Series Resonance Circuit – Working Principle, Frequency Response and Characteristics

Introduction

A resonant circuit is formed using resistance (R), inductance (L), and capacitance (C), and it exhibits a frequency-dependent response as the input frequency changes. In this article, we will examine the frequency response of a series resonance circuit and understand how its resonant and cut-off frequencies are determined.

So far, we know that a series RLC circuit connected to a fixed-frequency sinusoidal supply shows a certain steady-state behavior. But what happens if the circuit is supplied with a constant amplitude and variable frequency? This changing frequency significantly affects the behavior of the inductor and capacitor, leading to resonance.

Resonance in a Series RLC Circuit

In a series RLC circuit, there is a specific frequency at which the inductive reactance (X_L) becomes equal to the capacitive reactance (X_C).

X_L = X_C

At this point, the circuit is said to be in series resonance, and this frequency is known as the resonant frequency (f_r) of the circuit. Series resonance circuits are extremely important and are widely used in:

• AC mains filters
• Noise filtering circuits
• Radio and television tuning circuits
• Communication and signal processing systems

Behavior of Inductive Reactance

From the inductive reactance formula, it can be seen that the value of inductive reactance increases as frequency increases. As the frequency approaches infinity, the inductor behaves like an open circuit.

On the other hand, when the frequency approaches zero (DC), the inductive reactance approaches zero, and the inductor behaves like a short circuit. Therefore, inductive reactance is directly proportional to frequency.

Impedance in a Series Resonance Circuit

The total impedance of a series RLC circuit varies with frequency. When the circuit is dominated by capacitive reactance, the impedance curve takes a hyperbolic shape. When inductive reactance dominates, the response becomes non-symmetrical.

At resonance, the impedance of the circuit becomes minimum. Since impedance is very low at this point, the admittance becomes very high, and a large current may flow through the circuit. This is why resonant circuits must be designed carefully to prevent damage due to excessive current.

Voltages at Resonance

In a series RLC circuit, the supply voltage is the phasor sum of the voltages across R, L, and C:

V_S = V_R + V_L + V_C

At resonance, the voltages across the inductor and capacitor are equal in magnitude but opposite in phase. Since they are at +90° and -90° respectively, they cancel each other out:

V_L = – V_C

As a result, the entire supply voltage appears across the resistor:

V_S = V_R

For this reason, series resonance circuits are also called voltage resonance circuits, in contrast to parallel resonance circuits which are known as current resonance circuits.

Conclusion

A series resonance circuit shows minimum impedance and maximum current at the resonant frequency. The cancellation of inductive and capacitive voltages results in a unique voltage and current response, making these circuits extremely useful in tuning, filtering, and signal processing applications.