AP07_4-5.vp

1 Introduction
Many papers on improving VNA calibration procedure

have been published recently. The accuracy of the error
model is increased by using a CAD-based evaluation of the
calibration standards [1] and statistical processing of mea-
sured data of an over-determined set of calibration standards
[2]-[5]. Another improved calibration procedure optimizes
parameterized models of calibration standards to minimize
nonreciprocity in a known asymmetrical reciprocal two-port
device [6]. These techniques increase the accuracy of the
measured S-parameters while maintaining the requirements
on the hardware quality of the calibration standards at the
same level.

However, the measurement accuracy is substantially worse
for standards fabricated on a soft planar substrate than is
much longer than a quarter wavelength. Such an effect can be
seen clearly in [2], where the 95 % confidence limit of the
measured S-parameters is approximately ten times greater
for a Rogers 4350B soft substrate than for the measure-
ment carried out using HTCC material and a wafer-probe
connection.

The problem of measuring the S-parameters on a planar
lossy medium can be overcome by using the TDR preselection
method proposed in this paper. Also, an origin of errors is
explained assuming the SOLT calibration and correction
method.

2 Error sources
A typical of S-parameter measurement arrangement is

depicted in Fig. 1. An intrinsic calibration standard and a de-
vice under test (DUT) are connected to VNA ports through
feeding lines and connectors. The intrinsic calibration stan-
dard is assumed here as a lumped circuit. The connectors are
either soldered to the printed circuit board (PCB) or they just
touch the strip when a text fixture is used. The reference
planes are usually considered at the center of the PCB.

The overall error of VNA calibration is composed of sev-
eral particular errors that are described in this section. Each
of the particular errors can be assigned to a certain region of
the PCB shown in Fig. 1.

2.1 Variation of the manufacturing process
The limited accuracy of the manufacturing process affects

mainly the cross-section of the feeding lines (see Fig. 1). The
impedance of the feeding lines differs between items in the
calibration kit. Since the feeding lines are naturally distrib-
uted circuits, a small impedance difference of 1–2 ohms leads
to an error of hundredths in the measured S parameters.

A symptom of this error is the “fast rippled” reflection co-
efficient of a unitary reflecting standard that is shifted from
the reference plane of the calibration standards. Fig. 2 shows
an example of a typical tolerance zone for a shifted-short veri-
fication standard.

It should be emphasized that it is not possible to correct
this error with a different (better) characterization of the
calibration standards.

102 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 47 No. 4–5/2007

Improved Evaluation of Planar
Calibration Standards Using the TDR
Preselection Method
J. Vancl

Calibration and correction methods for the Vector Network Analyzer (VNA) are based on the fundamental assumption of the constant error
model, which is independent of connected calibration standards and/or devices under test (DUT). Unfortunately, this assumption is not
satisfied well for planar calibration standards fabricated by etching technology on soft substrates. An evaluation of the error model is affected
especially by variations in the manufacturing process and also by the reproducibility of an assembly. In this paper, we propose error
minimization by selecting the best combination of available calibration standards based on time domain reflection (TDR) measurement,
which can also be obtained by the fourier transformation from the measured S-parameters. The proposed method was verified experimentally
using short, open, load and thru (SOLT) standards fabricated on an FR4 laminate substrate which achieves the essential reduction of the
measurement error in the frequency range up to 15 GHz.

Keywords: Calibration standards, equivalent circuits, error correction, scattering parameters, vector network analyzer.

Fig. 1: Important regions of calibration and/or measurement er-
ror sources

2.2 Reproducibility of the assembly
Non-reproducibility of the assembly is minimized by an

averaging over several assemblies. An example of standard
deviation of measured data for coplanar and microstrip lines
is shown in Fig. 3. The contribution to the overall error can be
expected at a level of several thousandths.

2.3 Uncertainty of calibration standards
A basic set of calibration standards, such as Short, Open

and Match, is usually modeled using a full-wave electromag-
netic field simulator, taking into account the real geometrical
dimensions and the frequency dispersion of the material
parameters. Wrong characterization of intrinsic calibration

standards leads to spurious “slow ripple” of the measured
S-parameters. This error is shown in Fig. 4, where the reflec-
tion coefficient of the shifted calibration standards Short2
and Short3 is depicted.

However, uncertainty of intrinsic calibrations standards
can be essentially reduced by using an over-determined cali-
bration set, which improves the calibration accuracy by
measuring of more distinct calibration standards than the
required minimum [5].

2.4 Noise
The smallest error is due to noise generated by VNA.

Averaging applied to the measured data can reduce the noise.
However, this source of random error is in most cases negligi-
ble and thus it is skipped in this paper.

3 TDR preselection
Time-domain reflection measurement can provide infor-

mation about the impedance profile of the transmission line,
when the step pulse has a steep enough rise time. Therefore
the differences between the impedance profiles of the feeding
lines can be obtained. An example of the TDR response of the
calibration standards is shown in Fig. 5, where three regions
can be distinguished. The response has to be the same in a
time window of the cable and feeding line in order to keep the
error model constant. Obviously, it is different in the region
of intrinsic calibration standards. A zoomed region of the
feeding line is shown in Fig. 6.

Usually, several instances of each calibration standard are
used for VNA calibration in order to minimize the influence
of the variation in the manufacturing process [2]. An alterna-
tive approach is to select the best combination of calibration
standards with minimum differences of impedance profiles
within the feeding-line time window.

Acta Polytechnica Vol. 47 No. 4–5/2007

Fig. 2: Typical tolerance zone of the reflection coefficient of the
shifted-short verification standard due to variable imped-
ance of the feeding lines

Fig. 3: Typical standard deviations of measured data due to im-
perfect reproducibility of the assembly (FR4 substrate
inserted into the test fixture)

Fig. 4: Reflection coefficient of shifted calibration standards
Short2 and Short3

The feeding-line response of the calibration standards can
also be obtained by a Fourier transformation of the measured
S-parameters. Since we measure S-parameters only up to
15 GHz and the feeding lines are only 25 mm long, the reso-
lution of the feeding line response is too small for accurate
selection of the best combination of calibration standards.
However, the differences between the impedance profiles
(Fig. 7) are distinguishable and correspond to the TDR mea-
surement (Fig. 6).

A suitable criterion for selecting the best combination
CBEST is based on the standard deviation. The criterion for-
mula is

� �C
N

x xBEST
S

j k j
k

N ST
�

�
�

��

��arg min ,
1

1
2

, (1)

where

x
N

xj
S

j k
k

N S
�

�

�
1

1
, (2)

is average value of voltage response in time step j. NS and NT
is number of calibration standards and number of time steps,
respectively. Total number of possible combinations n is NI
raised to the power NS, where NI is the number of instances of
each calibration standard.

An advantage of the TDR preselection method is that for a
given number NI it is possible to achieve the same or smaller
variance of the feeding-line impedance profile in comparison
with statistical methods. This is because statistical methods
take into account all instances, while the TDR preselec-
tion method selects the combination with the lowest possible
variance.

4 Calibration scheme
TRL and SOLT are the most frequently used calibration

methods. TRL uses an 8-term error model and therefore it
does not enable crosstalk to be corrected. Moreover, the TRL
method cannot be used in conjunction with a fixed length
test-fixture. On the other hand, calibration of VNA using
TRL is much in terms of requirements on manufacturing and
evaluation of calibration standards. The SOLT method en-
ables correction of crosstalk, but realization of broadband
load is difficult. This problem can be overcome by using the
sliding load principle, but it is not suitable for calibration
standards manufactured on soft substrates because of poor
reproducibility of the reflection coefficient when the load is
slid along the transmission line. Another solution is it to com-
bine the two methods, where the broadband fixed load is
characterized using the TRL method and DC measurement
of the fixed load resistance [7]. Thus the SOLT calibration kit
containing the broadband fixed load is the optimal solution
for the calibration procedure on soft substrates.

The calibration procedure proposed in this paper is simi-
lar to the procedure used in [6], except for the criterion
function for the optimization step. The flowchart of the new
procedure is depicted in Fig. 8 and is described in the follow-
ing steps:
1) Short, Open and Load calibration standards are designed

using the EM simulator, and their equivalent circuits are
extracted, see Fig. 9a)-c). The thru standard is considered
as ideal.

2) Full two-port correction coefficients are computed using
measured and modeled S-parameters of S, O, L and T
standards. The 12-term error model is considered.

3) Measured data of shifted short S2 and shifted open O2
are corrected using the correction coefficients computed

104 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 47 No. 4–5/2007

Fig. 5: Time-domain reflection response measurement of calib-
ration standards (FR4 substrate inserted into the test-
-fixture)

Fig. 6: A detailed time-domain reflection measurement corre-
sponding to the feeding-line response

Fig. 7: A detailed feeding-line response obtained by Fourier
transformation of the measured S-parameters of the cali-
bration standards

in the previous step. The corrected reflection coefficients
are compared with the models of S2 and O2 shown in
Fig. 9d)-e).

4) The parameters of the equivalent circuits are optimized to
minimize the difference between the corrected measured
S parameters and modeled the S parameters of S2, O2.

Involving shifted short/open over determines the char-
acterization of the basic calibration kit, resulting in better
accuracy of the S parameter measurement. The reflection
coefficient of a shifted calibration standard, such as S2 and
O2, is much more sensitive than the criterion of reciprocity to
improper evaluation of the basic calibration standards S, O
and L. Thus the difference between estimated and modeled
reflection coefficients of O2 and S2 was used instead of the
reciprocity criterion used in [6].

5 Experiment

An experimental test of the proposed calibration method
was carried out using CPWG standards manufactured on an
FR4 substrate, each standard in six instances, see Fig. 10.

SHORT 1, OPEN, MATCH 4 and THRU were used as a
basic calibration set, SHORT 2 and OPEN 2 were used for
optimizing the values of CM, RM, LM, CO and LS (see Fig. 9),
while SHORT 3 was used as a verification standard.

The Agilent 86100C wideband scope including TDR
module 54754A (18 GHz) was used for measuring the TDR

response. The choice of the best combination was carried out
in Matlab in according to formula (1). Agilent E8364A PNA
was used for measuring the S parameters, and the calibration
procedure was carried out according to the flowchart shown
in Fig. 8. PCBs of the calibration standards were inserted
during measurement into the test fixture attached with SMA
connectors. Each calibration standard was measured five
times and the data was averaged in order to suppress the
influence of the assembly.

The experimental results for the best and worst com-
bination of calibration standards are shown in Fig. 11 and

Acta Polytechnica Vol. 47 No. 4–5/2007

Fig. 8: Flowchart of the process to optimize cal kit parameters.

Fig. 9: Equivalent circuits of calibration standards; (a) fixed load,
(b) open, (c) short, (d) shifted open, (e) shifted short

Fig. 10: CPWG calibration standards manufactured on an FR4
substrate (50×25×0.8 mm, �r � 4.7)

Fig. 11: Reflection coefficient of shifted calibration/verification
standards – the best combination

Fig. 12, respectively. It can be clearly seen that the pre-
selection method essentially reduces the “fast ripple” of the
measured reflection coefficients. We estimate that the final
uncertainty of measurement is �0.02 in magnitude and �2° in
angle.

6 Conclusion
A improved algorithm for evaluating of calibration stan-

dards using the new TDR preselection method was carried
out and experimentally verified. The experiment showed that
the measurement error of S parameters can be reduced even
by a factor of two when the worst and best cases are compared.
In contrast to statistical methods, only one set of calibration
standards is necessary for recalibring of the VNA.

Acknowledgment
The research described in this paper was supervised by

Ing. V. Sokol, Ph.D., FEE CTU in Prague and supported by

research program MSM6840770015 “Research of Methods
and Systems for Measurement of Physical Quantities and
Measured Data Processing” of CTU in Prague, sponsored by
the Ministry of Education and Sports of the Czech Republic,
and by grants 102/04/1079 and 13/03014/13117 of the Grant
Agency of the Czech Republic.

References
[1] Deal, W. R., Farkas, D. S.: CAD-based Method to De-

velop and Evaluate Calibration Standards. IEEE Micro-
wave Magazine, June 2006, p. 70–84.

[2] Chen, X.: Statistical Analysis of Random Errors from
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June 2005.

[3] Wong, K.: Uncertainty Analysis of the Weighted Least
Squares VNA. 64th ARFTG Conference, Orlando, 2004.

[4] Stumper, U.: Uncertainty of VNA S-Parameter Measure-
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Transaction on Instrumentation and Measurement, Vol. 54,
April 2005, p. 676–679.

[5] Satler, M. J., Ridler, N. M., Harris, P. M.: Over-deter-
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Employing Generalized Distance Regression, 62th

ARFTG Conference, Boulder, 2003, p. 127–140.
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Calibration in Planar Dispersive Media Through Adding
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[7] Padmanabhan, S., Dunleavy, L., Daniel, J. E., Rodrígues,
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[8] Vancl, J., Sokol, V., Hoffmann, K., Škvor, Z.: Improved
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Ing. Jan. Vancl
e-mail: vanclj1@fel.cvut.cz

Department of Electromagnetic Field

Czech Technical University in Prague
Faculty of Electrical Engineering
Technická 2
166 27 Prague, Czech Republic

Acta Polytechnica Vol. 47 No. 4–5/2007

Fig. 12: Reflection coefficient of shifted calibration/verification
standards – the worst combination