VNA Fundamentals Primer (Rohde Schwarz)

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    Fundamentals ofVector NetworkAnalysisPrimer

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    Fundamentals of Vector Network AnalysisVersion 1.1Published by Rohde & Schwarz USA, Inc.6821 Benjamin Franklin Drive, Columbia, MD 21046

    R&S is a registered trademark of Rohde & SchwarzGmbH&Co. KG. Trade names are trademarks of the owners

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    Contents

    Introduction ................. ................... ................... .................. .. 4

    What is a network analyzer? ................ ................... ........ 4

    Wave quantities and S-parameters .................. .............. 4

    Why vector network analysis? ................. .................. ..... 6

    A circuit example ................. ................... .................. ..... 7

    Design of a heterodyne Nport network analyzer ........... 10

    Block diagram ................. .................. ................... ......... 10

    Design of the test set .................. ................... ............... 11

    Constancy of the a wave ................ ................... ...... 11

    Re ection tracking ................................................... 12 Directivity .................. ................... ................... ......... 12

    Test port match and multiple re ections ................. 14

    Summary................... ................... ................... ......... 15

    Generator....................................................................... 16

    Reference and measurement receiver ................. ......... 16

    Measurement accuracy and calibration ................. ............ 19

    Reduction of random measurement errors ................ ... 19

    Thermal drift ................ ................... ................... ...... 19

    Noise ................... ................... ................... ............... 21

    Correction of systematic measurement errors .............. 22

    Nonlinear in uences............................................... 22

    Linear in uences..................................................... 23

    Calibration standards ................. ................... ................ 24

    Practical hints for calibration ................. ................... .... 2

    Linear measurements ................. .................. ................... .... 2

    Performing a TOM calibration ................ ................... .... 2

    Performing a TNA calibration ................. ................... .... 2

    Measurement of the re ection coef cient & the SWR 30

    Measurement of the transmission coef cient .............. 34 Measurement of the group delay ................. ................ 35

    Time-domain measurements .................. ................... .......... 38

    Time-domain analysis ................... ................... ............. 3

    Impulse and step response ................. ................... . 38

    Time-domain analysis of linear RF networks ......... 3

    Time domain measurement example ................. .......... 40

    Distance-to-fault measurement and gating ............ 40

    Conclusion ................. ................... .................. ................... . 4

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    Introduction

    What is a Network Analyzer?One of the most common measuring tasks in RF engi-

    neering involves analysis of circuits (networks). A net-work analyzer is an instrument that is designed to handlethis job with great precision and ef ciency. Circuits thatcan be analyzed using network analyzers range fromsimple devices such as lters and ampli ers to complexmodules used in communications satellites.

    A network analyzer is the most complex and versatilepiece of test equipment in the eld of RF engineering. Itis used in applications in research and development andalso for test purposes in production. When combinedwith one or more antennas, it becomes a radar system.Systems of this type can be used to detect invisible ma-terial defects without resorting to X-ray technology. Usingdata recorded with a network analyzer, imaging tech-niques were used to produce the following gure whichshows a typical material defect. (Figure 1.1.2)

    A similar system can be used to verify the radar visibilitywhich forms the basis for a dependable ight controlsystem. For such purpose the radar cross section (RCS)of an aircraft is an important quantity. It is typically mea-sured on a model of the aircraft like the following result.(Figure 1.1.3)

    For measurements with less demanding technical re-quirements such as measurement of a ll level without

    physical contact or determination of the thickness oflayers of varnish, simpler approaches are generally used.

    Wave Quantities and S-ParametersThe so-called wave quantities are preferred for use incharacterizing RF circuits. We distinguish between theincident wave a and the re ected wave b . The incidentwave propagates from the analyzer to the device undertest (DUT). The re ected wave travels in the oppositedirection from the DUT back to the analyzer. In the fol-lowing gures, the incident wave is shown in green andthe re ected wave in orange. Fig. 1.2.1 shows a one-portdevice with its wave quantities.

    The true power traveling to the one-port device is givenby |a| 2 and the true power it re ects by |b| 2. The re ectioncoef cient represents the ratio of the incident wave tothe re ected wave.

    = b/a (1.2-1)

    It is generally a complex quantity and can be calculatedfrom the complex impedance Z. With a reference imped -ance of typically Z 0 = 50

    1, the normalized impedance

    Fig. 1.1.2 Material defect Fig. 1.1.3 ISAR image of aBoeing 747 model

    Fig. 1.2.1 One-port device withincident and re ected waves.

    1) In RF engineering and RF measurement a reference impedance of 50 is used. In broadcasting systems a reference impedance of 75 is preferred. The impedance of

    50 offers a compromise which is closely related to coaxial transmission lines. By varying the inner and out conductor diameter of a coaxial transmission line we achieve

    its minimum attenuation at a characteristic impedance of 77 and its maximum power handling capacity at 30 .

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    z = Z/Z 0 is de ned and used to determine the re ectioncoef cient.

    = z-1/z+1 (1.2-2)

    The re ection coef cient can be represented in thecomplex re ection coef cient plane. To draw the normal -ized impedance z = 2 + 1.5j as point 1 in this plane, wetake advantage of the auxiliary coordinate system shownin Fig. 1.2.2 which is known as the Smith chart. Theshort-circuit point, open-circuit point and matching pointare drawn in as examples. (Figure 1.2.2)

    In a two-port device, besides the re ection at the twoports, there is also the possibility of transmission in theforward and reverse directions. (Figure 1.2.3)

    In comparison to the re ection coef cient, the scatteringparameters (S-parameters) s 11 , s 12 , s 21 and s 22 are de nedas the ratios of the respective wave quantities. For theforward measurement, a re ection free termination = 0(match) is used on port 2. This means that a 2 = 0. Port 1is stimulated by the incident wave a 10. (Figure 1.2.4)

    Under these operating conditions, we measure the inputre ection coef cient s 11 on port 1 and the forward trans-mission coef cient s 21 between port 1 and port 2.

    For the reverse measurement, a match = 0 is used onport 1 (a 1= 0). Port 2 is stimulated by the incident wavea20. (Figure 1.2.5)

    Under these operating conditions, we measure theoutput re ection coef cient s 22 on port 2 and the reversetransmission coef cient s 12 between port 2 and port 1.

    Fig. 1.2.2 Smith chartwith sample points.

    Fig. 1.2.3 Two-port devicewith its wave quantities.

    Fig. 1.2.4 Two-port device duringforward measurement.

    (1.2-3)

    Fig. 1.2.5 Two-port device duringreverse measurement.

    (1.2-4)

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    Why Vector Network Analysis?A network analyzer generates a sinusoidal test signal that

    is applied to the DUT as a stimulus (e.g. a 1). Consideringthe DUT to be linear, the analyzer measures the responseof the DUT (e.g. b 2) which is also sinusoidal. Fig. 1.3.1shows an example involving wave quantities a 1 and b 2 .They will generally have different values for the amplitudeand phase. In this example, the quantity s 21 representsthese differences.

    A scalar network analyzer only measures the amplitudedifference between the wave quantities. A vector networkanalyzer (VNA) requires a signi cantly more compleximplementation. It measures the amplitude and phase ofthe wave quantities and uses these values to calculate acomplex S-parameter. The magnitude of the S-parameter(e.g. |s 21 |) corresponds to the amplitude ratio of the wavequantities (e. g. b 2 and 1). The phase of the S-param-eter (e.g. arg(s 21)) corresponds to the phase differencebetween the wave quantities. This primer only considersvector network analysis due to the following bene ts itoffers:

    J Only a vector network analyzer can perform fullsystem error correction. This type of correctioncompensates the systematic measurementerrors of the test instrument with the greatestpossible precision.

    J Only vectorial measurement data can beunambiguously transformed into the time domain.This opens up many opportunities for interpretationand further processing of the data.

    In general both incident waves can be non-zero (a 1 0and a 2 0). This case can be considered as a superposi -

    tion of the two measurement situations a 1 = 0 and a 2 0with a 1 0 and a 2 = O. This results in the following:

    b1 = s 11 a 1 + s 12a2b2 = s 21 a 1 + s 22a2 (1.2-5)

    We can also group together the scattering parameterss 11 , s 12 , s 21 and s 22 to obtain the S-parameter matrix(S-matrix) and the wave quantities to obtain the vectorsa and b . This results in the following more compactnotation:

    B = Sa (1.2-7)

    Many standard components can be represented as one-or two-port networks. However, as integration increases,

    DUTs with more than two ports are becoming more com-monplace so that the term N-port has been introduced.For example, a three-port network (N = 3) is character-ized by the following equations:

    b1 = s 11a1 + s 12a2 + s 13a3b2 = s 21a1 + s 22a2 + s 23a3 (1.2-8)b3 = s 31a1 + s 32a2 + s 33a3

    The shorter notation (1.2-7) is also valid for a three-portnetwork. In formula (1.2-6), all that is required is expan -

    sion of the vectors a and b to three elements. The associ-ated S-matrix has 3 x 3 elements. The diagonal elementss11 , s 22 and s 33 correspond to the re ection coef cientsfor ports 1 to 3 which can be measured in case of re ec -tion-free termination on all ports with = 0. For the sameoperating case, the remaining elements characterize thesix possible transmissions. The characterizations can beextended in a similar manner for N > 3.

    (1.2-6)

    Fig. 1.3.1 Signals a 1 and b 2 .

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    J Deembedding and embedding are specialprocessing techniques that enable computationalcompensation of a test xture or computationalembedding into a network that is not physicallypresent. Both of these techniques require vectorialmeasurement data.

    J For presentation in Smith charts, it is necessary toknow the re ection coef cient vectorially.

    There are two common approaches for building vectornetwork analyzers.

    J Network analyzers based on the homodyne principleonly have a single oscillator. This oscillator providesthe stimulus signal and is also used to process theresponse. Most analyzers based on this principle arerelatively economical. However, due to their varioustechnical limitations, they are suited only for simpleapplications, e.g. for measuring ll levels based on

    the radar principle.

    J Precise investigation of circuits requires networkanalyzers that are based on the heterodyne principle.The network analyzer family described in this primeris based on this principle which is discussed ingreater detail in section 2.6.

    A Circuit ExampleFig. 1.4.1 shows a circuit that is commonly used in RFengineering: a frequency converter. This module con-verts a frequency f RF in the range from 3 GHz to 7 GHz toa xed intermediate frequency f IF = 404.4 MHz. To ensureunambiguity of the received frequency, a tunable band-pass lter (1) at the start of the signal processing chain

    is used. The ltered signal is fed via a semi-rigid cable (2) to a mixer (3) which converts the signal from frequencyfRF to frequency ~F A switchable attenuator (4) is usedto set the IF level. The LO signal required by the mixer isprepared using several ampli ers (5), a frequency doubler(6) and a bandpass lter (7). The module itself is con-trolled via a 48-pin interface and is commonly used in testreceivers and spectrum analyzers.

    Fig. 1.4.1A frequencyconverter module

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    Fig. 1.4.2 Input and output

    re ection coef cients ofthe tunable bandpass lter.

    Fig. 1.4.3 Forwardtransmission and phase oftransmission coef cient s 21 for the bandpass lter.

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    A network analyzer is useful, for example, for investigat -ing the tunable bandpass lter (1). The test ports of the

    network analyzer were connected to ports (1) and (2) ofthe lter. Fig. 1.4.2 shows the input and output re ectioncoef cients of the lter.

    The results were measured in the range from 3.8 GHz to4.2 GHz: Markers were used to precisely read off selectedmeasurement results. The term bandpass lter is derivedfrom the forward transmission shown in Figure 1.4.3.

    Besides these examples, there are many other measure -ments that we can conceivably make on the module in

    Fig. 1.4.1. The following table provides a brief summaryof some of the possibilities. (Table 1.4.1)

    Table 1.4.1 Usage of different measure- ments with typical DUTs in Fig 1.4.1.

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    The information contained in this primer is based on aheterodyne vector network analyzer. Due to the increas-ing importance of N-port DUTs, we will assume there arean arbitrary number of N ports.

    Block DiagramThe block diagram in Fig. 2.1.1 has four main components:

    J The test set separates the incident and re ectedwaves at the test port. The waves are fed to thereference channel or to the measurement channel.Electronic attenuators are used to vary the test portoutput power. Any generator step attenuators thatmight be present extend the lower limit of the outputpower range.

    Design of a HeterodyneNPort Network Analyzer

    J The generator provides the RF signal which we referto as the stimulus. The source switch which is usedwith the generator passes the stimulus signal to oneof the test ports which is then operated as an active

    test port.

    J Each test set is combined with two separatereceivers for the measurement channel and thereference channel. They are referred to as themeasurement receiver and the reference receiver 1,They consist of an RF signal section (heterodyneprinciple) and a digital signal processing stage.At the end of the stage, we have raw measurementdata in the form of complex numerical values.

    Fig. 2.1.1 Standard blockdiagram of an N-portvector network analyzer.

    1) In place of measurement channel the term test channel is also common. Furthermore the measurement receiver is also called test receiver.

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    J A computer is used to do the system errorcorrection and to display the measurement data. It

    also provides the user interface and the remotecontrol interfaces. The preinstalled software isknown as the rmware.

    In the rest of this section, we will examine the individualcomponents starting with the test set and continuingthrough the instrument and ending at the display of themeasured data.

    Design of the Test SetMeasuring the re ection coef cient DUT requires separa-tion of the incident and re ected waves traveling to andfrom the DUT. A directional element is required for thispurpose. In the following discussion, it is described as athree-port device.

    In gure 2.2.1, the two main signal directions of thedirectional element are shown in color. The wave a 1 produced by the generator is forwarded to port (2) withtransmission coef cient s 21, where it leaves the elementas wave b 2. In the case of a one-port DUT, the wave b DUT

    arises from the wave a DUT due to re ection with there ection coef cient DUT.

    bDUT = DUT a DUT (2.2-1)

    From the viewpoint of the DUT, the wave b 2 corre-sponds to the incident wave a DUT and the wave a 2 corre-sponds to the re ected wave b DUT. Formula (2.2-1) canthus be expressed using quantities a 2 and b 2:

    a2 = DUT b 2 (2.2-2)

    Finally wave a 2 reaches port (3) with the coupling

    coef cient s 32. At this port the measurement receiveris located. Ideally, S-parameters s 21 and s 32 would bothhave a value of 1. The signal path that leads directlyfrom port (1) to port (3) is undesired. Accordingly, wewould like to obtain the best possible isolation in whichs31=0. Re ection at port (2) back to the DUT also has anunwanted effect. In the ideal case, we would like thisre ection to disappear. Moreover, if we assume thatgenerator wave a 1 is constant, then wave quantity b 3 isdirectly proportional to re ection coef cient DUT of theDUT. In the real world, however, the ideal assumptionsmade above are not valid. We will remove them one-by-one in the following subsections.

    Constancy of the A WaveIn practice, it is possible to maintain the generator wavea) at an approximately constant level, e.g. within a limitof a 0 dBm 0.3 dB. The remaining inaccuracy of thea) wave would directly affect the measurement result.To prevent this, we can determine the value of the a 1 wave using an additional receiver which we refer to asthe reference receiver. To generate a reference channelsignal a power splitter can be used (see next gure).Both output branches of the power splitter are symmet-rical. It can be shown that these branches are directlycoupled to each other. The signals exiting as waves a 1 and a 1 are always the same, regardless to the

    Fig. 2.2.1 Measurement circuitwith directional element.

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    Fig. 2.2.2 Directional element with reference channel.

    possible mismatch on the output ports of the power split-ter. 1 If the DUT is connected to one branch, via a direc-tional element, the wave quantity a 1 can be used insteadof quantity a 1.

    2 (Figure 2.2.2)

    The re ection coef cient DUT is measured by the follow-ing ratio, which we refer to as the measured value M:

    M= b 3 /a1 (2.2-3)

    Re ection TrackingIn the real world, transmission coef cient s 21 and cou-pling coef cient s 32 have values less than 1. They aremultiplied to obtain the re ection tracking R .

    R = s 32s21 (2.2-4)

    For quantities M and R, we thus obtain the followingequation:

    M = R DUT (2.2-5)

    To illustrate the effects of R, several signi cant points ofthe Smith chart have been inserted into formula (2.2-5)

    1) This characteristic of the power splitter is essential for its function. Unlike the power splitter a power divider formed of three Zo/3 resistors is unsuitable for this use.

    2) Along with the drawings of this primer a consistent background color scheme is used (e.g. the DUTs background color is always a light purple).

    You can take Fig. 2.2.2 as a representative example.

    as value DUT. As a result the Smith chart in Fig. 2.2.3 istransformed into the red diagram which is compressedby magnitude IRI and rotated by angle arg(R).

    DirectivityCrosstalk from port (1) to port (3) bypasses the measure-ment functionality. S-parameter S 31 characterizes thiscrosstalk. To compare it to the desired behavior of thedirectional element, we introduce the ratio known as thedirectivity:

    D=s 31 /R (2.2-6)

    The directivity vectorially adds on the quantity DUT. Ac-cordingly, we must modify formula (2.2-5) as follows:

    M = R ( DUT + D) (2.2-7)

    To assess the measurement uncertainty, we factor out thequantity DUT in the formula above and form the complexratio x = D/ DUT. Furthermore the product R DUT is denot-ed as W.

    M = R DUT (1 + x) = W(1 + x) (2.2-9)

    Fig. 2.2.3 Ideal and distortedSmith chart for formula (2.2-5).

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    The expression (1 + x) characterizes the relative deviationof the measured quantity M, from value W. For a general

    discussion this relative deviation (1 + x) is shown in Fig.2.2.4 as superposition of the vectors 1 and x. Any assess -ment of the phase of the complex quantity x requires vec -torial system error correction. Without this correction, wemust assume an arbitrary phase value for x, resulting inthe dashed circle shown in Fig. 2.2.4. Any more accuratecalculation of (1 + x) is not possible.

    Based on the points in the circle, the two extreme valuesproduced by addition of 1-lxl and 1 + Ixl can be extracted.They are shown in Fig. 2.2.4 in blue and red, respectively.

    They designate the shortest and longest sum vectors,respectively. In RF test engineering, decibel values (dB)are commonly used in reference to magnitudes. The twoextreme values can also be represented on a decibelscale.

    20 lg(1 - lxl) dB and 20lg(1 + Ixl) dB (2.2-10)

    A third point of interest in Fig. 2.2.4 is where the phasedeviation produced by x reaches its maximum value:

    max = arcsin(x) (2.2-11)

    The following table provides an evaluation of formulas(2.2-10) and (2.2-11) for various magnitudes of x. The

    quantity of each column in the table can be found in Fig.2.2.4. All the values in the table are scaled in decibels(dB). To demonstrate the usage of this table, an exampleis provided as follows:

    We assume a directivity D of -40 dB and a value W of-30 dB in equation (2.2-9), as well as an ideal re ectiontracking resulting in W= DUT. To use table 2.2.1 we cal-culate the normalized value Ixl = IDl/l DUT I meaning -40dB - (-30 dB) = -10 dB in dB scale. According to the tablewe read of deviations |x+1| = 2.39 dB and |x-1| = -3.30

    dB. Together with the value W = -30 dB we calculate themagnitude limits of the measured value M: Upper limit M= W + 2.39 dB = -27.61 dB and lower limit M = W - 3.30dB = -33.3 dB.

    For the limit case where x = 1, i.e. the case in which thedirectivity D and the re ection coef cient DUT to be mea-sured are exactly equal, the measured value M is betweenb3 /a 1 = 0 and b 3 /a 1 = 2R* D corresponding to values of -and 6.02 dB. Accordingly, it is not possible to directly mea-sure re ection coef cients less than D. On the other hand,

    when measuring medium and large re ection coef cients,

    Fig. 2.2.4 Vectorial superposition of 1 and |x|.

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    the in uence of the directivity is negligible.

    Like the re ection tracking, the directivity can directly beshown in the Smith chart. Recalling formula (2.2-7), ad-dition of D to the value DUT corresponds to a shift of thered chart shown in Fig. 2.2.3 by the vector R*D.

    Test Port Match and Multiple Re ectionsBesides the DUT, it is also possible to assign a re ectioncoef cient to the test port. The term we use for this is testport match S. In practice, we have to assume a test portmatch S O. As a simpli cation, we rst assume that the

    remaining components in the network analyzer are ideal.The test port match is then determined solely by the direc-tional element, i.e. its scattering parameter s 22.

    The wave b DUT (= a 2) that has been re ected by the DUTis not fully absorbed by the test port (port (2)). Thismeans that part of this wave is re ected back to the DUT.Between the test port and the DUT, multiple re ectionsoccur. They are shown in Fig. 2.2.6 as a snaking arrow.Lets analyze this phenomenon in more detail. From the

    rst re ection at the DUT we obtain the contribution b 2 DUT to a 2. Part of this wave is re ected by the test port

    Table 2.2.1 Estimate of the measurementuncertainty for superposition of vectorial quantities.

    Fig. 2.2.5 Ideal and distorted Smith chartfor formula (2.2-7).

    Fig. 2.2.6 Multiple re ection at the test port.

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    with the re ection coef cient S. It travels again to theDUT where it makes a contribution b 2 DUT S DUT to the a 2

    wave. After this double re ection, we can generally stopour consideration of this phenomenon. We now add upthe contributions as follows:

    a2 = b 2 DUT + b 2 DUT S DUT (2.2-12)

    After factoring out b 2 DUT we obtain a formula with astructure that is similar to formula (2.2-9):

    a2 = b 2 DUT (1+ DUT S) (2.2-13)

    We can examine the measurement uncertainty intro -duced by the test port match in a similar manner toformulas (2.2-10) to (2.2-11) or Table 2.2.1 using (1 + x) as (1 + DUT S), If we want to take into considerationre ections that go beyond the double re ection, we canuse the following formula. It holds assuming IS DUT I

    0, its value remains at 1. The response that is generatedusing a unit step stimulus is known as the step response(t).

    The step response (t) can be calculated by integratingthe impulse response h( t) with respect to time

    (t) = h( )d (5.1-3)

    Vice versa, we can calculate the impulse response h( t)by taking the derivative of the step response (t) withrespect to time.

    h(t) = d/dt(t) (5.1-4)

    s -

    Fig. 5.1.1 Linear time-invariant network with Diracimpulse as stimulus.

    Fig. 5.1.2 Linear time-invariant network with an unitstep as stimulus.

    1) The notation b(t) = a(t) *h(t) has been introduced and should not be confused with the product a( t) * h( t)!

    2) Also called Heaviside function in mathematical literature.

    t

    s 0

    Time-Domain Analysis of Linear RF NetworksThe wave quantities of a one-port device can be catego-rized in terms of stimulus and response. The stimulus a(t)characterizes the behavior of the incident wave vs. time.The response b(t) characterizes the behavior of the re-

    ected wave vs. time. The following re ection quantitiescan be de ned:

    h(t) as the impulse response from a(t) = (t); b(t) = h(t)(5.1-5)

    The impulse response h(t) describes the rate of changeof the impedance characteristics over time lover distance.It is particularly useful for localizing irregularities and

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    discontinuities along a transmission line.

    (t) as the step response from a(t) = (t); b(t) = (t)(5.1-6)

    It is recommended to use the step response (t) if theimpedance characteristics of the DUT are of interest. Thesign and size of the response vs. time indicate whetherthe DUT is resistive, inductive or capacitive.

    Analysis of a network based on the quantities (t) andh (t) is known as time domain re ectometry (TDR). Intheory, any arbitrary measured quantity such as the

    impedance Z, the admittance Y or the S-parameters canbe represented in time domain as an impulse responseor step response. The following discussion is limited tothe re ection coef cient since it is the most commonlyused of these quantities.

    Time Domain Measurement ExampleNow, we will have a look at some typical measurementsthat are done using the time-domain transformation. Theycan be performed with any network analyzer designedto handle the time domain transformation. This featureis usually available as an option. The instrument shouldhave an upper frequency limit of at least 4 GHz other-wise the time/distance resolution will not be suf cient forsome of the examples.

    Distance-to-Fault Measurement and GatingDescriptionThis example can be reproduced using simple equipmentthat should be available at any test station. The aim ofthe measurement is to locate an irregularity (short) in atransmission line. Building upon this, measurements arethen made on a healthy section of the transmission lineusing a time gate.

    Test Setup:J Network analyzer f max 4 GHzJ Cable 1 with SMA connectors, l 1 = 48.5 cm

    1

    J Cable 2 with SMA connectors, l 2 = 102 cm1

    J Calibration kit, PC3.5 system

    J SMA T-junction (see Fig. 5.2.3)J Through (if the test ports at the analyzer are of

    type PC3.5)J Adapter N to SMA (if the test ports at the

    analyzer are of type N).

    Part 1: Determination of the Cable PropertiesTo perform cable measurements with the reference toa mechanical distance axis, it is necessary to know thepropagation speed of electromagnetic waves in the cable.We determine this speed in a reference measurement

    done on a cable of the same type.

    1. Make the following settings on the networkanalyzer:

    a. Stop frequency: f Stop = 8 GHz (4 GHzif necessary)b. Start frequency: f Start = 20 MHz(10 MHz if f Stop = 4 GHz)c. Number of points: N = 400 pointsd. Test port output power: -10 dBme. Measurement bandwidth: 1 kHz

    f. Measured quantity: s 11 g. Format: Real

    2. Connect the trough or the adapter (N to SMA) totest port 1. It should remain on the network analyzerduring all the subsequent work steps.

    3. Select the time domain transformation, type lowpassimpulse (see Fig. 5.2.1).

    4. All of the following measurements are one-portmeasurements so it is suf cient to perform a OSMcalibration at test port 1.

    5. Select cable 1 and measure its mechanical lengthl mech . You should orient yourself towards thereference planes of the two connectors (see Fig.3.2.4). Here: l mech = l 1 = 1.02 m

    6. Connect the cable to test port 1. Leave the otherend of the cable open (do not install an openstandard there).

    1) A slightly different length is also possible. Both transmission lines should be coaxial cables and be made of the same material (e.g. RG400).

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    7. Con gure the time axis as follows:a. Start time: t start = -2 ns

    b. Stop time: t stop = 18 ns8. The measurement result you obtain should be

    similar to that shown in Fig. 5.2.1. Use a marker (e.g.automatic maximum search) to measure the delay t p up to the rst main pulse (here: t p = 9.679 ns).Calculate the velocity factor v p / c 0 for the currentcable type.

    9. Enter the calculated velocity factor on the networkanalyzer (see Fig. 5.2.2) and switch to distancedisplay.

    10. The displayed marker value (Fig. 5.2.2) shouldcorrespond to the mechanical length l mech measured in step 5 of part 1.

    Measurement Tip:For a time-domain transformation inlowpass mode, a harmonic grid is re-quired. If you have not used the settingsas described at step 1 above, it is possiblethat the actual grid is not a harmonic one.In this case you have to modify the gridto meet the requirements of a harmonicgrid. The analyzer used here would informyou about the con ict and when using thebutton lowpass settings offer you somepossibilities to adapt the grid. However,the previous calibration that was done be-fore modifying the grid might become in-valid. For this reason, we recommend thatyou perform the calibration after lowpassmode has been con gured (like here).

    (5.2-1)

    Measurement Tip:If we want to display the trace withrespect to the mechanical length, we musteither enter the velocity factor v p /c 0 or theeffective relative permittivity r,eff = ( c 0 /v p)

    2 at the network analyzer. During a re ec -tion measurement, the signal rst travers -es the distance d from the test port to theirregularity. Next, it returns via the same

    path. The measured delay p is thus givenas p = 2 d/v p . When displaying re ectionquantities with respect to a distance axis,most analyzers take into account the rela-tionship d = t*v p /2, whereas they computed = t*v p for transmission quantities.

    Fig. 5.2.1 Delay for an open transmission line.

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    Part 2: Locating and Masking IrregularitiesA short-circuited T-junction (see Fig. 5.2.3) is used as ourirregularity. It is located between two transmission lineswith mechanical lengths l 1 and l 2.

    1. In part 1, step 1, we provided a well suitedcon guration for the network analyzer. Check ifthis con guration is also acceptable with the testsetup shown in Fig. 5.2.3.

    a. Check the stop frequencyt = 1/(28 GHz) = 62.5 ps, i.e. d = v p /2 =

    0.66 cmt = 1/ (24 GHz) = 125 ps, i.e. d = v p /2 =

    1.31 cm

    Fig.5.2.2 Veri cation of the length measurement.

    Distance resolution here 0.66 cn at f stop = 8 GHzor 1.31 cm at f stop = 4 GHz

    b. Check the frequency step sizeFrequency range: 0 Hz to 8 GHz400 measurement points from 20 MHz to 8 GHz

    N = 401T= 1/ f = (N-l) / f stop = 400/8 GHz = 50 nsAmbiguity range: -25 ns to 25 ns or 5.274 m

    at f stop = 8 GHz or -50 ns to 50 ns or 10.548 mat f stop = 4 GHz.

    The ambiguity range is thus greater than the totallength l 1 + l 2 of the cables.

    Fig. 5.2.3 Test setup:Transmission line with ashort circuited T-junction.

    Measurement Tip:The time resolution t for the transforma -tion in lowpass mode is given by t1/(2fstop). Based on this relation and thevelocity of propagation vp , we can calcu-late the distance resolution of the re ec -tion measurement as d = vp t/2 vp /(4fstop).

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    Measurement Tip:The discrete Fourier transform used in thevector network analyzer provides unam-biguous results only in the interval -T/2 toT/2 where T = 1/f The spectrum repeatsitself periodically outside of this interval.Based on the velocity of propagation vp,we obtain the ambiguity range in termsof distances as T* vp /4 for re ectionmeasurements.

    c. Check of the stop length 1.8968 mThe stop length is greater than the total length

    l 1 + l 2.2. Assemble the DUT as shown in Fig. 5.2.3 and

    connect it to test port 1 of the network analyzer. 3. Determine the distance to the irregularity

    ( rst main pulse) and to the end of thetransmission line (second main pulse); see Fig. 5.2.4.

    4. Consider whether you could optimize the timedomain transformation in the present case(Fig. 5.2.4) using a different window function.

    a. In the present case, no improvement ispossible using a different window since neither

    case a nor case b applies.5. De ne a time gate that encompasses the healthy

    section of the transmission line including its openend (here: 12 ns to 14.8 ns), Select a normal gateas the shape of the time gate. For the de nition ofthe time-domain transformation, select the rectanglewindow.

    6. Install the match at the end of the transmission line.Change the trace setting from distance display backto time-domain display.

    Measurement Tip:Selecting a Hann window usuallyrepresents a good compromise betweenthe pulse width of the window and thesuppression of side lobes. However, adifferent window can be better in the

    following cases:

    Case a: Two pulses with very similarvalues are very closely spaced and cannotbe distinguished due to the pulse widthof the Hann window. Here, the rectanglewindow represents a better choice.

    Case b: A second pulse is present at alarger distance from a rst pulse, but thesecond pulse has a signi cantly lower

    level. This weak pulse can be maskedby the side lobes of the Hann window,which have a minimum suppression of 32dB. In this case it is best to switch to theDolph-Chebyshev window with variablesidelobe suppression of, say, 80 dB.

    Fig. 5.2.4 Searching for the irregularity and theopen end of the transformation line.

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    7. Activate the time gate and display the re ectioncoef cient as a function of the frequency in theSmith chart. It could be necessary to use a referencevalue of 0.72 to zoom into the center of the chart.Compare the result with the trace measured directlyin the frequency domain. Your measurement resultmight look like shown in Fig. 5.2.5.

    Fig. 5.2.5 Complex re ection coef cient for Fig. 5.2.3 with and without the time gate.

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    Conclusion

    One of the most common measuring tasks in RF engineering involves analysis of circuits (networks) anetwork analysis, using a Vector Network Analyzer (VNA) is among the most essential of RF/microwmeasurement approaches. Circuits that can be analyzed using network analyzers range from simpledevices such as lters and ampli ers to complex modules used in communications satellites. As a mea-surement instrument a network analyzer is a versatile, but also one of the most complex pieces of precision test equipment and therefore great care has to be taken in the measurement setup and calibrationprocedures.

    For more information about Vector Network Analyzers, please visit http://www.rohde-schwarz.com.

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    About Rohde & Schwarz

    Rohde & Schwarz is an independent group ofcompanies specializing in electronics. It is aleading supplier of solutions in the elds of test and

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    Established more than 75 years ago, Rohde & Schwarzhas a global presence and a dedicated service networkin over 70 countries. Company headquarters are inMunich, Germany.

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