IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-29, NO. 4, DECEMBER 1980
REFERENCES
[1] C. A. Hoer, "The six-port coupler: A new approach to measuring voltage,current, power, impedance and phase," IEEE Trans. Instrum. Meas.vol IM-21, pp. 466-470, 1972.
[2] G. F. Engen, "The six-port reflectometer: An alternative network ana-lyzer," IEEE Trans. Microwave Theory Tech. vol. MTT-25, pp.1075-1080, 1977.
[3] H. Groll and W. Kohl "Versuche zur Automatisierung der Mikrowel-lenme,technik am Beispiel der Impedanzmessung im Bereich der cm-und mm-WelIen," Tagungsbericht 23. Int. wiss. Kolloquium; TH II-menau pp. 53-56, 1978.
[4] W. Kohl, "Rechnergesteuerte Impedanzme,Bverfahren fur den Milli-meterwellenbereich," dissertation, TU Munchen, 1979.
[5] B. Parzen, "Impedance Measurement with Directional Couplers andSupplementary Voltage Probe," Proc. Inst. Rad. Eng., vol 37, pp.
1208-1211, 1949.[6] R. Yoemans, "Die Messung komplexer Reflexionsfaktoren mit Richt-
kopplern und Zusatzsonden im X-Band," Diplomarbeit, Lehrstuhl furMikrowellentechnik, TU Munchen, 1979.
[7] H. M. Cronson and L. Susman, "A new calibration technique for au-tomated broadband microwave measurements," in Proc. 6th Eur. Mi-crowave Conf., Rome, pp. 205-209, 1976.
[8] H. Niedermeier, "Rechnergesteuerte Impedanzmessung mit zweiRichtkopplern und zwei Zusatzonden im Ka-Band," Diplomarbeit,Lehrstuhl f. Mikrowellentechnik, TU Muchen, 1979.
[91 P. I. Somlo and D. L. Hollway, "Conductive contacting spheres on thecentre of the broad wall of rectangular waveguides," Electron. Lett.,vol. 8, no. 20, pp. 507-508, 1972.
[10] W. Kohl and G. Olbrich, "Quarzgenaue Frequenzmessung im Fre-quenzband 26.5-40 GHz," Mikrowellenmagazin, M. I pp. 16-18,1979.
PETER D. LACY, FELLOW, IEEE, AND WILLIAM OLDFIELD, MEMBER, IEEE
Abstract-Precision coaxial airlines and waveguides are used asin-situ impedance standards for reflection measurement over ex-tremely wide frequency spans. Tedious visual data interpretation isreplaced by digital data reduction. Intrinsic limitations of bridges ordirectional couplers are virtualy eliminated. UHF-through-millimetermeasurements can be made witb reflection-coefficient accuracy limitsof 3-30 X 10-4 depending on the physical tolerances of the referencelines.
INTRODUCTION
THE PRECISION swept-frequency reflectometer usesa precisely dimensioned coaxial airline or waveguide of
suitable length for the frequency resolution required as anin-situ impedance reference. The unknown impedance at thefar end of the reference above creates a rotating unknown re-flection phasor at the near end of the line, at the reflectionsensor, during swept-frequency measurement. Thus the re-flection signal is at all times directly compared with thephysical impedance reference. A waveguide reflection mea-surement is described by Hollway and Somlo [1] and thecoaxial arrangement by Lacy and Oldfield [2].
In the previous papers, the resulting data are shown insweep-frequency form that includes a sinusoidal ripple relatedto the length of the standard airline impedance reference. Thedata need to be graphically analyzed by the user. This paperpresents two algorithms for digital data reduction by means
Manuscript received June 28, 1980.The authors are with Wiltron Company, Mountain View, CA.
Fig. 1. Transmission line impedance references.
of two methods: A) averaging over a weighted window centeredat the frequency under observation which is wider in frequencyspan than one ripple cycle; and B) ripple amplitude extractionby a similar windowed discrete Fourier transform. Referencecalibration is initially performed and is included in the datareduction process.
GENERAL DESCRIPTION
Fig. I shows several transmission-line impedance references.Coaxial 14- and 7-mm airlines have precision connectors, abeaded "general precision connector" at one end, and an un-beaded "laboratory precision connector" at the other end. Thelaboratory precision unbeaded connector end is utilized inprecise reflection measurement to optimize the accuracy. A3.5-mm airline is also illustrated. This line uses compensated
LACY AND OLDFIELD: CALCULABLE PHYSICAL IMPEDANCE REFERENCES
GENERAI PURPOSE IINTERFACE BUS *4-Port Reflection Bridge(IEEE 488) with Internal Detector
Fig. 2. Block diagram of precision automated swept reflectometer.
connectors at either end which mate with low reflection to theSMA connector interface that is dielectric filled. This con-nector, termed "WSMA" [3], has precision mating inter-connector members which are longlife and are replaceable sothat the connector is suitable for the repeated connectionsencountered in measurement practice. A waveguide impedancestandard for the 26.5- to 40-GHz range is illustrated to indicatethe applicability to waveguide measurements and to providea precision reflection measurement method for the millimeterwave range.
Fig. 2 is a block diagram of the precision, automated, sweptreflectometer system. Impedance reference is shown in placewith the unknown being connected at the far end. The reflec-tion sensor is an autotester, that is, a four-port reflection bridgewith an internal diode detector. An external reference may beconnected to the autotester which has either the characteristicimpedance for the impedance standard or a different offsetimpedance that can be used to facilitate certain measurementtechniques. The entire measurement system is under interfacebus control of the desk computer shown at the upper left-handcorner of the block diagram. This computer programs themicrowave sweep generator to provide a step-frequency sweepof the measurement band desired. The output data from theinternal diode scalar detector are then put into the scalarnetwork analyzer. In the analyzer, a logrithmic amplifierprovides a high sensitivity and wide dynamic range for thesedata. The logrithmic analog data are converted to digital formand sent on the interface bus to the desk computer where theprocessing algorithms are carried out. The data can then beplotted or tabulated on a device in the upper right-hand cornerof the block diagram.
Fig. 3 shows the precision reflectometer; (a) is a flowgraphof the reflectometer showing the directivity and test-port matchparameters of the directional sensor. The impedance referenceline is indicated only as a line length of magnitude L. Theunknown is placed at the far end of the line and designated FP.
The measurement equation is shown below. The output of thereflectometer I" has a term due to the directivity D and alinear fractional term containing the unknown Fx, the linelength, and the test-port match F,. The swept-frequencymeasurement will cause the two phasors in the right-hand termof the measurement equation to rotate with respect to fre-quency. It is these expressions which contain the frequencysweep data that are essential to the digital processingmethod.
Fig. 4 illustrates the phasor responses that are encounteredduring the swept-frequency measurement. Diagram (a) indi-cates a phasor sum of a reference vector indicated by unity andan unknown x with an angle 0 with respect to the referencephasor. As the frequencies change, the phasor rotates aroundthe dotted locus shown in the phasor diagram. The resultantphasor is designated r; (b) shows the perspective of the phasorr versus the frequency axis co, with a helix axis A(w), whereA is unity at the origin. All frequency-sensitive parameters ofthe system and other intrinsic slowly varying instrumentalquantities are contained in the m agnitude of A (co).
Fig. 4(a) shows the plot of the magnitude r versus frequency,where r is equal to A VI1 + X2 + 2X cos 0 . It should be notedthat the magnitude of the phasor is utilized in the data pro-cessing rather than the squared form, since the squared form
_e d
391
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-29, NO. 4, DECEMBER 1980
would contain a cross product of the unknown rotating valuer and the reference magnitude which may be other than unity.In the magnitude form the sinusoidal quantity x is independentof the reference phasor value.
In both Methods A and B, a short is placed at the mea-
surement port. A frequency run of the raw data is taken. Themeasured function is
A(@) ID + 1 exp (-i2fL) 1[ 1 - Pm exp (-i2fL)
In Method A, the magnitudes are ID!I 0.01 and IP,!0.06. Attention is focused on the numerator of the second term.Relative to that unity reflection reference, D circulates in thepositive direction and rm in the negative direction; however,rP1 dominates. The error averaging mode will determine
A(w)[1 + Irml2/4].Next the unknown is applied at the test port and error aver-
aging will provide:
PrxJ(w)[i +X2/4]where x is either ID orlrjm l or a composite. Thus the first-order errors of the reflection sensor are eliminated. Withfurther program elaboration, the quadratic error magnitudescan be obtained and used for second-order error suppres-sion.
In Method B, the short-circuit calibration is again per-
formed with an "offset" (differing from Z0) termination on
the reference port of the reflection bridge. A value of 0.1(20-dB return loss) for IDI has typically been used. This will
0~~ ~ ~
04 ~~~~~~~~~~~A r
Window Cepstrum ofWindow
XO () I X(
Method A ERROR AVERAGCING(LOW PASS FILTE1R
(a)
1~~~~~7
Cepstrun forRipple Extraction
Real Part of lAr - Ripple OccurrencelW(C) exp(jC)r*4 in Swept Frequency Trace]
IXr(C ||f X(@ + 4, W(*) expCAJr*)d*|
Method B - RIPPLE AMPLITUDE EXTRACTION(BANDPASS FILTER AND A MPLITUDE DETECTOR)
(b)Fig. 5. Digital signal processing methods.
dominate but Pm will also contribute a second-order cor-rection term. The ripple extraction method will provide thelocal ripple amplitude
A (co)|r@which is then normalized using the short calibration reference.The two processing methods require that in the vicinity of eachfrequency two quantities are determined. In Method A, thelocal average is determined and Method B extracts the peakdeviation from the average. The windowed Fourier transformdetermines that peak deviation for the ripple frequency de-termined by the prescribed line length L of the physical im-pedance reference.
Fig. 5 shows the processing methods. In Method A, theripple pattern of Fig. 4(c) is observed on either side of thefrequency under consideration by a window that will averagethe error. This is equivalent to low-pass filtering of the ripplewaveform seen in Fig. 4(c). The window shape of Fig. 5(a) isa smoothing filter with a transform or cepstrum shown to theright. The equation below shows how the actual data X(U) areprocessed by averaging over the window -A to +A. In Fig.5(b), the same window is used to view the ripple waveform but,in this case, to extract the characteristic sinusoid or ripplevariation that is seen on the waveform. To do this a windowedFourier transform is performed on the data in the vicinity ofthe desired measurement frequency. The window is shown asan envelope, and the real part of the transform exponential [cos(23L) + i sin (2iL)I is illustrated. The corresponding imag-inary part of this transform is implicit in the transform equa-
392
LACY AND OLDFIELD: CALCULABLE PHYSICAL IMPEDANCE REFERENCES
1 X T C .'!1,lAX,,1!IFTiTHIId7T 1.i!111
-B 42NPVi! i.l XlfilniaTi ll U I i XPi2 6 10 14 18
Fig. 6. Measurement of a 20-dB return loss termination. (a) Raw sweepreflection data. (b) Processed data with error averaging applied.
tion. The right of Fig. 5(a) shows the cepstrum for extractionof the ripple where the ripple of frequency is designated by Xr.
The transform equation below shows the extraction of thecomplex phasor x and the detection of its magnitude.
The symmetric weighted observation window that has beenused extends over a total of three ripple cycles. It is a Kaiser-Bessel [4], [5] function with the following weights:
65 percent in the center cycle30 percent in the second cycle5 percent in the outer third cycle.
With this window the largest sidelobe level is -54 dB.
MEASUREMENT RESULTS
In Fig. 6 the measurement of a 20-dB return loss termina-tion is illustrated. In this case, the reflection sensor is operatedin optimum with a Zo reference impedance in place, the airlineon the measurement port, and the unknown at the end of theairline. A data run is taken with the short in place and thesedata are averaged to give the unity reflection reference data.Then the unknown is applied at the test port. The frequencysweep is made; in this case a 20-dB return loss termination isto be measured, and the bridge directivity is in the order of 36dB. This creates a measurement uncertainty of I dB, shownin the raw sweep reflection data of Fig. 6. The uncertainty dueto directivity is then removed by low-pass filtering of this rawsweep-reflection data. Then the processed sweep data are re-
ferenced to the previous calibration sweep and the resultantdata are plotted in Fig. 6(b). The 20-dB return loss offsettermination shows a broad ripple due to distributive compen-sation within the offset termination.
Fig. 7 shows the results of a measurement with a calculablereflection due to a 1-in line with a physical impedance otherthan the characteristic impedance of the transmission line.These are referred to as two-port reflection standards [6]. In
Fig. 7. Calculable physical impedance reference. (a) I -in section of lowimpedance line-raw data. (b) Processed data for (a).
this measurement, the ripple extraction method is used witha 20-dB offset termination placed as the reference on the re-
flection bridge. The 1-in section of low- or high-impedance linewill provide calculable mismatches at frequencies where theline length is an odd multiple of one-quarter wavelength. Thiswill occur in the vicinity of 3, 9, and 15 GHz. The complexreflection locus on a Smith Chart would show a circle touchingthe center at 0 frequency and at frequencies at which the linesection is integral multiples of one-half wavelength. Themaximum reflection magnitude will then occur at the oddquarter-length wavelength frequency points. Fig. 7(b) showsthe processed data based on the raw data obtained in the sweepof Fig. 7(a). This measurement method has been taken on eightdifferent impedance sections. In this series of measurements,the rms deviation of the peak reflection from calculated valuewas found to be 0.001. The average deviation over the mea-
sured value was 0.002. However, the physical measurementwas limited to 0.001, and the equivalent accuracy of thestandard line was 0.001.
Another plot is shown for a high-precision resistive termi-nation measured from 10 MHz to 18.5 GHz. The results are
plotted in Fig. 8. In the raw sweep data shown, the terminationbeing measured and the processed return loss data using theripple amplitude extraction algorithm are given in Fig. 8(b).The raw data shown in Fig. 8(a) exhibit an increase in rippleamplitude below I GHz. This was directly traced to a bow in
393
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-29, NO. 4, DECEMBER 1980
2 dB
0
It Jr i'd.1dilk ti + I T
.~~~~~~~IlUilll !1,lltllliiil!iiliillilI : I: : I: 1 1 gi t
Frequency, GHz
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3L1.i !1_11,11 ililT ill l11111T 11 111111111!11111 11111i3srJji 4 I9I 101214illiIlllidII IT iT lil±T!
11iil11i11 11iiiiHIII llIIII 11I1111 111111111 111iiill lllliIilN .T IiliIil!iII lliHTHIT H IH 1I 11Iii IIIITTmI1IT il III IIIII II '!II ii III
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(b)Fig. 8. Precision termination data. (a) Raw sweep data for 50-Q taken with30-dB return loss bridge reference. (b) Processed return loss LPC-7 ter-mination data using ripple amplitude extraction algorithm.
LACY AND OLDFIELD: CALCULABLE PHYSICAL IMPEDANCE REFERENCES
the axis of the center conductor of the impedance referenceline.
FURTHER APPLICATIONS
The ripple-measurement process has been used for wave-guide reflection measurements. To utilize the characteristicripple pattern generated by the length of the impedance ref-erence, the frequency measurement steps are modified by thewaveguide dispersion characteristic to provide a constant rippledensity over the waveguide band. This has been demonstratedin the 26.5- to 40-GHz range to make measurements with across-guide coupler having a nominal 20-dB directivity. In thiscase, the physical accuracy of the waveguide impedance ref-erence governs the reflection measurement accuracy.
Another reflection measurement made using these tech-niques is the evaluation of a single adapter from a 7-mm pre-cision connector to an SMA interface. In this case, the mea-surement is made at the end of the 7-mm airline placed on thereflection sensor. At the test port, the adapter connection ismade, and then the other side of the adapter, at the SMA in-terfaces, a 3.5-mm airline is placed with an interface com-patible with the SMA interface. The far end of the secondairline of 3.5 mm is then terminated. The measurement processwill look for the characteristic ripple in the frequency domaincorresponding to the length of the 7-mm reference airline only.It thus will be able to separate that reflection from any sub-sequent reflections by the ripple frequency discrimination sincea more distant reflection will have a higher frequency rotationand ripple projection in the frequency sweep domain. Likewise,this type of measurement can be utilized to look at only one endof a cable connector under measurement or, in the limit,multiple reflections along the cable can be located by meansof a full-scale ripple frequency analysis of the reflectiondata.
The directivity of the reflection bridge or direction couplercan be measured quite easily by calibrating with a short andthen placing an offset termination at the far end of the line. Inthis case directivities from 35 to 50 dB may be easily plottedversus frequency over the entire frequency range desired.Another application of the digital processing is the measure-ment of source match. In this case, a source under measure-
ment is fed through a reference impedance to a mismatcheddetector (5-dB return loss has been used) and the ripple ex-traction technique is applied. The source impedance matchmay be plotted versus frequency.
CONCLUSION
Fig. 9 shows a photograph of a complete measurementsystem. The RF measurement components and the deviceunder test are shown in front of the microwave sweep gener-ator. The scalar network analyzer is shown above in the rack.The scope display shows the raw sweep data for operatorevaluation. The desk computer and data plotter are shown tothe left. The limiting intrinsic accuracy limitation of the pre-cision reflectometer is determined from the "in-place" physicalairline impedance reference. This may be easily inspected andgauged. The length of the reference line will determine thefrequency resolution.The measurement system calibration depends on the
physical line impedance plus a reference level determined byplacing a short at the measurement port in Fig. I and takingan ''error averaged" frequency run.The number of RF components involved is minimal, but this
involves no sacrifice of measurement accuracy and stronglysupports reliability. All of the system is commercially available,to be supplemented with computer programs for the algorithmsabove presented.
REFERENCES
[I] D. L. Hollway and P. 1. Somlo, "Origin of high-resolution, swept-fre-quency reflectometry," Microwave J., Aug. 1973. D. L. Hollway and P.1. Somlo, "A high-resolution swept-frequency reflectometer," IEEETrans Microwave Theory Tech., Apr. 1969.
[2] P. Lacy and W. Oldfield, "A precision swept reflectometer," MicrowaveJ., Apr. 1973.
[3] "Connector relievers nagging SMA measurement problems," Micro-waves, Jan. 1979.
[4] F. J. Harris, "On the use of windows for harmonic analysis with the dis-crete fourier transform," Proc. IEEE, Jan. 1978.
[5] F. F. Kuo, and J. F. Kaiser, System Analysis by Digital Computer. NewYork: Wiley, 1966.
[6] R. W. Beatty, "Calculated and measured S 1, S21, and group delay forsimple types of coaxial and rectangular waveguide 2-port standards,"NBS Tech. Note 657, Dec. 1974.
