Module 2 : Transmission Lines. Lecture 13 : Application of Transmission Lines continues. Objectives. In this course you will learn the following

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1 Objectives In this course you will learn the following What is the resonant section of a transmission line? Frequency response of a resonant section of a line. Input impedance of a resonant section of a line. Voltage and current on a resonant section of a line.

Transmision Lines as Resonant Circuits If the length of a short or open circuited line is exact multiple of, the imput impedance of the line is zero or.

2 Transmision Lines as Resonant Circuits If the length of a short or open circuited line is exact multiple of, the imput impedance of the line is zero or. Let us plot the input impedance as a function of frequency ` ', for a given length of transmission (short circuit or open circuit). and a given termination Figure shows the variation of reactance as a function of frequency for open and short circuited sections of a transmission line. It is clear that around frequencies.., for which the length is an integer multilple of, the impedance variation is identical to an L-C resonant circuit. In the vicinity of these frequencies the line can be used as a LC - resonant circuit.

Frequency response of Resonant Circuit The impedance characteristics of a series and a parallel resonant circuit are shown in the figure below Comparing Figure (1) with Figure (2), one can observe

3 Frequency response of Resonant Circuit The impedance characteristics of a series and a parallel resonant circuit are shown in the figure below Comparing Figure (1) with Figure (2), one can observe that a short circuited line behaves like a parallel resonant circuit around frequencies and, whereas around and its behaviour is like a series resonant circuit. In general a short circuited section of a line is equivalent to a parallel resonant circuit. Similarly, the line is equivalent to a series resonant circuit. A converse is true for an open circuited section of a line i.e., if the length of the line is equal to odd multiples of, the line behaves like a series resonant circuit, and if the length of the line is equal to even multiple of, the line behaves like a parallel resonant circuit.

4 Input Impedance of Resonant Line Input impedance of a resonant lossless line is either. However, in practice, the lines have finite loss. This loss has to be included in the calculations while analysing the resonant lines. The complex propagation constant has to be used in impedance calculations of a resonant line. The input impedance of a short or open circuited line having propagation constant can be written as Note that although has been taken complex for a low-loss transmission line, is almost real. Substituting for, we get For a low-loss line, taking, we have. Also. Hence we get Similarly for an open circuited line we get For resonant lines, is integer multiples of i.e., is integer multiples of. If we take odd multiples of,, and we get On the other hand if we take even multiples of,, giving Conclusion A parallel resonant section of a line has an impedance and a series resonant section has an impedance. One can cross-check the result with that of an ideal loss-less line. In the absence of any loss the parallel resonant circuit shows infinite impedance and a series resonant circuit shows zero impedance at the resonance.

Voltage & Current on a Resonant Section of a line Consider a short circuited section of a line having length equal to odd multiples of. This line is equivalent to a parallel resonant circuit.

5 Voltage & Current on a Resonant Section of a line Consider a short circuited section of a line having length equal to odd multiples of. This line is equivalent to a parallel resonant circuit. Let the line be applied with a voltage between its input terminals as shown in Figure(a). The voltage and current standing wave patterns on the line are shown in Figure(b,c). The voltage is zero at the short-circuit-end of the line and is maximum at the input end of the line. similarly, the current is maximum at the short-circuit end and minimum at the input end of the line. The maximum value of the voltage on the line is and maximum value of current is. For a short-circuited line the voltage and current on the line are given as

6 Recap In this course you havel learnt the following What is the resonant section of a transmission line? Frequency response of a resonant section of a line. Input impedance of a resonant section of a line. Voltage and current on a resonant section of a line.

7 Recap In this course you havel learnt the following What is the resonant section of a transmission line? Frequency response of a resonant section of a line. Input impedance of a resonant section of a line. Voltage and current on a resonant section of a line.

EECS 117. Lecture 5: Transmission Line Impedance Matching. Prof. Niknejad. University of California, Berkeley

EECS 117. Lecture 5: Transmission Line Impedance Matching. Prof. Niknejad. University of California, Berkeley EECS 117 Lecture 5: Transmission Line Impedance Matching Prof. Niknejad University of California, Berkeley University of California, Berkeley EECS 117 Lecture 5 p. 1/2 Open Line I/V The open transmission