Keysight Technologies Network Analyzer Basics

Transmission Line Terminatedwith Short, OpenNext, let’s terminate our line in a short circuit.Since purely reactive elements cannot dissipate any power, and there is nowhere else forthe energy to go, a reflected wave is launchedback down the line toward the source. ForOhm’s law to be satisfied (no voltage acrossthe short), this reflected wave must be equal involtage magnitude to the incident wave, andbe 180 out of phase with it. This satisfies thecondition that the total voltage must equal zeroat the plane of the short circuit. Our reflectedand incident voltage (and current) waves willbe identical in magnitude but traveling in theopposite direction.Now let us leave our line open. This time,Ohm’s law tells us that the open can supportno current. Therefore, our reflected currentwave must be 180 out of phase with respectto the incident wave (the voltage wave will bein phase with the incident wave). This guarantees that current at the open will be zero.Again, our reflected and incident current (andvoltage) waves will be identical in magnitude,but traveling in the opposite direction. For boththe short and open cases, a standing-wavepattern will be set up on the transmission line.The valleys will be at zero and the peaks attwice the incident voltage level. The peaks andvalleys of the short and open will be shifted inposition along the line with respect to eachother, in order to satisfy Ohm’s law asdescribed above.12

Transmission LineTerminated with 25 ΩFinally, let’s terminate our line with a 25 Ωresistor (an impedance between the full reflection of an open or short circuit and the perfecttermination of a 50 Ω load). Some (but not all)of our incident energy will be absorbed in theload, and some will be reflected back towardsthe source. We will find that our reflected voltage wave will have an amplitude 1/3 that ofthe incident wave, and that the two waves willbe 180o out of phase at the load. The phaserelationship between the incident and reflectedwaves will change as a function of distancealong the transmission line from the load. Thevalleys of the standing-wave pattern will nolonger be zero, and the peak will be less thanthat of the short/open case.The significance of standing waves should notgo unnoticed. Ohm’s law tells us the complexrelationship between the incident and reflectedsignals at the load. Assuming a 50-ohmsource, the voltage across a 25-ohm loadresistor will be two thirds of the voltage acrossa 50-ohm load. Hence, the voltage of thereflected signal is one third the voltage of theincident signal and is 180 out of phase with it.However, as we move away from the loadtoward the source, we find that the phasebetween the incident and reflected signalschanges! The vector sum of the two signalstherefore also changes along the line, producing the standing wave pattern. The apparentimpedance also changes along the linebecause the relative amplitude and phase ofthe incident and reflected waves at any givenpoint uniquely determine the measured impedance. For example, if we made a measurementone quarter wavelength away from the 25-ohmload, the results would indicate a 100-ohmload. The standing wave pattern repeatsevery half wavelength, as does the apparentimpedance.13

High-FrequencyDevice CharacterizationNow that we fully understand the relationshipof electromagnetic waves, we must alsorecognize the terms used to describe them.Common network analyzer terminology hasthe incident wave measured with the R (forreference) receiver. The reflected wave is measured with the A receiver and the transmittedwave is measured with the B receiver. Withamplitude and phase information of thesethree waves, we can quantify the reflectionand transmission characteristics of our deviceunder test (DUT). Some of the common measured terms are scalar in nature (the phasepart is ignored or not measured), while othersare vector (both magnitude and phase are measured). For example, return loss is a scalarmeasurement of reflection, while impedanceresults from a vector reflection measurement.Some, like group delay, are purely phaserelated measurements.Ratioed reflection is often shown as A/R andratioed transmission is often shown as B/R,relating to the measurement receivers usedin the network analyzer14

Reflection ParametersLet’s now examine reflection measurements.The first term for reflected waves is reflectioncoefficient gamma (ΓΓ). Reflection coefficient isthe ratio of the reflected signal voltage to theincident signal voltage. It can be calculatedas shown above by knowing the impedancesof the transmission line and the load. Themagnitude portion of gamma is called rho (ρ).A transmission line terminated in Zo will haveall energy transferred to the load; henceVrefl 0 and ρ 0. When ZL is not equal to Zo,some energy is reflected and ρ is greater thanzero. When ZL is a short or open circuit, allenergy is reflected and ρ 1. The range ofpossible values for ρ is therefore zero to one.Since it is often very convenient to showreflection on a logarithmic display, the secondway to convey reflection is return loss. Returnloss is expressed in terms of dB, and is a scalarquantity. The definition for return loss includesa negative sign so that the return loss value isalways a positive number (when measuringreflection on a network analyzer with a logmagnitude format, ignoring the minus signgives the results in terms of return loss).Return loss can be thought of as the numberof dB that the reflected signal is below theincident signal. Return loss varies betweeninfinity for a Zo impedance and 0 dB for anopen or short circuit.As we have already seen, two waves traveling inopposite directions on the same transmissionline cause a “standing wave”. This conditioncan be measured in terms of the voltagestanding-wave ratio (VSWR or SWR for short).VSWR is defined as the maximum value of theRF envelope over the minimum value of theenvelope. This value can be computed as(1 ρ)/(1–ρ). VSWR can take ?15

impedance graphically? Since there is a one-toone correspondence between complex reflection coefficient and impedance, we can mapone plane onto the other. If we try to map thepolar plane onto the rectilinear impedanceplane, we find that we have problems. First ofall, the rectilinear plane does not have valuesto infinity. Second, circles of constant reflection coefficient are concentric on the polarplane but not on the rectilinear plane, makingit difficult to make judgments regarding twodifferent impedances. Finally, phase anglesplot as radii on the polar plane but plot asarcs on the rectilinear plane, making it difficultto pinpoint.Smith Chart ReviewOur network analyzer gives us complex reflection coefficient. However, we often want toknow the impedance of the DUT. The previousslide shows the relationship between reflectioncoefficient and impedance, and we could manually perform the complex math to find theimpedance. Although programmable calculators and computers take the drudgery outof doing the math, a single number does notalways give us the complete picture. In addition, impedance almost certainly changes withfrequency, so even if we did all the math, wewould end up with a table of numbers thatmay be difficult to interpret.A simple, graphical method solves this problem. Let’s first plot reflection coefficient usinga polar display. For positive resistance, theabsolute magnitude of varies from zero(perfect load) to unity (full reflection) at someangle. So we have a unit circle, which marksthe boundary of the polar plane shown on theslide. An open would plot at 1 0o; a short at1 180o; a perfect load at the center, and soon. How do we get from the polar data to16The proper solution was first used in the1930’s, when Phillip H. Smith mapped theimpedance plane onto the polar plane, creatingthe chart that bears his name (the venerableSmith chart). Since unity at zero degreeson the polar plane represents infinite impedance, both plus and minus infinite reactances,as well as infinite resistance can be plotted.On the Smith chart, the vertical lines onthe rectilinear plane that indicate values ofconstant resistance map to circles, and thehorizontal lines that indicate values of constantreactance map to arcs. Zo maps to the exactcenter of the chart.In general, Smith charts are normalized to Zo;that is, the impedance values are divided byZo. The chart is then independent of the characteristic impedance of the system in question.Actual impedance values are derived by multiplying the indicated value by Zo. For example,in a 50-ohm system, a normalized value of0.3 - j0.15 becomes 15 - j7.5 ohms; in a75-ohm system, 22.5 - j11.25 ohms.Fortunately, we no longer have to go throughthe exercise ourselves. Out network analyzercan display the Smith chart, plot measureddata on it, and provide adjustable markers thatshow the calculated impedance at the markedpoint in several marker formats.

Transmission ParametersTransmission coefficient is defined as thetransmitted voltage divided by the incidentvoltage. If Vtrans Vinc , the DUT has gain,and if Vtrans Vinc , the DUT exhibits attenuation or insertion loss. When insertion lossis expressed in dB, a negative sign is addedin the definition so that the loss value isexpressed as a positive number. The phaseportion of the transmission coefficient is calledinsertion phase. There is more to transmissionthan simple gain or loss. In communicationssystems, signals are time varying —they occupya given bandwidth and are made up of multiplefrequency components. It is important thento know to what extent the DUT alters themakeup of the signal, thereby causing signaldistortion. While we often think of distortion asonly the result of nonlinear networks, we willsee shortly that linear networks can also causesignal distortion.17

Linear VersusNonlinear Behavior–Before we explore linear signal distortion, letsreview the differences between linear and nonlinear behavior. Devices that behave linearlyonly impose magnitude and phase changes oninput signals. Any sinusoid appearing at theinput will also appear at the output at the samefrequency. No new signals are created. Whena single sinusoid is passed through a linearnetwork, we don’t consider amplitude andphase changes as distortion. However, when acomplex, time-varying signal is passed througha linear network, the amplitude and phaseshifts can dramatically distort the timedomain waveform.–––Non-linear devices can shift input signals infrequency (a mixer for example) and/or createnew signals in the form of harmonics or intermodulation products. Many components thatbehave linearly under most signal conditionscan exhibit nonlinear behavior if driven witha large enough input signal. This is true forboth passive devices like filters and evenconnectors, and active devices like amplifiersCriteria for DistortionlessTransmissionNow lets examine how linear networks cancause signal distortion. There are three criteriathat must be satisfied for linear distortionlesstransmission. First, the amplitude (magnitude)response of the device or system must be flatover the bandwidth of interest. This means allfrequencies within the bandwidth will be attenuated identically. Second, the phase responsemust be linear over the bandwidth of interest.And last, the device must exhibit a “minimumphase response”, which means that at 0 Hz (DC),there is 0 phase shift (0o n*180 is okay ifwe don’t mind an inverted signal).How can magnitude and phase distortion occur?The following two examples will illustratehow both magnitude and phase responsescan introduce linear signal distortion.18

Magnitude Variationwith FrequencyHere is an example of a square wave (consisting of three sinusoids) applied to a bandpassfilter. The filter imposes a non-uniform amplitude change to each frequency component.Even though no phase changes are introduced,the frequency components no longer sum to asquare wave at the output. The square wave isnow severely distorted, having become moresinusoidal in nature.Phase Variationwith FrequencyLet’s apply the same square wave to anotherfilter. Here, the third harmonic undergoes a180 phase shift, but the other componentsare not phase shifted. All the amplitudes of thethree spectral components remain the same(filters which only affect the phase of signalsare called allpass filters). The output is againdistorted, appearing very impulsive this time.19

Deviation From Linear PhaseNow that we know insertion phase versus frequency is a very important characteristic of acomponent, let’s see how we would measureit. Looking at insertion phase directly is usuallynot very useful. This is because the phase has anegative slope with respect to frequency due tothe electrical length of the device (the longerthe device, the greater the slope). Since it isonly the deviation from linear phase whichcauses distortion, it is desirable to remove thelinear portion of the phase response. This canbe accomplished by using the electrical delayfeature of the network analyzer to cancel theelectrical length of the DUT. This results in ahigh-resolution display of phase distortion(deviation from linear phase).Group DelayAnother useful measure of phase distortion isgroup delay. Group delay is a measure of thetransit time of a signal through the deviceunder test, versus frequency. Group delay iscalculated by differentiating the insertion phaseresponse of the DUT versus frequency. Anotherway to say this is that group delay is a measureof the slope of the transmission phase response.The linear portion of the phase response isconverted to a constant value (representing theaverage signal-transit time) and deviations fromlinear phase are transformed into deviationsfrom constant group delay. The variations ingroup delay cause signal distortion, just asdeviations from linear phase cause distortion.Group delay is just another way to look atlinear phase distortion.–––When specifying or measuring group delay,it is important to quantify the aperture in whichthe measurement is made. The aperture isdefined as the frequency delta used in thedifferentiation process (the denominator inthe group-delay formula). As we widen theaperture, trace noise is reduced but lessgroup-delay resolution is available (we areessentially averaging the phase response overa wider window). As we make the aperturemore narrow, trace noise increases but wehave more measurement resolution.20

Why Measure Group Delay?Why are both deviation from linear phase andgroup delay commonly measured? Dependingon the device, both may be important.Specifying a maximum peak-to-peak valueof phase ripple is not sufficient to completelycharacterize a device since the slope of thephase ripple is dependent on the number ofripples which occur over a frequency range ofinterest. Group delay takes this into accountsince it is the differentiated phase response.Group delay is often a more easily interpretedindication of phase distortion.The plot above shows that the same valueof peak-to-peak phase ripple can result insubstantially different group delay responses.The response on the right with the largergroup-delay variation would cause moresignal distortion.CharacterizingUnknown DevicesIn order to completely characterize anunknown linear two-port device, we mustmake measurements under various conditionsand compute a set of parameters. Theseparameters can be used to completelydescribe the electrical behavior of our device(or network), even under source and loadconditions other than when we made our measurements. For low-frequency characterizationof devices, the three most commonly measuredparameters are the H, Y and Z-parameters.All of these parameters require measuringthe total voltage or current as a function offrequency at the input or output nodes (ports)of the device. Furthermore, we have to applyeither open or short circuits as part of themeasurement. Extending measurements ofthese parameters to high frequencies is notvery practical.21

Why Use S-Parameters?–––––At high frequencies, it is very hard to measuretotal voltage and current at the device ports.One cannot simply connect a voltmeter orcurrent probe and get accurate measurementsdue to the impedance of the probes themselvesand the difficulty of placing the probes at thedesired positions. In addition, active devicesmay oscillate or self-destruct with the connection of shorts and opens.---Clearly, some other way of characterizinghigh-frequency networks is needed thatdoesn’t have these drawbacks. That is whyscattering or S-parameters were developed.S-parameters have many advantages over thepreviously mentioned H, Y or Z-parameters.They relate to familiar measurements such asgain, loss, and reflection coefficient. They aredefined in terms of voltage traveling waves,which are relatively easy to measure.S-parameters don’t require connection ofundesirable loads to the device under test. Themeasured S-parameters of multiple devicescan be cascaded to predict overall system performance. If desired, H, Y, or Z-parameterscan be derived from S-parameters. And veryimportant for RF design, S-parameters areeasily imported and used for circuit simulationsin electronic-design automation (EDA) toolslike the Keysight Technologies, Inc. AdvancedDesign System (ADS). S-parameters arethe shared language between simulationand measurement.An N-port device has N2 S-parameters. So, atwo-port device has four S-parameters. Thenumbering convention for S-parameters is thatthe first number following the “S” is the portwhere the signal emerges, and the secondnumber is the port where the signal is applied.So, S21 is a measure of the signal coming outport 2 relative to the RF stimulus entering port1. When the numbers are the same (e.g., S11),it indicates a reflection measurement, as theinput and output ports are the same. Theincident terms (a1, a2) and output terms(b1, b2) represent voltage traveling waves.22

Measuring S-ParametersS11 and S21 are determined by measuring themagnitude and phase of the incident, reflectedand transmitted voltage signals when the output is terminated in a perfect Zo (a load thatequals the characteristic impedance of the testsystem). This condition guarantees that a2 iszero, since there is no reflection from an idealload. S11 is equivalent to the input complexreflection coefficient or impedance of the DUT,and S21 is the forward complex transmissioncoefficient. Likewise, by placing the source atport 2 and terminating port 1 in a perfect load(making a1 zero), S22 and S12 measurementscan be made. S22 is equivalent to the outputcomplex reflection coeff

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