Resonance
In both series and parallel RLC circuits, resonance occurs when XC = XL.
In a series circuit
VC = VL at resonance
ZT = minimum
(purely resistive)
IT = maximum
Below resonance the circuit is primarily capacitive
At resonance the circuit is purely resistive
Above resonance the circuit is primarily inductive
In a parallel circuit
IC = IL at resonance
ZT = maximum
(purely resistive)
IT = minimum
Below resonance the circuit is primarily inductive
At resonance the circuit is purely resistive
Above resonance the circuit is primarily capacitive
The shape of a circuit’s resonance response is determined by an important factor called the Q
factor. A higher Q translates to a sharper response characteristic.
Series Circuit Resonance Curves
Parallel Circuit Resonance Curves
Series Resonance
In a series circuit, Q can be determined by the ratios
XL
X
OR C
R
R
Interestingly, the voltage across both the capacitor and inductor at resonance are directly
related to the Q factor, as shown above.
Q is also affected by the ratio
L
. A larger ratio means a larger Q factor.
C
Parallel Resonance
A parallel circuit at resonance behaves slightly differently to a series circuit. A parallel
circuit designed to resonate is often referred to as a tank circuit. Tank circuits are used a
great deal in communication systems.
Ideal tank circuit
An ideal tank circuit consists of a capacitive element in parallel with an inductive element,
and no resistance. Since there is no resistance the Q of the circuit is theoretically infinite.
At resonance, since the capacitor and inductor currents are 180° out of phase, the net circuit
current is zero. This means that theoretically no current is supplied to the circuit at
resonance. Also, since Z = V/I, the impedance seen by the source is theoretically infinite.
Practical tank circuit
In a practical tank circuit, there will be some resistance associated with the inductor. Thus
the Q of the circuit will not be infinite, and can be determined by the ratio
XL
.
R
The simple formula for finding the resonant frequency of a series circuit applies equally to a
parallel tank circuit provided it has a Q of 10 or greater.
Selectivity and bandwidth
Selectivity is a measure of how sharp the response curve of a resonant circuit is. The sharper
the response, the more selective the circuit is.
The responses shown in the above figure are significant since they demonstrate that a
resonant circuit can be used to restrict the passage of frequencies to a small proportion of the
total frequency range, centered around the resonant frequency. The circuit therefore behaves
as a filter, as it filters out all but the frequencies of interest. This range of frequencies is
typically referred to as the bandwidth of the filter.
Applications
Tuned Amplifiers
Antenna input to a receiver
TV Receiver