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 (INATEL), 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 AMARAL PEREIRA
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.

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 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 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_ocZ_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[ Z + Z_otanh(y1) / Z_o+ Z_Ltanh(y1) ]

tanh(y1) = √ Z_5c / Z_oc

where

Z_L = the load impedance;

Γ = the wave propagation factor; and

l = the length of the transmission line.