# resonance in rlc circuits

Discussion in 'General Electronics Chat' started by joshpig, Jan 26, 2016.

1. ### joshpig Thread Starter New Member

Jan 26, 2016
4
0
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 )

Thanks

Last edited: Jan 26, 2016
2. ### Dodgydave AAC Fanatic!

Jun 22, 2012
5,159
772
The resonant frequency is when Xc = Xl,

joshpig likes this.
3. ### ErnieM AAC Fanatic!

Apr 24, 2011
7,442
1,628
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.

joshpig likes this.
4. ### SLK001 Well-Known Member

Nov 29, 2011
852
243
Resonance is like what Dodgy said. The frequency of the resonance is derived as follows:

joshpig and Dodgydave like this.
5. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,301
339
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?

joshpig likes this.
6. ### joshpig Thread Starter New Member

Jan 26, 2016
4
0
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 ?

7. ### Dodgydave AAC Fanatic!

Jun 22, 2012
5,159
772
Xl and Xc are the reactances(AC resistance) of the inductor and capacitor,your circuit has a v+ symbol, is it a dc supply?

joshpig likes this.
8. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,301
339
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.

joshpig likes this.

Jan 26, 2016
4
0
10. ### Brownout Well-Known Member

Jan 10, 2012
2,375
998
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.

joshpig likes this.
11. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,301
339
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.

Last edited: Jan 27, 2016
joshpig likes this.
12. ### joshpig Thread Starter New Member

Jan 26, 2016
4
0
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?

13. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,301
339
Here you go:

Here's a zoomed in view of the crossing at ω = 21778.3

Last edited: Jan 27, 2016
joshpig likes this.
14. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,301
339
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:

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:

joshpig likes this.