Determine Twisted-line
Characteristic Impedance
This approach shows how to calculate and measure the characteristic
impedance of balanced twisted bifilar transmission lines using a
commercial vector network analyzer.
ANTONIO ALVES FERREIRA JUNIOR
Electronic and Electrotechnical Department
National Telecommunications Institute (INATEl), 510 João de Camargo Ave.
37540-000, Santa Rita do Sapucaí,
Minas Gerais, Brazil; e-mail: antonioa@inatel.br, Internet: www.inatel.br;
JOSE ANTONIO JUNSTINO RIBEIRO
Telecommunication Department
National Telecommunications Institute (lNATEl), 510 João de Camargo Ave.
37540-000, Santa Rita do Sapucaí,
Minas Gerais, Brazil; e-mail: justino@inatel.br, Internet: www.inatel.br;
WILTON NEY DO AMARA L PEREIRA
1. This simple diagram shows the connection scheme for
measuring a abalanced transmission line with a VNA
Electrical Engineering Department
University of Taubate (UNITAU), s/n Daniel Danelli St., 12060-440, Taubate,
Sao Paulo, Brazil; e-mail: wilton.pereira@uol.com.br, Internet: www.unitau.br.
B
alanced twisted bifilar transmission lines are
often used in high-frequency signalprocessing applications, in impedance
transformers, signal combiners, and power
dividers. To apply these transmission lines
and structures based on them in highfrequency circuits and systems, the characteristic
impedance of the twisted lines must be known. Once a
solution has been found for connecting these balanced
lines to the unbalanced ports of standard test equipment,
it is possible to use a commercial vector network
analyzer (VNA) for accurate measurements of
characteristic impedance on balanced twisted bifilar
transmission lines.
One of the keys for using a commercial VNA in analyzing the characteristic impedance of a balanced
twisted bifilar transmission line is to minimize
measurement errors caused by the mating of the
balanced line and the unbalanced VNA. The
characteristic impedance is an important parameter of
the line, used in many applications including in the
design of wideband impedance transformers.¹ The
procedures and calculations that will be applied for
analyzing these balanced lines follow classical design
theory for uniform transmission lines.²
Previous authors have proposed methods for
determining the characteristic impedance of a balanced
twisted transmission line. Their approaches are based on
making impedance measurements on the conductors and
ground plane³ and using these as a reference for the
corresponding admittance value.4 Some characteristic
impedance expressions based on transmission-line
conductors and dielectric material properties have been
presented in severa I publications,5 using distributed line
parameters.6 The characteristic impedance has alsa been
abtained by means of measurements of a transmissian
2. This plot compares the measured and calculed values for the
input impedance, ZIN as a function of frequency.
line's input impedance under open-circuit and shortcircuit conditions at the load for the operating
frequency.7
The measurement method presented here was
validated by laboratory testing in which reliable
measurement techniques were essential. Special
precautions were taken to minimize measurement
errors. The VNA was calibrated in the frequency band
of interest using standard connectors under open-circuit,
short-circuit, and specified load conditions. Measurements of scattering parameters (Sparameters) were
made by applying swept-frequency test signals in the
frequency band of interest. The reflection characteristics
were analyzed by means of the input impedance and reflection input coefficient S11 parameter measurements.
The input complex impedance was obtained using the
Smith chart and setting the corresponding reactive
component values for the test frequency of interest.
Twisted line impedance
values versus frequency
FREQUENCY
MHz
|Zo|
(Ω)
Θ
(DEG.)
40
50
60
70
80
90
100
110
120
130
38.7300
37.8732
37.1237
36.5242
35.9403
35.3873
34.8063
34.2746
33.3970
32.3561
-3.1951
-2.6552
-2.1681
-1.7382
-1.3441
-0.9987
-0.5798
-0.0466
0.4133
0.9807
Most commercial test equipment features
unbalanced terminaIs, making it difficult to evaluate a
balanced transmission line. Fortunately, there are
different methods to sidestep this incompatibility, such
as the use of a balanced-unbalanced (balun) transformer.
A balun, which converts balanced networks to
unbalanced networks, was used in the current approach.
Several types of baluns are commercial available, and
their behavior and performance must be checked with
rigorous procedures in order to ensure that the electrical
contributions of the balun do not influence the final
measurement results for the balanced transmission line.
The VNA used in the testing was calibrated using
the balan and appropriate adapters as required. Figure 1
shows the calibration scheme. Using the measured
values from the VNA, the characteristic impedance of
the balanced transmission tine can be found2,8,9 by using
Eq. 1:
Where
Zoc = the input impedance with the transmission line
terminated in an opencircuit condition and
Zsc = the input impedance with the transmission tine
terminated in a short-circuit condition.
Measurements with the load make it possible to
check the previously obtained values under the opencircuit and closed-circuit conditions. In making such
checks, the equations for the transmission line's input
impedance corresponding to the propagation factor can
be applied as in Eqs. 2 and 3:
where
ZL = the load impedance;
Г = the wave propagation factor; and
l = the length of the transmission line.
where ZL is the load impedance, Г is the wave
propagation factor and l the length of the line.
Following this, Eqs. 1 and 3 are substituted into Eq. 2
using the measured values of Zoc and Zsc. Applying the
load impedance ZL, the input impedance value, Zin, can
be calculated and compared to the measured value for
the same load. All measurements showed good
agreement among the results for the line terminated with
an open circuit, short circuit, and the load. Figures 2 and
3 show a comparison between the measured and
calculated values for modules and arguments of Zin
within the frequency band of interest. The transmission
line that was used has 28AWG gauge conductors with
five twists per centimeter and 20-cm length. The load
impedance for these experiments was apure resistance
of 20 V.
The lines terminated under shortcircuit and opencircuit conditions with series and parallel resonances
were compared to waveguide transmission lines
according to their line lengths. The experimental results
reveal both the real and imaginary parts of the
impedance in both cases. Figures 4, 5, 6, and 7 show the
input impedances for the transmission lines with the
other end of each line under open-circuit and short-
4. this plot shows the real part of the input impedance for the
transmission line with open-circuit load conditions.
3. These plots compare the measured and calculed phase for
the input impedance of the balanced transmission line as a
function of frequency.
circuit conditions in the frequency band of interest.¹ For
the transmission line with an open-circuit load, the first
resonance accurs with a null reactance (series
resonance). For the transmission line with a short-circuit
load, the line shows a maximum impedance (parallel
resonance). The lines show a large increase or decrease
5. this plot shows the imaginary part of the input impedance for
the transmission line with open-circuit load conditions.
to the comparison waveguide transmission lines in order
to ensure a valid match in the relationship between the
balanced transmission lines and the waveguide.
However, good agreement was found between the
measurements for the balanced lines and theoretical values which served to validate the measurement method.
The first resonance always occurs at a frequency where
the line length is equal to a quarter wavelength. Because
of the presence and problem presented by resonances,
measurements should not be performed at a point where
the transmission line length is an integer multiple of the
quarter wavelength. This can be checked by means of
Eq. 4:
l = k vp
f
where
k = the fractional wavelength,
vp = the propagation velocity of the wave, and
f = the frequency of the wave.
6. This plot shows the real part of the input impedace for the
transmission line with short-circuit load conditions.
7. This plot show the imaginary part of the input impedance for
the transmission line with short-circuit load conditions.
in impedance in proximity to resonances. In an ideal
transmission line, one value would tend towards infinity
while the other value would tend towards zero, with
different variations in the ratio of the two values. Small
changes in frequency reveal large differences in the
measured line parameters, which would imply that
measurements in the proximity of these resonant conditions should be avoided in order to maintain accuracy.
For both cases, using the shortcircuit and opencircuit loads, the resonant frequencies were found to
have slightly different values. This was thought to be
due to the nonideal short-circuit and open-circuit
conditions established for the transmission lines during
the measurements, which would require slight changes
If the propagation velocity of the wave in the
transmissio line is not known, it can be determined
through previous parameters measurements by classical
methods.9 The table offers examples of the test results
for the measurement method presented here, with values
for the characteristic impedance module and argument
as functions of frequency. The authors aIs o have results
available for other transmission line types with different
diameters and twists number using this same
measurement method.
Balanced lines offer many advantages in terms of
noise suppression and rejection of RFI and EMI in highfrequency circuits. With the increasing transfer of video,
data, and voice through wired and wireless means, the
need for noise-free transmissions at high data rates will
only grow through time, requiring effective
measurement and analysis approaches for handling
devices and circuits based on single-ended designs,
differential, designs, and a combination of the two. The
measurement approach presented here is based on the
use of commercially available VNA systems and their
calibration standards and can be applied with the help of
conventional measurement methods with proper attention to detail.
In summary, this report has shown that careful
calibration and measurement practices were needed to
make this measurement approach effective for
determining the characteristic impedance of a balanced
line with a commercial VNA. The main issue concerns
undesired resonances which can degrade the
measurement accuracy. However, with care, this balunbased measurement method can be applied to finding
the characteristic impedance for a wide range of
balanced transmission lines. And for unbalanced
transmission lines, the balun is not needed, but the
equations and the measurement procedure are useful
and effective.
REFERENCES
1. A. A. Ferreira Jr" "Projeto de transformador de impedância de radiofreqüência com
controle da faixa de passagem," Dissertação de Mestrado, Instituto Nacional de
Telecomunicações, Santa Rita do 5apucaí, MG, Brazil, 2006.
2. R. A. Chipman, Unhas de Transmissão. Trad. Ivan José de Albuquerque,
McGraw-Hill, 5ao Paulo, 1976.
3. D. B. 5inclair, "Measuring Balanced Impedances with the R-F Bridge," General
Radio Experimenter, Vol. 17, pp. 3-5, 5eptember 1942.
4. F. E. Terman, and J. M. Pettit, Eiectronic Measurements, 2nd ed., McGraw-Hill,
New York, 1952.
5. P. Lefferson, "Twisted Magnet. Wire Transmission Une," IEEE Transactions on
Parts, Hybrids, and Packaging, Vol. PHP-7, No. 4, December 1971, pp. 148-154.
6. J. H. 8roxon 11, and D. K. Unkhart, "Twisted-Wire Transmission Unes," RF
Design, June 1990, pp. 73-75.
7. C. C. Kuo, M. Y. Kuo, and M. 5. Kuo, "Modeling and Analysis of Wideband Power
Transmission Line Transformers," in Proceedings of the 11 th Annual Applied Power
Electronics Conference and Exposition, San Jose, CA, 1996, pp. 441-446.
8.S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication
Electronics, 3rd ed., Wiley, New York, 1994.
9. W. L. Everitt, and G. E. Anner, Communication Engineering, 3rd ed., McGraw-Hill,
New York, 1956.