If a series lc circuit has two inductors and one capacitor can it have more than one resonant frequency?

 

If a series lc circuit has two inductors and one capacitor can it have more than one resonant frequency?

There will be only one resonance in a simulation where the inductors and capacitors are pure and ideal, with no parasitic capacitances or inductances. A more complete simulation model may show more resonances.

In a practical circuit, the inductors will have parasitic parallel capacitances, and the capacitors and wiring will have parasitic series inductances. The result may be multiple resonances: the inductors may show parallel self-resonances, and there may be more than one series resonance.

 

No. In a series circuit there will be an equivalent series inductance of the two inductors assuming the inductors are not coupled. This also assumes that the parasitics are of second order smallness and the frequencies are not pushed to the point where lumped circuit elements no longer model the physical situation.

 

That's generally true, and certainly capacitor inductance is not usually so much of a problem up to low MHz frequencies. At a hundred MHz the picture is different: I don't suppose that the original poster is likely to be concerned with such frequencies, but then again we don't know for sure.

Inductors can be quite another story though, especially if not designed for particularly low self-capacitance. The parallel self-resonance often sets a practical upper limit on the inductance which can be used, even at modest radio frequencies. If not taken account of, inductor self resonances can result in spurious responses.

 

What if one of the inductors were the secondary coil of
a transformer, would there then be more than one resonant frequency?

 

Possibly could be due to the internal capacitances of the transformer.
It even applies to larger inductors as well as small ones depending on the frequency you're dealing with.

All inductors have a self resonant frequency.

 

If you look at a graphical picture of reactance versus frequency for an inductor and a capacitor you can quickly conclude that in a series LC circuit there is only one point of intersection. Algebraically the point is defined as the frequency for which:

ωL = 1 / (ωC)

In order to have additional resonances we need different models of inductive and capacitive reactance. The existence of such models has been hinted at but never explicitly defined. We know that inductive reactance deviates, concave up, from linearity at high frequencies. Does that imply the existence of a second point of intersection? I don't think so. I'm less sure about deviations in the model for capacitive reactance at high frequencies from the usual hyperbola. Again I doubt the existence of a pair of reactance models that allow for two points of intersection which would be required for a second point of resonance.

 

Here is the result of a simulation of a practical series resonant circuit using two separate coils. Note the two series and two parallel resonances.

Clearly this situation can only occur in the presence of significant parasitic capacitances, but in the real world these do exist. Multiple resonances of this type can lead to unwanted effects, for instance in filter circuits.

Note that you don't need to get up to VHF to see this sort of thing: these resonances are occurring at quite low radio frequencies. The parasitic capacitances shown are large, but by no means impossibly so.

 

Here is the result of a simulation of a practical series resonant circuit using two separate coils. Note the two series and two parallel resonances.

Clearly this situation can only occur in the presence of significant parasitic capacitances, but in the real world these do exist. Multiple resonances of this type can lead to unwanted effects, for instance in filter circuits.

Note that you don't need to get up to VHF to see this sort of thing: these resonances are occurring at quite low radio frequencies. The parasitic capacitances shown are large, but by no means impossibly so.

View attachment 27149

I would argue that your circuit is not the same as described by the OP, even in spirit. It is true that you have two inductors and at least one capacitor, but it is hardly a "series" circuit anymore. For each inductor there is a series path through the other inductor as well as a path around the other inductor. Also no complicated reactance models to get two points of intersection. Maybe the OP can comment on the practical application of such a network.

 

I would argue that your circuit is not the same as described by the OP, even in spirit. It is true that you have two inductors and at least one capacitor, but it is hardly a "series" circuit anymore. For each inductor there is a series path through the other inductor as well as a path around the other inductor. Also no complicated reactance models to get two points of intersection. Maybe the OP can comment on the practical application of such a network.

Well, it's an attempt at a simple model model of two real inductors and a capacitor with parasitic elements. One could probably demonstrate something of the kind with actual components and an impedance / network analyser. There is no doubt that this kind of thing happens in practice: difficulties with spurious resonances have been with us since the days of great grandfather's TRF radio set. At higher frequencies this of course becomes more problematic, and eventually everything has to be regarded as more or less of a transmission line, but that's definitely heading OT.

How much relevance this has to the OP's question is another matter: (s)he may have only had the behaviour of ideal components in mind, and it might be better not to pursue this further unless we hear otherwise.