WIXLIB

Network Analyzer Basics- EE142 Fall 07Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Lightwave Analogy to RF twork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Why Do We Need to Test Components? Verify specifications of “building blocks” for more complex RF systemsCreate models for simulationCheck our simulation models against a real circuitEnsure good match when absorbingpower (e.g., an antenna)KPWRNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142FM 97

The Need for Both Magnitude and PhaseS211. Complete characterizationof linear networksS11S22S122. Complex impedance neededto design matching circuits4. Time-domain characterizationMag3. Complex values neededfor device modelingTime5. Vector-error correctionHigh-frequency transistor modelErrorBaseCollectorEmitterNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142MeasuredActual

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 wireHigh frequencies wavelength or length of transmission medium need transmission lines for efficient power transmission matching to characteristic impedance (Zo) is very importantfor low reflection and maximum power transfer measured envelope voltage dependent on position along lineNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Transmission line Zo Zo determines relationship between voltage and current wavesZo is a function of physical dimensions and εrZo is usually a real impedance (e.g. 50 or 75 ohms)1.5Twisted-pairattenuation is lowest at77 ohms1.4Waveguide1.3abCoaxialεrhnormalized values1.250 ohm standard1.11.00.90.8hpower handling capacity peaksat 30 ohms0.7w10.6ww20.510CoplanarNetwork Analyzer BasicsJoel DunsmoreCopyright 2007203040characteristic impedancefor coaxial airlines (ohms)MicrostripEECS1425060 70 80 90 100

Power Transfer EfficiencyRSFor complex impedances, maximum powertransfer occurs when ZL ZS* (conjugate match)RLRs1.2 jXLoad Power(normalized)1-jX0.80.6RL0.40.20012345678910RL / RSMaximum power is transferred when RL RSNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Transmission Line Terminated with ZoZs ZoZo characteristic impedanceof transmission lineZoV incVrefl 0! (all the incident poweris absorbed in the load)For reflection, a transmission line terminated in Zobehaves like an infinitely long transmission lineNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Transmission Line Terminated with Short, OpenZs ZoV incVreflIn-phase (0o) for open,out-of-phase (180o) for shortFor reflection, a transmission line terminated ina short or open reflects all power back to sourceNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Transmission Line Terminated with 25 ΩZs ZoZL 25 ΩV incVreflStanding wave pattern does notgo to zero as with short or openNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

High-Frequency Device NSMISSIONREFLECTIONReflectedIncident SWRS-ParametersS11, S22Network Analyzer BasicsJoel DunsmoreCopyright 2007ReflectionCoefficientΓ, nceR jX,G jB BRGroupDelayGain / LossS-ParametersS21, se

Reflection ParametersReflectionCoefficientΓVreflected ρVincidentReturn loss -20 log(ρ),ρΦ EmaxEmin ZL ZOZ L ZOΓVoltage Standing Wave RatioVSWR EmaxEmin 1 ρ1-ρFull reflection(ZL open, short)No reflection(ZL Zo)0ρ1 dBRL0 dB1VSWR Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Transmission ParametersVVIncidentDUTTransmission Coefficient ΤVInsertion Loss (dB) - 20 LogVVGain (dB) 20 LogVNetwork Analyzer BasicsJoel DunsmoreCopyright 2007TransV TransmittedTransmittedVTransIncident - 20 logInc 20 logIncEECS142 τττ φ

Linear Versus Nonlinear BehaviorA * Sin 360o * f (t - to)ALinear behavior: Timeto Sin 360o * f * tATimef1phase shift to * 360o * fDUTInputinput and output frequencies are the same(no additional frequencies created)output frequency only undergoesmagnitude and phase changeFrequencyOutputNonlinear behavior:f1 FrequencyTime fNetwork Analyzer BasicsJoel DunsmoreCopyright 2007Frequency1EECS142output frequency may undergofrequency shift (e.g. with mixers)additional frequencies created(harmonics, intermodulation)

Criteria for Distortionless TransmissionLinear NetworksLinear phase overbandwidth of interestConstant amplitude overbandwidth of interestPhaseMagnitudeFrequencyFrequencyNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Magnitude Variation with FrequencyF(t) sin wt 1/3 sin 3wt 1/5 sin 5wtTimeTimeMagnitudeLinear NetworkFrequencyNetwork Analyzer BasicsJoel DunsmoreCopyright 2007FrequencyEECS142Frequency

Phase Variation with FrequencyF(t) sin wt 1 /3 sin 3wt 1 /5 sin 5wtLinear NetworkTimeMagnitudeTimeFrequency0 FrequencyFrequency-180 -360 Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Deviation from Linear PhaseUse electrical delay to removelinear portion of phase responseRF filter responseLinear electrical length addedDeviation from linear phasePhase 1 /DivooPhase 45 /Div(Electrical delay function) FrequencyyieldsFrequencyLow resolutionNetwork Analyzer BasicsJoel DunsmoreCopyright 2007FrequencyHigh resolutionEECS142

Group DelayFrequencyωtgGroup delay ripple ωPhasetoφAverage delay φFrequencyGroup Delay (t ) g d φdωφωφ 1360o*dφdf in radians in radians/sec group-delay ripple indicates phase distortionaverage delay indicates electrical length of DUTaperture of measurement is very importantin degreesf in Hertz (ω 2 π f)Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

PhasePhaseWhy Measure Group Delay?ff d φdωGroupDelayGroup Delay d φdωfSame p-p phase ripple can result in different group delayNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142f

Characterizing Unknown DevicesUsing parameters (H, Y, Z, S) to characterize devices: gives linear behavioral model of our devicemeasure parameters (e.g. voltage and current) versus frequency undervarious source and load conditions (e.g. short and open circuits)compute device parameters from measured datapredict circuit performance under any source and load conditionsH-parametersV1 h11I1 h12V2I2 h21I1 h22V2Network Analyzer BasicsJoel DunsmoreCopyright 2007Y-parametersI1 y11V1 y12V2I2 y21V1 y22V2Z-parametersV1 z11I1 z12I2V2 z21I1 z22I2h11 V1I1V2 0(requires short circuit)h12 V1V2I1 0(requires open circuit)EECS142

Why Use S-Parameters?relatively easy to obtain at high frequencies measure voltage traveling waves with a vector network analyzer don't need shorts/opens which 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 our electronic-simulation tools a1S 21IncidentTransmittedb2S 11ReflectedDUTb1TransmittedS 22ReflectedPort 2Port 1S 12Incidentb 1 S 11 a 1 S 12 a 2b 2 S 21 a 1 S 22 a 2Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142a2

Measuring S-Parametersa1ForwardS 11 S 21 SbSIncidentIncidenta2 0b1 a1ba2 0S 22 2 a1a2 0S 12 a1 entSDUTb2 a2bEECS142a1 0b222Reversea212a1 01 a2ReflectedLoadNetwork Analyzer BasicsJoel DunsmoreCopyright dentbTransmitted21Incident

Equating S-Parameters with CommonMeasurement TermsS11 forward reflection coefficient (input match)S22 reverse reflection coefficient (output match)S21 forward transmission coefficient (gain or loss)S12 reverse transmission coefficient (isolation)Remember, S-parameters are inherentlycomplex, linear quantities -- however, weoften express them in a log-magnitude formatNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Generalized Network Analyzer Block SEPARATIONINCIDENT (R)REFLECTED(A)TRANSMITTED(B)RECEIVER / DETECTORPROCESSOR / DISPLAYNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Source Supplies stimulus for systemSwept frequency or powerTraditionally NAs used separate sourceMost Agilent analyzers sold today haveintegrated, synthesized sourcesNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

IncidentTransmittedDUTSignal SeparationReflectedSOURCESIGNALSEPARATIONINCIDENT (R)REFLECTED(A)TRANSMITTED(B)RECEIVER / DETECTORPROCESSOR / DISPLAYmeasure incident signal for reference separate incident and reflected signals splitterbridgeDetectordirectionalcouplerNetwork Analyzer BasicsJoel DunsmoreCopyright 2007Test PortEECS142

Consider the Wheatstone Bridge:If the bridge is balanced Vd Vd-, and Idet 0Vd R1 R 4R2 VinR3 Vin Then; Vd R2R3R1 R 2R3 R 4 I det 0VinIdetFurther, it can be shown, that the input impedance of abalanced bridge follows the equation: Zin 2 R1 R3 R2 R 4Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

We can morph this Wheatstone Bridge into a “Directional Bridge”with explicit ports by noting that the floating voltage source can bereplaced with a transformer coupled port, and Rdet can beconnected through a transmission line (representing a cable or port)RsR1Vd R4Vd-VsR2R3Isolated PortNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

We would like the bridge to be matched so Rs2 R1*R3 R2*R4.In this condition, Vin Vs/2.If we fix R4 Rs, then R2 Rs as well, and we can replace R4 witha transmission line or cable of impedance Rs. Now we have threewell defined ports, and we can see that the port replacing thedetector port is isolated.Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

So, in the isolation direction it is clear that no signal appears atthe isolated port, as the current divides equally across the bridge,if the test port is terminated in RsNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Now we can set the forward loss of the bridge. The voltage onthe test port is equal to the voltage across R1. We have completeflexibility to set any ratio we want. In this case let’s choose thevoltage to be 5/6 of Vin. Then Vd Vd- (1/6)Vin. The loss fromInput Port to output port is 20*log(5/6) -1.58 dB.These are quite convenient values: R4 50 - R2 50R1/(R2 R1) 5/6 - R1 5*R2 250;And because R1*R3 R2*R4 - R3 10;Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Now lets look how to “reverse” the power flow, and see what couplesinto the isolated port (we’ll now call it the Coupled Port) when we putthe source at the test port, and redraw the figure (no connectionchanges) to highlight the coupled port.Now the coupled port appears in oneleg of the bridge. Next we’ll move thesource from the input to the test port(and make the input into a port as well)Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Finally, we can compute the coupling factor of the bridge. In thecoupling direction, the voltage across the coupled port is 1/6 *VTP,or -15.5 dB. We can set either the loss of the bridge or thecoupling, but once we set one, the other is determined.Network Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Just as clearly, with the signal driven from the test port, there willbe the same loss to the Input Port as there was in the otherdirection, but now the signal will be coupled to the Coupled PortNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Let’s check two cases: Assume the test port is open circuit (R4infinite), then the voltage at the isolated point will be(1/2)*(5/6)*(1/6)*Vs, exactly the same as the combination of lossand coupling, assuming a total reflection at the test port.RsR1Test PortOpenVd VsInput PortR2R3Isolated PortNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142

Now Assume the test port is short circuit (R4 0). Surprisingly (ornot, if you’re a real electrical engineer) the voltage at the isolatedport will be (1/2)*(5/6)*(1/6)*Vs, exactly the same as the open, butwith a sign change! Thus it is again the combination of loss andcoupling, assuming a total reflection at the test port, but thereflection is negative.RsR1Test PortShortVd VsInput PortR2R3Isolated PortNetwork Analyzer BasicsJoel DunsmoreCopyright 2007EECS142