Andrew Carter

Electrical Engineer

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Knowing the Series and Parallel Resonance

Posted Feb 18, 2012 at 12:23 pm

A special frequency determined by the values of the resistance, capacitance and inductance refers to the resonance in AC circuits. The resonant frequency point occurs where the inductive reactance of the inductor becomes equal in value to the capacitive reactance of the capacitor with varying frequency.

Series Resonance

One of the most important circuits used in electrical and electronic circuits is the series resonance circuit that can be found in various forms such as in noise filters, AC mains filters and in radio and television tuning circuits where a very selective tuning circuit for the receiving of different frequency channels is produced. The resonance of a series RLC circuit occurs when the inductive and capacitive reactance are equal in magnitude but cancel each other because they are 180 degrees apart in phase.

Figure 1 Series Resonance

A series resonant circuit plot of current is shown below where the circuit current amplitude increase from bottom to top while the frequency increases from left to right. The resonant frequency formula shown below holds as true for simple series LC circuits as it does for simple parallel LC circuits since the peak can be seen to be at the plotted frequency point of 157.9 Hz which is the closest analyzed point to the predicted resonance point of 159.55 Hz.

Figure 3

Figure:1 Measurement in frequency domain

Figure 2 Measurement in frequency domain

The total impedance of a series LC circuit approaches zero as the power supply frequency approaches resonance. Due to high current flows and substantial individual component impedances, extremely high voltages can be formed across the individual components of series LC circuits at resonance. It is possible to produce dangerously high voltage across the capacitor and the inductor.

The average power dissipated in a series resonant circuit can be expressed in terms of RMS voltage and current as follows:

Figure 4

Parallel Resonance

The resonance of a parallel RLC circuit is a bit more involved than the series resonance. There are three different ways that can define the resonant frequency as they converge on the same expression as the series resonant frequency with small resistance in the circuit. In many ways, a parallel resonance circuit is exactly the same as the series resonance since both are 3-element networks that contain two reactive components making them a second-order circuit. Both are influenced by variations in the supply frequency and both have a frequency point where their two reactive components cancel each other out influencing the characteristics of the circuit.

Figure 5 Parallel Resonance

The total impedance of a parallel LC circuit approaches infinity as the power supply frequency approaches resonance. A tank circuit draws no current from AC power source as the total impedance increases to infinity with capacitive and inductive reactance equal to each other.