission tracking (B/R) Mismatch Mismatch
Six forward and six reverse error terms yields 12 error terms for two-port devices
Page 54 Types of Error Correction
– Response (normalization) • Simple to perform thru • Only corrects for tracking (frequency response) errors • Stores reference trace in memory, then does data divided by memory – Vector • Requires more calibration standards • Requires an analyzer that can measure phase • Accounts for all major sources of systematic error
SHORT
OPEN thru S11a LOAD S11m
Page 55 What is Vector-Error Correction? Errors
– Vector-error correction… Measured • Is a process for characterizing systematic error terms Actual • Measures known electrical standards • Removes effects of error terms from subsequent measurements
– Electrical standards… • Can be mechanical or electronic • Are often an open, short, load, and thru, but can be arbitrary impedances as well
Page 56 Using Known Standards to Correct for Systematic Errors
– 1-port calibration (reflection measurements) Only three systematic error terms measured Directivity, source match, and reflection tracking
– Full two-port calibration (reflection and transmission measurements) Twelve systematic error terms measured Usually requires 12 measurements on four known standards (SOLT)
– Standards defined in cal kit definition file Network analyzer contains standard cal kit definitions CAL KIT DEFINITION MUST MATCH ACTUAL CAL KIT USED! User-built standards must be characterized and entered into user cal-kit
Page 57 Reflection: One-Port Model
Error Adapter RF in Ideal RF in 1 ED = Directivity E = Reflection tracking S11 RT A ED ES S11A ES = Source Match S11M S11M S11M = Measured ERT S11A = Actual To solve for error terms, we measure 3 standards to generate S11A 3 equations and 3 unknowns S11M = ED + ERT 1 - ES S11A
– Assumes good termination at port two if testing two-port devices – If using port two of NA and DUT reverse isolation is low (e.g., filter passband): Assumption of good termination is not valid Two-port error correction yields better results
RF Back to Basics Page 58
58 Before and After A One-Port Calibration
Data after 1-port calibration
Data before 1-port calibration
Page 59 Two-Port Error Correction Reverse model Forward model Port 1 Port 2 E RT'
S Port 1 E X Port 2 21 A b a1 2 E L' S S E D' 11A 22 A E S' b b a 2 S 21 E TT 2 1 a A 1 E S E D S 11 S 22 a A A 2 E TT' S 12 A b1 E L E X'
E S 12 RT A S11m - ED S22m - ED ' S21m - E X S12m - E X ' ( )(1 ES ' ) - E L ( )( ) ERT ERT ' ETT ETT ' S11a = E D = fwd directivity E L = fwd load match S11m - ED' S22m - ED ' S21m - E X S12m - E X ' (1 ES )(1 ES ' ) - E L ' EL ( )( ) E S = fwd source match E TT = fwd transmission tracking ERT ERT ' ETT ETT ' E RT = fwd reflection tracking E X = fwd isolation S21m - E X S22m - ED ' = rev load match ( )(1 (E '-E )) E D' = rev directivity E L' E E ' S L S = TT RT E S' = rev source match E TT' = rev transmission tracking 21a S11m - ED S22m - ED' S21m - E X S12m - E X ' E E X' = rev isolation (1 ES )(1 ES ' ) - EL ' EL ( )( ) RT' = rev reflection tracking ERT ERT ' ETT ETT '
S12m - E X ' S11m - ED Each actual S-parameter is a function of ( )(1 (ES - EL ' )) ETT ' ERT S12a = all four measured S-parameters S11m - ED S22m - ED ' S21m - E X S12m - E X ' (1 ES )(1 ES ' ) - EL ' E L ( )( ) Analyzer must make forward and reverse ERT ERT ' ETT ETT '
sweep to update any one S-parameter S22m - ED ' S11m - ED S21m - E X S12m - E X ' ( )(1 ES ) - EL ' ( )( ) ERT ' ERT ETT ETT ' Luckily, you don't need to know these S22a = S11m - ED S22m - ED ' S21m - E X S12m - E X ' (1 ES )(1 ES ' ) - EL ' EL ( )( ) equations to use a network analyzers!!! ERT ERT ' ETT ETT '
Page 60 ECal: Electronic Calibration
– Variety of two- and four-port modules cover 300 kHz to 67 GHz – Nine connector types available, 50 and 75 ohms – Single-connection calibration dramatically reduces calibration time makes calibrations easy to perform minimizes wear on cables and standards eliminates operator errors – Highly repeatable temperature-compensated characterized terminations provide excellent accuracy USB Controlled
Microwave modules use a transmission line shunted by PIN-diode switches in various combinations
Page 61 Errors and Calibration Standards
UNCORRECTED RESPONSE 1-PORT FULL 2-PORT
SHORT SHORT SHORT
DUT OPEN OPEN OPEN thru LOAD Convenient LOAD LOAD Generally not accurate DUT No errors removed DUT Easy to perform thru Use when highest For reflection measurements accuracy is not Need good termination for DUT required high accuracy with two-port Highest accuracy Removes frequency devices response error Removes these Removes these errors: errors: Directivity Directivity ENHANCED-RESPONSE Source match Source, load match Reflection tracking Reflection tracking Combines response and 1-port Transmission Corrects source match for transmission tracking measurements Crosstalk
Page 62 Demonstration VNA showing Band Pass Filter Uncalibrated, Response Cal and Full 2 port calibration
Page 63 Wrap-Up Page 64
– Transmission Lines
– S-Parameters
– The Smith Chart
– Network Analysis Measurements
– Calibration and Error Correction For more information, www.keysight.com/find/na
Page 65