RLC Circuit

[Carel_Integrated]

Hi guys, I need to do a few calculations regarding the RLC circuit, buy have no idea where to start or how to do it. I need to calculate at which frequency the input voltage will be in phase with the output voltage for the RLC circuit. Any hints, tips or guidance will be greatly appreciated as I have no idea where to start.

 

[Sceadwian]

This has to be for a school project? Simply look back at the methods that have been shown to you previously and a solution should be quiet obvious.

You could alternately simulate this circuit in something like LTSpice's AC analysis to determine the resonant frequency, but that's not much easier if you've never used it.

 

[Carel_Integrated]

You mean by using formula f = 1 / {2*pi*sqrt(L*C)}

 

[duffy]

I think somebody threw you a curve. Just looking at it, I can see the input-output voltage phase difference is only going to approach 0° as the input frequency approaches 0Hz. That's when the Xl and Xc phasors approach zero and infinity, respectively.

There's a schematic and equation here, but the formula will just give you crap.
https://en.wikipedia.org/wiki/RLC_circuit#Other_configurations

Sure you got the question right?

 

[Carel_Integrated]

Yes. the exact question was: "At which frequency will the output voltage be in phase with the input voltage?"
R1 and C1 can be replaced by a single complex impedance called X(CR). The thing is - I haven't seen an RLC circuit like this before. Usually everything is in series or parallel. Now here, the Inductor is n series {with a capacitor which is in parallel with a resistor}. This makes my brain scrambled eggs.

 

[duffy]

Take the resistor out for a minute. You STILL can't get this one in phase. The L and C have phasors pointing in opposite directions.

 

[Ratchit]

Carel_Integrated,

Yes. the exact question was: "At which frequency will the output voltage be in phase with the input voltage?"

Shouldn't be too hard. First, find the transfer function. Then determine the phase equation from the transfer function. Next determine the frequency at which the phase is zero from the phase equation.

Ratch

 

[Carel_Integrated]

Take the resistor out for a minute. You STILL can't get this one in phase. The L and C have phasors pointing in opposite directions.

What you are saying makes sense to me because the capacitor will store energy and by the way it is connected it's easy to see why it can never be in phase, except when the frequency is zero and when no source is applied. The teacher says that zero is not the correct answer {and the biggest problem is arguing with him}. Maybe he didn't look at the circuit himself (or he made a mistake). Even with the resistor - it is still not possible at whichever frequency (except zero when powered off). Correct?

 

[MrAl]

Hi,

The phase angle Theta can be calculated from:
Theta=atan2(IP,RP)
with:
IP=-(w*L*R)/((R-w^2*C*L*R)^2+w^2*L^2)
and
RP=(R^2-w^2*C*L*R^2)/((R-w^2*C*L*R)^2+w^2*L^2)

and this shows that the only time we can get a zero phase shift is at zero frequency. At infinite frequency we get -pi.

So this problem seems ill defined or else they just wanted you to see the fact that it is never really zero.

 

[Ratchit]

Carel_Integrated ,

What you are saying makes sense to me because the capacitor will store energy and by the way it is connected it's easy to see why it can never be in phase, except when the frequency is zero and when no source is applied. The teacher says that zero is not the correct answer {and the biggest problem is arguing with him}. Maybe he didn't look at the circuit himself (or he made a mistake). Even with the resistor - it is still not possible at whichever frequency (except zero when powered off). Correct?

It will be interesting to see your teacher prove it. The phase will be zero when DC is applied. The phase will not be defined unless a source is applied. Keep us informed.
Ratch

 

[MrAl]

Hi,

You mean it will be interesting to see the teacher TRY to prove it <chuckle>

Unless he wants to call the infinite frequency zero phase because the output goes to zero, but i dont buy that either.

Carel:
If he still insists, ask him to give the correct frequency off by say plus or minus 20 percent without giving the true 'correct' frequency, this way we can test it and show that it is not correct for any frequency within that plus or minus 20 percent band. This way he doesnt have to 'give away' the right answer.
For example, if he says "1kHz" and that can be off by plus or minus 20 percent, then we can test all the frequencies between 800Hz and 1200Hz and show that none of those meet the criterion.

 

[RCinFLA]

Convert the parallel R1, C1 to its series equivalent. Then find the resonance of the resultant series cap and series inductor.

If you have a calculator with polar to rectangular and rectangular to polar forms of complex number it is a snap.

 

[Ratchit]

RCinFLA ,

Convert the parallel R1, C1 to its series equivalent. Then find the resonance of the resultant series cap and series inductor.

A problem with the series to parallel conversion and vice versa is that it is only valid at one chosen frequency. Which frequency did you have in mind?

Ratch

 

[crutschow]

My simulations indicate that the resistance is too low to get zero phase shift at the LC resonant frequency. If you change the LC values to 3.6μH and 5μF respectively to lower the resonant impedance while maintaining the same resonant frequency, then you will achieve zero phase shift at near the LC resonant frequency.

 

[MrAl]

Hi,

If you are suggesting that perhaps they provided the wrong values for L and C, with the formula i posted back in post #9 if we calculate the resonant frequency and the phase shift we get the following...

L=3.7e-6
C=5e-6
R=111
f=1/(2*pi*sqrt(L*C))=37002.7726576795
w=2*pi*f
IP=(w*L*R)/((R-w^2*C*L*R)^2+w^2*L^2)
RP=(R^2-w^2*C*L*R^2)/((R-w^2*C*L*R)^2+w^2*L^2)
PA=-angle(RP,IP)*180/pi=-89.9999999999 degrees

With L=3.6uH we get a phase angle PA=-90.000000000.
'angle' is a function that calculates the four quadrant phase angle of the real part (RP) and imaginary part (IP).

 

[Ratchit]

crutschow,

My simulations indicate that the resistance is too low to get zero phase shift at the LC resonant frequency. If you change the LC values to 3.6μH and 5μF respectively to lower the resonant impedance while maintaining the same resonant frequency, then you will achieve zero phase shift at near the LC resonant frequency.

You are certainly correct averring that the resistor "shorts" out the coil. The mathematics give a complex number ω for resonance using the present values. Only if the resistor is higher than 860 ohms, will you be able to calculate an ω>0

Ratch

 

[MrAl]

Hi,

You can lower or raise the resistance as small or big as you want it and the phase shift is always going to be -90 degrees at the resonant frequency.

 

[meowth08]

Hi,

Why don't you try making bode plots for the frequency response analysis. What you will look at is the phase response. It's not exact but bode plot is a good tool for approximations. You can do it with a pen and paper.

meowth08

 

[crutschow]

Hi,

You can lower or raise the resistance as small or big as you want it and the phase shift is always going to be -90 degrees at the resonant frequency.

No. If you remove the resistor it becomes a series LC circuit for which the external current and voltage are in phase at the resonant frequency.

 

[MrAl]

Hi,

If you remove the resistor then you get an impossible circuit that is no longer an RLC circuit and that is not the circuit that is being examined here.

If you do get zero degrees between the current and voltage that's very nice, but that's not what is being analyzed here. It's the voltage across the capacitor that the OP is interested in, not the current. And it looks like this phase is always -90 degrees at the resonant frequency.