## Reactance Properties of Transmission Lines:

Reactance Properties of Transmission Lines : Just as a suitable piece of transmission line may be used as a transformer, so other chosen transmission-line configurations may be used as series or shunt inductive or capacitive reactances. This is very advantageous indeed. Not only can such circuits be employed at the highest frequencies, unlike LC circuits, but also they are compatible with Reactance Properties of Transmission Lines.

### Open and Short Circuited lines as tuned circuits:

The input impedance of a quarter-wave piece of transmission line, short-circuited at the far end, is infinity, and the line has transformed a short circuit into an open circuit. This applies only at the frequency at which the piece of line is exactly λ/4 in length. At some frequency near this, the line will be just a little longer or shorter than λ/4, so that at this frequency the impedance will not be infinity. The further we move, in frequency, away from the original, the lower will be the impedance of this piece of line. We therefore seem to have a parallel-tuned circuit, or at least something that behaves as one. Such a line is often used for this purpose at UHF, as an oscillator tank circuit or in other applications.

If the quarter-wave line is open-circuited at the far end, then, by a similar process of reasoning, a series-tuned circuit is obtained. Similarly, a short-circuited half-wave line will behave as a series-tuned circuit, in the manner described in the preceding section. Such short- or open-circuited lines may be employed at high frequencies in place of LC circuits. In practice, short-circuited lines are preferred, since open-circuited lines tend to radiate.

### Properties of lines of various lengths:

Restating the position, we know that a piece of transmission line λ/4 long and short-circuited at the far end (or λ/2 long and open-circuited at the far end) looks like an open circuit and behaves exactly like a parallel-tuned circuit. If the frequency of operation is lowered, the shunt inductive reactance of this tuned circuit is lower and the shunt capacitive reactance is higher. Inductive current predominates, and therefore the impedance of the circuit is purely inductive. Now, this piece at the new frequency is less than A/4 long, since the wavelength is now greater and the length of line is naturally unchanged. We thus have the important property that a short-circuited line less than λ/4 long behaves as a pure inductance. An open-circuited line less than λ/4 long appears as a pure capacitance. The various possibilities are shown in Figure 7-10, which is really a table of various line lengths and terminations and their equivalent LC circuits. ### Stubs:

If a load is connected to a transmission line and matching is required, a quarter-wave transformer may be used if ZL is purely resistive. If the load impedance is complex, one of the ways of matching it to the line is to tune out the reactance with an inductor or a capacitor, and then to match with a quarter-wave transformer. Short-circuited transmission lines are more often used than lumped components at very high frequencies; a transmission line so used is called a stub (see Figure 7-11).

The procedure adopted is as follows: 