This study shows how the wire gauge and number of twists per centimeter used in balanced twisted bifilar transmission lines can impact the characteristic impedance of those lines.

Balanced twisted bifilar transmission lines have broad applications for any circuits in which impedance transformations are required. By using a vector network analyzer (VNA), it is possible to measure the characteristic impedance of these balanced transmission lines in order to design desired impedance transformations. Measurements with a VNA can be made by using a balancedunbalanced (balun) transformer that converts a balanced network to an unbalanced network. In the present report, different varieties of balanced twisted bifilar transmission lines were evaluated for their absolute and corresponding phase angle values of characteristic impedance. In order to fully understand the construction of balanced twisted bifilar transmission lines, some physical parameters were modified from test to test, including the number of conductor twists per centimeter and the conductor diameter. The effects of those changes on the balanced twisted bifilar transmission lines will be presented.

The characteristic impedance of a transmission line is an important parameter when designing radio communications circuits and systems. Knowing this parameter can aid in the design of impedance transformers, in optical communications receivers, in impedance- matching applications for solidstate amplifiers, for antenna coupling, signal combiners and dividers, and in high-frequency signal processing.^{1-4} This work presents the experimental results of absolute (|Zo|) and the phase (?) values as functions of frequency. Care was taken to mitigate errors during measurements by taking into account the contributions of test fixtures and performing proper calibration techniques.

The measured values of characteristic impedance were obtained in a test laboratory according to classical test procedures as described in a previous article.^{5} The characteristic impedance calculation follows the classical methods for determining the characteristic impedance of a transmission line. For the measurements, an RF vector network analyzer (VNA) with terminals having a reference impedance of 50 Ohms was used. The VNA employed calibrated balun transformers, one covering 10 to 100 MHz and the other spanning 100 to 420 MHz for a total bandwidth of 10 to 420 MHz. The baluns incorporate balanced and unbalanced terminals at 50 and 200 Ohms, respectively, requiring the use of coaxial adapters. The test system was calibrated together with the baluns to reduce their influence on the measurement results. Calibrations were performed by means of opencircuit and short-circuit terminations as well as a 200-Ohm load, to match to the balun's impedance transformation ratio of 1:4 and resulting output impedance of 200 Ohms.

Since characteristic impedance changes with the number of twists per centimeter of conductor and with the conductor diameter it was necessary to achieve high precision and uniformity in all of the conductor twists. A machine controlled by an electronic circuit was developed so that the line conductors were regularity twisted and the number of twists per centimeter of conductor could be tightly controlled. When the twist reaches the desired value, this parameter is identified, as shown in * Fig. 1*.

^{6}

Measurements were made for a number of different conductors, changing the conductor diameter and the number of twists per centimeter in each case. The conductors under test were enamel film isolated copper with specified gauges of 24AWG, 26AWG, 28AWG, and 30AWG. The transmission lines were constructed with 2, 3, 4, and 5 twists per centimeter. The line length was 20 cm and the test frequency band was adjusted from 40 to 130 MHz in 10-MHz steps. Above 130 MHz, the lines take on a resonant behavior and the measured values are not accurate or reliable.^{5}

* Figures 2, 3, 4, 5* compare absolute values of characteristic impedance as a function of frequency for the different conductor gauges with different numbers of twists per centimeter.

*show the phase-angle values for the same respective conductor gauges and twists per centimeter.*

**Figures 6, 7, 8, 9***and*

**Table 1***summarize the results of characteristic impedance for balanced twisted bifilar transmission lines with changing frequency for the same respective conductor gauges and twists per centimeter, while*

**2***presents the absolute values of characteristic impedance for the same transmission lines at 14 MHz determined by using another method.*

**Table 3**^{3}Fairly close agreement was achieved with these results, considering that different procedures and frequencies were used.

In some cases, the results for the balanced twisted bifilar transmission lines do not vary in any regular or predictable ways. No matter what efforts were made to deliver consistent transmission-line structures, using uniformly spaced and formed twists in the conductors, some irregularities in the constructions would lead to inconsistent results in terms of the characteristic impedance. It is also possible that even in transmission lines with the same number of twists per centimeter of conductor length, that the turns were closed or uneven, causing irregularities in the characteristic impedance. In addition, parasitic effects can impact the measurements, leading to inaccuracies in the final results.

It was observed that when a conductor's diameter was reduced, while maintaining the same number of wire twists per centimeter and at the same frequency, the absolute value of the characteristic impedance increased. By increasing the number of twists per centimeter for the same conductor and performing the evaluation at the same frequency, the absolute value of the characteristic impedance decreases. Because of changes in distributed capacitance and inductance, a reduction in the transmission-line diameter for the same number of twists per centimeter and at the same frequency results in an increase in the characteristic impedance. By maintaining the transmission-line diameter and performing evaluations at the same frequency, the characteristic impedance decreases as the number of twists per centimeter increases. Because of small effects of external inductance in the balanced twisted bifilar transmission lines, conductor resistance makes a significant contribution to the characteristic impedance of the lines at higher frequencies. The value grows with the square root of the frequency because of skin effects.^{7} However, because of the effects of capacitance, there is a decrease in the characteristic impedance of the balanced twisted bifilar transmission lines with an increase in frequency. The proximity of the conductors can also play a strong role in the final impedance value.^{8}

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The results obtained here are preliminary and must be refined in order to obtain a more precise theoretical model for calculating the characteristic impedance of a balanced twisted bifilar transmission line. Such calculations should be possible by means of an equation that takes into account such parameters as wire diameter and the number of wire twists per centimeter, yielding the characteristic impedance as a function of frequency. For the same transmission lines, distributed parameters such as resistance, inductance, conductance, and capacitance, the attenuation and phase factors, and the propagation velocity, were calculated and presented.^{6} Different values of characteristic impedance can be obtained for other conductor types, by applying the proper material parameters and transmission-line types.

**REFERENCES**

1. I. J. Bahl, "Broadband and Compact Impedance Transformers for Microwave Circuits," *IEEE Microwave Magazine*, Vol. 7, No. 4, August 2006, pp. 56-62.

2. M. Dong and H. D. S. Salvy, "Analyzing 4:1 TLTs for Optical Receivers," *Microwaves & RF*, March 2005.

3. The ARRL Handbook for Radio Communications, American Radio Relay League, Inc., Newington, CT, 2008.

4. A. A. Ferreira, Jr., J. A. J. Ribeiro, and W. N. A. Pereira, "Designing Wideband RF Impedance Transformers," *Microwaves & RF*, Vol. 46, No. 3, March 2007, pp. 78-88.

5. A. A. Ferreira, Jr., J. A. J. Ribeiro, and W. N. A. Pereira, "Determine Twisted-Line Characteristic Impedance," *Microwaves & RF*, Vol. 47, No. 1, January 2008, pp. 66-74.

6. A. A Ferreira, Jr., "Projeto de transformador de impedncia de radio freqncia com controle da faixa de passagem," Master dissertation, National Institute of Telecommunications INATEL, Santa Rita do Sapuca, Minas Gerais, Brazil, 2006.

7. S. Ramo, J. R. Whinnery, and T. Van Duzer, *Fields and Waves in Communication Electronics*, Wiley, New York, 1994.

8. R. A. Chipman, Theory and Problems of Transmission Lines, McGraw-Hill, New York, 1968.