Q of a Circuit

Author: J.B. Hoag

As current surges back and forth in a resonant circuit, the electrical energy is alternately shifted back and forth between the magnetic field of the coil and the electric field of the condenser, losing a certain proportion of the total into the resistance at each alternation. In order to maintain oscillations, the generator must supply a small amount of energy each cycle. This is analogous to the small push we give to a swing; only a little push is needed at the end of each swing to keep it going. Electrically, the interest lies in the comparison between the total energy in the circuit to that which is dissipated (and must be re-supplied by the generator). This ratio is called the "Q" (quality) of the circuit. In practice, nearly all of a circuit's resistance is in the coil. It may then be shown that

Practical radio frequency coils have Q's from 50 to 200 and occasionally 500. Audio frequency coils range from 1 to 10 and occasionally are as low as 1/2. The higher the Q, the better.

The rate at which current dies down in a resonant circuit, after the source has been disconnected, is called the damping of the circuit, whose measure is called the decrement δ. Q = π/δ. A high Q circuit is lightly damped, has a small decrement, a sharp resonance peak, and a high selectivity.

This example shows the fall-off of the resonant oscillation after switching off the source oscillator vfg1. The resonance frequency of the LC circuite is approx. 500 kHz. The switch S1 opens after 50 us.