Question

A.C. Fundamentals - Bandwidth of a Series Resonant Circuit

Answer 1

In the context of A.C. (alternating current) fundamentals, a series resonant circuit is an electrical circuit that consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. When an AC voltage is applied to this circuit, it exhibits resonance at a particular frequency where the reactive components cancel each other out, leading to a higher current magnitude and a lower impedance.

The bandwidth of a series resonant circuit refers to the range of frequencies around the resonant frequency within which the circuit exhibits a response that is reasonably close to its maximum. In other words, it's the range of frequencies over which the circuit remains in a state of resonance.

The bandwidth of a series resonant circuit is determined by the Q factor (Quality factor) of the circuit. The Q factor is a measure of how selective the circuit is in terms of responding to a specific frequency. A higher Q factor indicates a narrower bandwidth, while a lower Q factor indicates a wider bandwidth.

Mathematically, the bandwidth (BW) of a series resonant circuit can be approximated using the formula:



=

res

BW=
Q
f
res
    ​

    ​


Where:



BW is the bandwidth of the circuit,

res
f
res
    ​

 is the resonant frequency of the circuit, and

Q is the quality factor of the circuit.

In terms of the components of the circuit:


R is the resistance,

L is the inductance,

C is the capacitance,

res
f
res
    ​

 is the resonant frequency, and

Q is given by

=
1



Q=
R
1
    ​

C
L
    ​

    ​

.

It's important to note that this formula provides an approximation of the bandwidth, assuming that the resistance is relatively small compared to the reactance of the inductor and capacitor at the resonant frequency. In practical circuits, other factors and losses can also influence the bandwidth.

In summary, the bandwidth of a series resonant circuit is determined by its Q factor and is related to the width of frequencies over which the circuit exhibits a significant response around its resonant frequency.