RLC Circuit - Other Configurations

Other Configurations

A series resistor with the inductor in a parallel LC circuit as shown in figure 7 is a topology commonly encountered where there is a need to take into account the resistance of the coil winding. Parallel LC circuits are frequently used for bandpass filtering and the Q is largely governed by this resistance. The resonant frequency of this circuit is,

This is the resonant frequency of the circuit defined as the frequency at which the admittance has zero imaginary part. The frequency that appears in the generalised form of the characteristic equation (which is the same for this circuit as previously)

is not the same frequency. In this case it is the undamped resonant frequency

The frequency at which the impedance magnitude is maximum is given by,

where is the quality factor of the coil. This can be well approximated by,

.

Furthermore, the exact maximum impedance magnitude is given by,

.

For values of Q greater than unity, this can be well approximated by,

.

In the same vein, a resistor in parallel with the capacitor in a series LC circuit can be used to represent a capacitor with a lossy dielectric. This configuration is shown in figure 8. The resonant frequency in this case is given by,