## 019/100 Open-Circuit Transmission Line

100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design

November 2019

Michael Benker

**Example 2.11-2B: Calculate the input impedance of a quarter wave open-circuited microstrip transmission line for a given length of**** time.**

The reactance of a lossless open circuit transmission line can be modeled as being equal to the characteristic impedance multiplied by the cotangent of the electrical length of the transmission line in degrees.

X = Z * cot(Θ)

To construct this circuit, a termination of 1 MOhms is used to simulate an open circuit. As the electrical length in degrees varies with frequency (the wavelength), a static electrical length of a transmission line varied over many frequencies will suffice to demonstrate the reactance of a varying electrical length transmission line. The following circuit was created with a transmission line optimized for 10 GHz, similar to the Short-circuited Transmission Line:

The results above are consistent with the theoretical model of an open circuit transmission line being modeled by a cotangent relationship. At the optimized frequency (at which the transmission line length is quarter-wave) it can be observed that the impedance of the line is measured to be zero. At a half-wave length and other multiples of a half wave length, the transmission line generates high levels of resonance.

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