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 Joo de Camargo Ave.

37540-000, Santa Rita do Sapuca,

Minas Gerais, Brazil; e-mail: [email protected], Internet: www.inatel.br;

JOSE ANTONIO JUNSTINO RIBEIRO

Telecommunication Department

National Telecommunications Institute (INATEL), 510 Joo de Camargo Ave.

37540-000, Santa Rita do Sapuca,

Minas Gerais, Brazil; e-mail: [email protected], Internet: www.inatel.br;

WILTON NEY DO AMARAL PEREIRA

Electrical Engineering Department

University of Taubate (UNITAU), s/n Daniel Danelli St., 12060-440, Taubate,

Sao Paulo, Brazil; e-mail: [email protected], Internet: www.unitau.br.

Balanced twisted bifilar transmission lines are often used in high-frequency signal-processing applications, in impedance transformers, signal combiners, and power dividers. To apply these transmission lines and structures based on them in high-frequency 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 plane^{3} 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 several publications,^{5} using distributed line parameters.^{6} The characteristic impedance has also been obtained by means of measurements of a transmission line's input impedance under open-circuit and short-circuit 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.

Most commercial test equipment features unbalanced terminals, 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 line can be found ^{2, 8, 9} by using Eq. 1:

Z_{o-}√Z_{oc}Z_{5c}

where

Z_{oc} = the input impedance with the transmission line terminated in an opencircuit condition and

Z_{sc} = the input impedance with the transmission line terminated in a short-circuit condition.

Measurements with the load make it possible to check the previously obtained values under the open-circuit 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:

Z_{in} = Z_{o}otanh(*y*1) / Z_{o}+ Z_{L}tanh(*y*1) >

tanh(*y*1) = √ Z_{5c} / Z_{oc}

where

Z_{L} = the load impedance;

Γ = the wave propagation factor; and

l = the length of the transmission line.

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where Z_{L} is the load impedance, Γ 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 Z_{oc} and Z_{sc}. Applying the load impedance Z_{L}, the input impedance value, Z_{in}, 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. Figure 2 and Figure 3 show a comparison between the measured and calculated values for modules and arguments of Z_{in} 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 a pure resistance of 20 V.

The lines terminated under shortcircuit and open-circuit 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-circuit conditions in the frequency band of interest. ^{1} For the transmission line with an open-circuit load, the first resonance occurs 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 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 open-circuit 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 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:

1 = *k (*V* _{p}*/

*ƒ*)

where

k = the fractional wavelength,

v_{p} = the propagation velocity of the wave, and

f = the frequency of the wave.

If the propagation velocity of the wave in the transmission 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 also 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 high-frequency 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 balun-based 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

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