Anonymous

# How can I calculate the resonant frequency of an LC network when I only know the phase angle?

So here is the problem; I have an LC network that is being driven by an inverter at exactly 50 KHz. My inverter also has a feature that can measure the phase angle of the voltage/current in degrees (leading or lagging). From this information, I want to be able to determine the the actual resonant frequency of the network. Generally the resonant point is +/- 10 KHz and the phase angle is +/- 60°.

Update:

Thanks for that answer and useful information! Let me try to add a little more information: The inverter is driving a large network with unknown L and C. The inverter can resolve peak voltage, peak current and phase angle. From the information avaiable it is trivial to determine the real power and from that approximate C and R(just trust me on that one). The purpose of the exercise is to find a way to resolve L using the available information. My original idea was to calculate F-res and then plug in all of the variables and solve for L in the standard resonant freq equation F-res = 1 /(2 * PI * SQRT(L*C)).

Relevance

The resonant frequency is 1/(2*pi*sqrt(L*C))

You have given insufficient information.

For series, assuming losses of the capacitor and the core and insulation losses in the inductor are negligible:

V/I = (R + jwL + R) = R + j(wL - 1/wC)

where R is the equivalent series resistance of the network, and w = 2*pi*frequency.

For parallel, with the same assumptions as above:

V/I = (jwL + R)(-j/wC)/(jwL - j/wC + R) = (L/C - jR/wC)/(jwL - j/wC + R)

The resonant frequency in Hz is 1/(2*pi*sqrt(LC)). If you can solve for L and C then you can find resonance.

Note that as w goes higher and higher, the series looks more and more like just the inductor, and the parallel looks more and more like just the capacitor, which is what expected.

But given just the information that you have given, just the phase angle of the voltage/current, you can not solve for the resonant frequency. There are too many unknowns, L, C and R, when all you have is just the one known quantity, phase angle.

If you had both the amplitude of V/I and the value of R in addition to the phase --OR-- if you had the amplitude of V/I and the phase at two different frequencies -- you might could find resonance with some accuracy. Depending on the network, there are other combinations of measurements that can used.

Note that if you assume R is negligible, the phase for the series goes to -90 degrees if 50kHz is below resonance, and to +90 degrees above resonance. For the parallel it goes to +90 degrees if 50kHz is below, and to -90 degrees if above.

You need to dig into the problem and figure out what else is given, what else is known from measurements. You really need MORE DATA.

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Even if peak V & I are known, you still can't do it. You need at least one more independent known value.

As an example. Say V=10, I=1, and phase=+80 degrees (current lags voltage).

There are an infinite number of possibilities. Check the calculations yourself. Just picking two:

1)R=1.74, L=8.21E-5, C=2E-7 Resonance=39.3kHz

2)R=1.74, L=3.65E-5, C=2E-6 Resonance=18.6kHz

Theoretically, there are infinite possibilities. Realistically, there's still a really wide range.

If the phase is 0 degrees (zero) then the resonance is 50kHz. Then you don't need the V and I measurements. But that's the only case that is knowable, given the few measurements that you are providing.

• it extremely is impossible to respond to without understanding the best configurations. in many situations, if all C and L could be arranged in sequence or parallel configurations, i could attempt to decide the mixture fee first, then attempt to calculate the resonance frequency. remember, C without L does not impression resonance and vise versa. do you desire to place up the best circuit?