Which type of transmission line has a finite length and is not terminated in its characteristic impedance?

A transmission line that has a finite length and is not terminated in its characteristic impedance is known as a resonant transmission line. This type of line will resonate at certain frequencies due to the effects of its physical dimensions and the way it interacts with the wavelength of the signals passing through it. When a transmission line does not have the appropriate termination, reflections can occur, leading to standing waves along the line, which is characteristic of resonant behavior.

Resonant transmission lines can be particularly sensitive to the frequency of the signal, leading to increased voltage (or current) at certain points along the line based on constructive interference. This is crucial in applications where specific frequency response and impedance matching are needed.

Transmission lines that are infinite would not be practical in a finite system, and distributed transmission lines typically refer to the way capacitance and inductance are considered along the length of the line rather than its termination. Shorted transmission lines would be terminated in a way that creates a direct connection (short circuit) at the end, which does not fulfill the condition of not being terminated in its characteristic impedance. Thus, resonant transmission lines are uniquely identified by the characteristics of finite length and improper termination, leading to their resonance effects.