Designing and Characterizing TRL Fixture Calibration ... · PDF fileDesigning and...

Designing and Characterizing TRLFixture Calibration Standards forDevice Modeling

By Julien Fleury and Olivier BernardCalifornia Eastern Laboratories

To measure and characterizedevices, California EasternLaboratories (CEL) uses dif-

ferent fixtures and calibrationmethods. One is the through-reflect-line, or TRL, which can beused to calibrate the HP8510 net-work analyzer.

Like other calibration methods,the TRL introduces a 12-term errorcorrection vector for each frequen-cy point. To calculate these terms,standards for which S-parameters are knownmust be measured. These standards include ashort order open a through and a delay line withknown electrical delay. The TRL calibration cor-rects phase and magnitude errors introduced bythe sliding of reference planes and the insertionloss of cables, fixtures and connectors. Precisioncalibration standards should be used becauseeach defect in a standard will be transformedinto calibration errors.

This application note explains how to charac-terize and build a proficient TRL calibration kitfor the HP8510 Network Analyzer. The firstpart explains how to characterize a TRL cali-bration kit. The second part describes how toimprove the calibration kit using the measure-ments made on it. First, the TRL is described inmore detail.

Calibration of a network analyzerIn any measurement, systematic error

sources change the response of a device undertest (DUT). Annuling the effects of cables, con-nectors, mismatched lines and couplers requiresa calibration that provides correction term vec-tors for each frequency point. With multiple fre-

quency points, this vector becomes a matrix.Two popular correction vectors are the eight-term and 12-term correction vectors.

The 12-term error correctionTwelve-term error correction permits the

correction of six terms in forward and six inreverse mode. These six terms are:

• ED, the directivity term• ER, the reflection tracking term• EL, the load match term• ET, the transmission tracking term• ES, the source match term• EX, the isolation term

These are seen in the flow graph (Figure 1),which represents the forward error terms.

This correction is the most efficient, is avail-able on high quality network analyzers and it cor-rects all systematic errors provided by the net-work analyzer. The eight-term calibration is oftenused in less expensive network analyzers. It issimpler but does not correct all the systematicerrors, such as the errors introduced whenswitching to an alternate measurement direction.

26 · APPLIED MICROWAVE & WIRELESS

Figure 1. Flow graph of the forward path 12-term error correc-tion.


The eight-term error correctionThe eight-term error correction models are each

accessed by a quadripole defined by its S-parameters.There are four terms per port and two ports. In somenetwork analyzers, isolation is corrected also, which isnot included in the eight-term correction. This kind ofcorrection can be modeled by the flow graph (Figure 2).

The TRL calibrationThe TRL calibration uses the through, the delay line

and a reflection standard, either an open or a short.Each of the four S-parameters is calculated for eachstandard. That means that 12 parameters are measured.

Using a system of equations, it is then possible tofind 10 of the 12 error terms. The two missingterms are the forward and reverse isolation termswhich can not be extracted from that set of equa-tions. If the user wants to calibrate these parame-ters, isolation calibration with two loads (as in theOSLT calibration) is necessary.

The flow graph of each TRL standard is shown inFigure 3.

Characterization of a TRL calibration kit

Errors sourcesErrors appear when the standard used for the

calibration is different from the fixture of the deviceunder test. For example, if the fixture strip does nothave the same board thickness as the through stan-dard, its frequency response will not be the same asthe standard. The systematic error will not be thesame as the standard and the correction will notremove this error. The difference between thisstandard and the fixture strip response will beadded to the component response, biasing theresults. Therefore, one critical factor when buildinga calibration kit is the repeatability of each stan-dard and test fixture. Each standard must only dif-fer by that aspect of the electrical characteristicwhich was intended to change. For example the

only desirable difference between a through and a delayline is the phase. All other parameters (including inser-tion loss) should be identical. In practices this is impos-sible, but differences should be minimized. Differencesbetween standards and fixtures are numerous. Thebiggest difference is often the assembly of the connectorbecause it is a human process. Other variables, such asstrip thickness, are negligible because processes arerepeatable. Therefore, it is very important to test eachconnector and measure each return loss. These mea-surements can be done in the time domain as explainedin the Time domain measurement section.

Because standards are not perfect, they are an errorsource. The network analyzer assumes that standardsare perfect during the calibration. For example, thereflect standard does not have a reflection coefficientequal to one (see Figure 4). Some of the incident signalradiates. The higher the frequency, the greater the radi-ation. The correction vector becomes less and less pre-cise as the frequency increases. The imperfect aspect ofthe open can be modeled with a frequency dependentnonlinear capacitance and return loss in the calibrationkit definition of the HP8510 network analyzer.Nonlinear modeling and implementation on the HP8510is explained in the Modeling standard errors section.

A good calibration kit standard can provide poorresults if it is not well implemented in the HP8510. Theelectrical delay of each delay line should be measured

Figure 2. Flow graph of the eight-term error correction.

Figure 3. Flow graphs of TRL standards.

0 5 10 15 20 25-2.2

-1.8

-1.4

-1.0

-0.6

-0.2

0.2

S22 : dBMag

Freq : GHz

S22

: dBM

ag

Perfect

Real

Figure 4. Response of a reflect line (S22).


with good precision. If the delay is not the same as theparameter implemented in the HP8510, there is a linearfrequency dependant systematic phase error (see Figure5). The measurement of delay lines is a substantial partof the calibration definition.

The difference between a perfect open, a perfectthrough and a perfect line can be defined on the Smithchart by a phase shifting. To avoid having several stan-dards too close on the Smith chart, the phase of delaylines must comply with several rules. The S12 differen-tial phase of the delay line has to be within a 20 to 160degree limit, when compared to the through line.

The frequencies corresponding to these 20 and 160

degree limits are found by perform-ing an electrical delay measure-ment explained in the Electricaldelay measurement section.

Time domain measurementA good way to find the physical

location of a defect on a fixture is touse a time domain measurement onthe HP8510 network analyzer. Thefrequency domain is ineffective atlocating the position of a defect.Assuming that the speed of an elec-trical impulse is constant, timebecomes proportional to distance,and viewing a time domain signal isequivalent to viewing a “distancedomain” signal.

Looking at S11, which refers toreflection coefficient on port 1, orS22, which refers to the reflectioncoefficient on port 2 is like viewingthe reflection coefficient versus dis-tance. The translation from the fre-

quency to time domain is implemented by a fast fouriertransform (FFT). The user must set up the frequencydomain with appropriate values to achieve good resultsin the time domain.

First, the calibration should be done at the highestfrequency and with a large number of points. The widerthe bandwidth, the more precise the time domain willbe. The step between two discrete time points will besmall when the frequency domain bandwidth is large.

The reference planes should be located so the connec-tor is at zero seconds in the time domain. With the 8510,use a short-open-load (SOL) calibration from 45 MHz to24 GHz using a 50 MHz step (479 points) with a good cal-

ibration standard, such as SMA or 2.6 mm cali-bration kit.

When the calibration is done, switch the net-work analyzer into “time domain” mode. Next,change the scale to display an appropriatecurve. A typical curve for a transmission line(delay line or through) is two peaks spaced witha quasi-null flat part. The two peaks identifythe connector return losses and the flat partidentifies the matched line (see Figure 6). Atypical curve for a reflection line is also twopeaks. The first peak deals with the connectorinsertion loss and should be as small as possi-ble, the second peak refers to the reflection onthe reference plan of the fixture (short or open).It should be close to one.

Frequency domain measurementIt is possible to measure the S-parameter of

Figure 5. S12 phase, (a) with perfect offset definition; and (b) with 10 ps delayoffset error.

0 2 4 6 8 10 12 -45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

Figure 6. Time domain measurement of a delay line.

(b)(a)


fixtures in frequency domain with the HP8510 networkanalyzer. This measurement provides useful informa-tion on S-parameter versus frequency. It is used tomodel lines, open and short (with respectively nonlinearresistor, capacitance and inductor) and provides infor-mation about the maximum usable frequency. It alsosupplies information about the electrical delay of lines.This measurement will be developed in the Electricaldelay measurement section.

To characterize a fixture in the frequency domain thenetwork analyzer is initially calibrated using a methodsuch as an SOL.

For a transmission line (through or delay) the inser-tion loss (S12 and S21) should be very small (under 0.5dB). Insertion loss varies as the square root of frequen-cy, so the insertion loss increases with frequency.Depending on the desired precision, the user assigns amaximum usable frequency for the transmission linefixture with this curve. If that maximum usable fre-quency is not high enough, it is possible to introduce anonlinear offset loss in the network analyzer whichmodels loss varying with the square root of frequency.S11 and S22 must be less than –20 dB.

For a reflection line (open or short), the transmissioncoefficient (S12, S21) should be very small, at least –30dB. That means there is little coupling between the tworeflection lines and good isolation between the twoports. The reflection coefficient (S11, S22) should beclose to 0 dB. As with the transmission lines, it is possi-ble to introduce a nonlinear model made of a resistorand a capacitor for the open and a resistor and an induc-

tor for the short. The modeling aspect isexplained in the Line and substrate section.

Electrical delay measurementThe TRL kit uses transmission lines of dif-

ferent lengths and it is important to preciselymeasure the electrical length of the throughand the delay lines. By definition, the throughhas a null electrical delay, which means the tworeference planes of the fixture are overlapped.

The through is then used as a reference forthe electrical delay measurement. The network

analyzer is calibrated with the calibration kit throughstandard. After calibration with the through standard,the phase of S12 and S21 should be zero. Next, the delayline is inserted and the phase versus frequency is mea-sured to determine the accurate frequency range of thedelay line. It is also possible to measure the differentialelectrical length of the delay line by using the analyzerto null out a length or ideal line. With a flat phase curve,errors are easily observed.

Improvement of a TRL calibration kit

Physical errors correctionEven though nonlinear errors are modeled on the

HP8510 network analyzer, the fixtures have to be asperfect as possible.

ConnectorsThe connectors must be consistent on all standards

and fixtures. They should come from the same manufac-turer with consistent assembly. The pin of each connec-tor must be in contact with the substrate strip to insurea smooth transition from the connector to the strip andreduce the coax to microstrip discontinuities. A low pro-file solder joint should keep the pin in contact with thestrip (Figure 7). Substrate and connector grounds mustbe void of gaps and cracks. The reflection coefficientshould be the same for all connectors of all fixtures(standards and component fixtures). Test each connec-tor with the time domain measurement.

Lines and substrateThe substrate should be the same for all fixtures. The

lines should be a 50-ohm lines. Long lines should be test-ed with time domain measurement. It is also possible tocalculate the impedance of the line with Linecalc fromADS. There should be no solder on the strip, which couldchange the impedance and be inconsistant.

Modeling standard errorsThe frequency range of non-ideal standards are

extended by nonlinear models in the calibration kit def-initions of the network analyzer. This modeling is sum-marized in Table 1.

Figure 7. Diagram of a well-built connector.

Table 1. TRL standards modelization.


The units of these parameters are:

LineThe nonlinear model of a line includes a series non-

linear frequency dependant resistor. The model assumesthat insertion loss varies as square root of frequency andthat therefore, the equivalent resistor varies as squareof frequency.

R = aloss · f2 (1)

To calculate the proportional factor aloss, the equiva-lent resistor at one frequency must be known. The fre-quency chosen is 1 GHz. When that value is known,equation 2 provides aloss:

(2)

At 1 GHz, these equations provide R = Requ.The loss of a line depends also on its length. Equations

(1) and (2) are valid for the electrical length of the mea-sured line. The value included in the HP8510 networkanalyzer must be translated to a 1 s electrical delay line.The offset loss implemented in the HP8510 is:

(3)

OpenThe nonlinear modeling of an open is a series resistor

followed by a parallel nonlinear frequency dependantcapacitor. The total impedance of the model in harmon-ic domain is:

(4)

where

R = aloss · f2

C = C0 + C1f + C2f2 + C3f3

so

(5)

Values for C0, C1, C2, C3 must be within the limitsshown in Table 2.

When signal is reflected at the end of the line, it pass-es through the line twice. The offset loss is calculated fora one-way path. The user must divide the equivalentresistor modeled by two so that the roundpath insertionloss becomes a one-way path insertion loss.

The values of R, C0, C1, C2, C3 can be found with anoptimization engine (included in Agilent’s ADS). Theway to do such an optimization is explained in theOptimization with ADS section.

ShortThe nonlinear model of a short is a series resistor fol-

lowed by a parallel nonlinear frequency dependantinductor. The total impedance of the model in the har-monic domain is:

Zequ = R + jLw (6)

where

R = aloss · f2

Rloss

equ GHz=α 1

1810

Zj f C C f C f C f

j C C f C f C fequ

loss=

+ + + +

+ + +

1 20 1 2

23

3

0 1 22

33

ωα

ω

( )( )

Rloss

equ GHz=α 1

1810

Z RjCequ = +

1

ω

Offset Losss

R

Electrical Length−

−

Ω=

α lossequ GHzR

= 11810

R C F L H C F L H

HzC

FHz

CF

Hz

CF

HzL

HHz

LH

Hz

LH

Hz

Ω

Ω[ ] [ ] [ ] [ ] [ ]

, , , ,

, , ,

, , ,

0 0

2 1 2 2

3 2 1 2 2

3 2

α

Table 2. Limit values for coefficient of the nonlinearcapacitor in a HP8510 network analyzer.

Minimum value Variable Maximum value Units–10–11 C0 10–11 F–10–23 C1 10–23 F/Hz–10–32 C2 10–32 F/Hz2

–10–41 C3 10–41 F/Hz3

Table 3. Limit values for a coefficient of the nonlinearinductor in a HP8510 network analyzer.

Minimum value Variable Maximum value Units–10–8 L0 10–8 H–10–20 L1 10–20 H/Hz–10–29 L2 10–29 H/Hz2

–10–38 L3 10–38 H/Hz3


L = L0 + L1f + L2f2 + L3f3

so

Zequ = aloss · f2 + jw(L0 + L1f + L2f2 + L3f3) (7)

Values for L0, L1, L2, L3 must be within the limitsshown in Table 3. The equivalent resistor must be divid-ed by two for one-way path insertion loss. The values ofR, L1, L2, L3 and L4 can also be determined via opti-mization.

Optimization with ADSOptimization may be used to

converge the model to the mea-sured response of the device. First,the fixture is measured in the fre-quency domain and the data isacquired in s2p format, asexplained in the Frequency domainmeasurement section.

The optimization variables areincluded in a VarEqu block. Theparameters to optimize are shownin Table 4. Figure 9 illustrates the

results of the optimization performed in Figure 8.

Building a TRL calibration kit with the HP8510Network Analyzer

Several parameters must be known to build a TRLcalibration kit (see Table 5).

There are also some optional fields for the calibrationkit. These optional fields define the nonlinear model ofthe standards. If a nonlinear model is not desired, thesefields are set to zero.

Once the needed parameters are known, the calibra-tion is implemented using the procedure shown inFigure 10. The HP8510 memorizes the standard para-meters in its memory addresses from No. 1 to No. 21,therefore 20 standards may be defined for each calibra-tion kit.

The first step in implementing a calibration kit is toassign standard addresses for each class. One or severalstandard memory numbers are attributed for each class(There are three for the TRL calibration kit: through,reflect and delay lines). To do so, the user has to go tothe specify class menu. The first menu that appear is thespecification of class for the reflect standard of the 2port and 1 port calibration. These standards are not

used in a TRL calibration kit.After pressing “more,” themenu shows the specification ofclasses for the transmissionstandards of the 2 port and 1port calibration. These stan-dards are also not needed. Afterpressing “more,” the menushows the response and TRLcalibration standard specifica-tion. The choices are:

• Response• TRL thru• TRL reflect• TRL line • Adapter

The user now attributes one

Table 4. Optimization equations for TRL standards.

Table 5. Parameters known to build a TRL calibration kit.

Figure 8. Example of a short nonlinear model optimization with ADS.


or several standard addresses for each of the three TRLclasses. To do this, select the standard and enter theaddress number on the HP8510 numeric panel separat-ed by the x1 button. For example, to implement a threedelay lines TRL cal kit, the procedure could be:

• Press TRL THRU• Press 1 followed by x1• Press TRL REFLECT• Press 2 followed by x1• Press TRL LINE• Press 3, x1, 4, x1, 5, x1

If the user chooses to implement the response cali-bration kit, the addresses for the response calibrationmust be defined and the thru and/or the delay lines areused. Then:

• Press RESPONSE• Press 1, x1, 3, x1, 4, x1, 5, x1

At this point, the addresses of the standards areimplemented for each class. The user now modifies thelabel of the three classes (thru, reflect and line), usingthe label class menu. This menu is the same as the spec-ified class menu but instead of entering the addresses of

the standard, the user enters the labelof the standard. Assuming that thereflect in the example above is a short,the label could be:

• TRL THRU Æ “Through”• TRL REFLECT Æ “Short”• TRL LINE Æ “Delay_lines”

The classes are defined, addressedand labeled. The user now enters theparameter of the standard using thedefine standard menu. The user entersthe address of the standard to define.The standard choices are :

• Short• Open• Load• Line/Thru

In the example above, if the user isdefining the standard implemented inaddress No. 1, No. 3, No. 4 or No. 5,which are the through and the lines,Line/Thru should be selected. If defin-ing the standard implemented inaddress No. 2, which is the reflect stan-dard, short should be selected.

For each address corresponding to a standard, theuser enters all the parameters included in the tableabove. The parameters are:

Short:• Nonlinear coefficients L0, L1, L2, L3 for nonlinear

modeling, enter 0 (zero).• Offset delay. Including :

• Offset delay. Should be zero in most cases ifthe short is at the reference plane. Other-wise,measure the electrical delay between the ref-erence and the short plane and enter it.

• Offset loss. Should be zero if the user does notwant a frequency dependant model. Other-wise, enter the calculated or simulated value.

• Offset Z0. Should be 50 in most cases.• Minimum frequency. There is no frequency

compliance for the reflect standard. The usermay enter 10 MHz.

• Maximum frequency. There is no frequencycompliance for the reflect standard. The usermay enter 100 GHz.

• Coax/Waveguide. The user enters the type ofcable used, typically Coax.

• Label Standard. The user enters the name ofthe standard.

Figure 9. Example of optimization results on a short nonlinear modelization.

Figure 10. Simplified block diagram of TRL calibration kit implementation ina HP8510 network analyzer.


Open:• Nonlinear coefficients C0, C1, C2, C3. If the user

does not want nonlinear modeling, enter zero.• Offset delay. Including :

• Offset delay. Should be zero in most cases ifthe open is at the reference plane. Otherwise,measure the electrical delay between the ref-erence and the open plane and enter it.

• Offset loss. Should be zero if the user does notwant a frequency dependant model.Otherwise, enter the calculated or simulatedvalue.

• Offset Z0. Should be 50 in most cases.• Minimum frequency. There is no frequency

compliance for the reflect standard. The usermay enter 10 MHz.

• Maximum frequency. There is no frequencycompliance for the reflect standard. The usermay enter 100 GHz.


• Label Standard. The user enters the name of thestandard.

Load:• Fixed/Sliding/Offset. Enter the type of load used.

Most often, the load is a fixed type.• Offset delay. Including :

• Offset delay. Should be zero in most cases ifthe load is at the reference plane. Otherwise,measure the electrical delay between the ref-erence plane and the load plane and enter it.

• Offset loss. Should be zero if the user does notwant a frequency dependant model. Other-wise, enter the calculated or simulated value.

• Offset Z0. Should be 50 in most cases.• Minimum frequency. The user enters the min-

imum valid frequency of the load.• Maximum frequency. The user enters the

maximum valid frequency of the load.• Coax/Waveguide. The user enters the type of

cable used, typically Coax.• Label Standard. The user enters the name of the

standard.

Line/Thru:• Offset delay. Including :

• Offset delay. Is zero for the through standardby definition. The user enters the measuredoffset for the different delay lines.

• Offset loss. Should be zero if the user does notwant a frequency dependant model. Otherwiseenter the calculated or simulated value.

• Offset Z0. Should be 50 in most cases.• Minimum frequency. The user enters the min-

imum valid frequency of the delay line. Thereis no minimum frequency for the through(enter a value < 45 MHz).

• Maximum frequency. The user enters themaximum valid frequency of the delay line.There is no maximum frequency for thethrough (enter a value > 50 GHz).


• Label Standard. The user enters the name of thestandard.

Now, the user programs the TRL options in the TRLoptions menu. The user then selects Line Z0 in the CalZ0 menu and Thru in the Set Ref menu. The lowbandfrequency is set to 45 MHz.

When measuring very high insertion loss devices, it isnecessary to do an isolation calibration. To do so, definethe forward and reverse isolation using the same

Table 6. Summary organization of a TRL calibration kit in a HP8510 net-work analyzer.

Figure 11. TRL calibration kit with two delaylines and a short.


method explained above and associate the reverse andforward isolation with the address No. 6. In the definestandard menu, the address No. 6 is a load type. Theuser now labels the calibration kit in the label kit menuand press CalKit done.

The calibration kit implementation is now finished.The example above is summarized in Table 6. Figure 11is an example of calibration kit standards. Figure 12shows measured data on a DUT with these standardsused to calibrate the HP8510.

ConclusionBecause calibration permits the deletion of the sys-

tematic error, it is an important step of the measure-ment process. A good calibration depends on a good cal-ibration kit and the application of state-of-the-art cali-

bration techniques. Incorrect or biased measurementsresult in incorrect nonlinear models and skewed charac-teristics in datasheets. Good designs require accuratecomponent data.

References1. HP HP8510B — Operating and Programming

Manual, Hewlett-Packard, Inc.2. Charlie Woodin, TRL Calibration.3. V. Y. C. Leong, “Microstrip-Based Implementation

of the ‘Thru-Reflect-Line’ Calibration Technique forVector Network Analyzer,” Journal of the Institution ofEngineers, Singapore, Vol. 33, No. 6, October 1993.

4. M. Mabrouk and S. Tedjini, LEMO-URA 833,“Mesure de circuits MMIC en Boitier par AutocalibrageTRL de 2 a 18 GHz,” Confirmation et Validation D'uneAnalyse Theorique, Enserg-INPG, B.P. 257, 38016Grenoble, France.

5. Don Metzger, “Improving TRL* Calibrations ofVector Network Analyzer,” Microwave Journal, May1995.

Author informationJulien Fleury is an application design engineer at

California Eastern Laboratories. He received both abachelor of science degree in electrical engineering anda master of science degree in electrical engineering inRF design from Ecole Supérieure d'Ingénieurs enElectrotechnique et Electronique (ESIEE), an engineer-ing school in Paris, France, in 2001. This article was apart of his MSEE thesis. His interests also include auto-mated test equipment. He amy be reached via E-mail:[email protected]; or Tel: +33-6-64-83-89-66.

Olivier Bernard is the manager of strategic marketingat California Eastern Laboratories. He received hisBSEE and MSEE in RF design from ESIEE and subse-quently an MSEE in electrophysics from the Universityof Southern California in Los Angeles. He has been indesign and engineering management positions in thefield of RF and microwave for more than 10 years andhas published more than a dozen design and technicalarticles. He may be reached via E-mail: [email protected]; or Tel: 408-206-0875.

Figure 12. De-embedded measurement of a SiGe bipolartransistor with TRL calibration.

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