When Inductors and
Capacitors 'Marry'

"For them life may be perfect harmony,
but not when they're singing the wrong tune!"

When one couples an inductor and a capacitor to each other there will be a resonant circuit. Sure, the 'tightness' with which they are coupled will affect the Q (quality) of the resonant circuit, but this does not alter the fact that such a circuit exists. The usual unknown parameter is the frequency at which this circuit will oscillate.

Along comes some form of 'excitement' (much like shaking a bowl of jelly) and the circuit will start to oscillate (the jelly wobbles). If the frequency of the 'excitement' is near that of the resonant frequency of the circuit, then the circuit will be 'excited' more (shake the jelly at the right speed and the jelly will wobble more - sorry for my simple analogy, but there are electrical engineers who still don't understand resonance!).

There is one thing also not generally known and that is the resonant circuit absorbs the excitation energy if this energy is close or on the resonant frequency (the closer, the more it absorbs). This is shown later in the section on "Interpreting the Readings".

The frequency at which resonance occurs is simply determined by where the reactance of inductance and capacitance are equal. This means a small inductance and a larger capacitance could have the same resonant frequency as that of a large inductance and small capacitance. If both elements are large then the resonance frequency will be low. If small, then the frequency will be relatively higher.

Taking this into account, things like power factor correction capacitors coupled with transformers or motors could be affected by a low order harmonic. On the other end of the scale, the inductors and capacitors in EMC filters are relatively tiny and therefore could be affected by simple things like mains borne HF signalling systems (where many kHz are used).

But damage is related to power and the ability of the components to conduct this energy. If the power of the excitation frequency is small by comparison to power flowing in the elements, then damage is probably nothing more than a little heat. If, however, there were merely a few watts of HF around then the tiny components used in an EMC filter could be blown to destruction!

There is this belief amongst some that if you alter either the inductance or capacitance you stop resonance. Sorry to disappoint you, but you don't! What you do accomplish is to move the frequency at which the two elements oscillate, and thereby provide a little 'distance' between any excitation frequency and what the resonant circuit will sing along to. The term 'de-tuning' is therefore one of the most accurate used in this regard.

Resonance (including ferroresonance described below) can take place anywhere in a system and is not just limited to the main components. Metering circuits could be as affected as, say, the main transformer and power factor correction capacitors. If the former, easily created when driving inductor based meters from capacitive VTs, then all that happens is the metering system shows up faults that don't truly exist. If the main components, then things get a lot worse! And, worse still, if the metering system does not show this to be happening!


A capacitor on its own, although it can, has very little chance of showing signs of resonance (we're staying out of the realms of radio frequencies here where the wiring alone is inductance). However, an inductor is not so innocent. Just being there, and there are lots of inductors used in the delivery of power, can lead to resonance occuring in the most unexpected of cases!

Wires have inherent capacitance. By simply taking a length of wire and winding it in a tight circle causes the capacitance (known as 'stray capacitance') to increase dramatically. The capacitance is not a physical component, but an unseen yet very real physical attribute.

I suppose you've cottoned on by now that should the inductive reactance and the reactance of the stray capacitance be equal at a frequency that exists on the said inherent resonant circuit that has been created by winding the inductor, then one is going to see the results of this resonance! Yip, you're spot on!

Although not impossible in 'power' components (power transformers, etc.), this effect is more likely to be experienced in metering circuits where relatively large inductances are created in the tightly wound coils of many turns made with very thin wire. Also, such meters are usually fed with long wires which add to the capacitance across these coils.

Have fun trying to explain this to some folk!


Now there is a nasty beast when it comes to resonance, and that is when the resonant frequency moves! To electrical engineers this concept may be rather difficult to understand, but to electronics engineers it is easily understood as it is an almost everyday experience! (remember what we keep saying about power quality being an electronics orientated subject - again, the facts substantiate this).

If one subjects an inductor to a static magnetic field, the inductance changes (in most cases it drops, but I have experienced it going up too!). Anyone who has worked with audio telecoms circuits will know exactly what I mean, especially when used in 2 to 4 wire convertors.

If the resonance is occurring at many times the mains frequency, then a new aspect of the resonant characteristics comes into play. When subjecting this inductor to mains means the inductive component that is playing a part in the resonance is subjected to a bias that changes 100 times a second (in 50Hz areas). This means the moving resonant frequency only equals the excitation frequency at certain points on the waveform.

There are some devices that deliberately cause this to happen, but this is not desired when delivering power. To rid the system of this sort of 'parasitic oscillation' requires 'detuning' in the correct direction. Detuning in the wrong direction (moving the frequency higher instead of lower, or vice versa) will simply mean the resonance will occur on a different part of the cycle. Unfortunately, there is no rule as to what is the correct direction.

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© 31.07.03