resonance in rlc circuits

Thread Starter

joshpig

Joined Jan 26, 2016
4
Hi!
If you want to find the resonant frequency for the voltage and current in a load (load is a combination of resistor, capacitor, inductor), in a circuit which has another capacitor and inductor. Would you use just the components outside the load, or include those in the load in the equation 1/(2pi)(LC^1/2).?

I'm not sure if I've explained this very well but we shall see :))
cirucit.JPG
Thanks
 
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ErnieM

Joined Apr 24, 2011
8,011
You need to work out an equivalent circuit where there is but a single resistor, capacitor, and inductor.

Then Dave's doggy formula works perfectly.
 

The Electrician

Joined Oct 9, 2007
2,751
Hi!
If you want to find the resonant frequency for the voltage and current in a load (load is a combination of resistor, capacitor, inductor), in a circuit which has another capacitor and inductor. Would you use just the components outside the load, or include those in the load in the equation 1/(2pi)(LC^1/2).?

I'm not sure if I've explained this very well but we shall see :))
View attachment 99452
Thanks
It all depends on your definition of resonance. For example, see this page for the three common definitions of resonance: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/parres.html

Your circuit is not exactly like that one, but the given definitions of resonance will give different results when applied to your problem.

Which definition of resonance will you use?
 

Thread Starter

joshpig

Joined Jan 26, 2016
4
Thank you for the fast responses :)
I am just trying to find the frequency at which current flowing through the load and the voltage across it to be in phase, now i was guessing that this is the resonant frequency as that is when the circuit is purely resistive? is that correct?

And is Xi/Xc referring to the impedance ?
 

The Electrician

Joined Oct 9, 2007
2,751
Thank you for the fast responses :)
I am just trying to find the frequency at which current flowing through the load and the voltage across it to be in phase, now i was guessing that this is the resonant frequency as that is when the circuit is purely resistive? is that correct?

And is Xi/Xc referring to the impedance ?
You said that your "load is a combination of resistor, capacitor, inductor". Show the circuit of the load in detail. Together with the additional L and C you showed in post #1, the expression for the frequency at which the load current is in phase with the load voltage can be determined.
 

Brownout

Joined Jan 10, 2012
2,390
You have to consider all reactances. However, you can simplify things a little by considering only the circuit to the left (initially) and making a thevinen equivalent.
 
If you derive an expression for the imaginary part of the impedance seen by the source, and plot it vs. frequency, there are 3 frequencies in the vicinity of ω = 20k for which the imaginary part is zero. Those could be considered resonance frequencies.

Resonance1.png
 
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Thread Starter

joshpig

Joined Jan 26, 2016
4
Wow brilliant thanks! I would love to see how you did that, if you have that derivation to hand it would be great to see it?
 
To get some more insight into the behavior around resonance, let's plot both the real part (blue) and the imaginary part (red) of the impedance:

Resonance6.png

The real part becomes very small at the lowest and highest resonance frequencies. At the middle resonance, ω = 21778.5, the real part is 8.46 ohms, a more reasonable value. The resonance there is the useful one. It's a fairly high Q resonance but the external inductance was treated as ideal.

Here's the calculation of the value of the real part at the 3 resonances:

Resonance7.png
 
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