# V and I not in phase at resonance Frequency in RLC network?

Discussion in 'General Electronics' started by Diego Stutzer, Oct 14, 2003.

1. ### Diego StutzerGuest

Hi,
Well, I'm really confused.
I simulate a simple serial R-C-L-Network (all in series).

As far as I know the total (input-)Impedance of the network is:
Z = R + jwL - j/(wC) resp. the resonance frequency (where Zin=R) is
1/sqrt(L*C).
At resonance frequency, the Impedance should be real and therefore in
my hummel opinion Voltage and Current schould be in phase.

The funny thing is, when i build up such a network in Schematics
Simulator, the current is displaced (relative to the voltage) about
lambda/4 - obviously not in phase!?

Can anyone tell my where I made a mistake?
Or why this Problem is showing up?
Thanks to anyone reading this and especially to those who post
D. Stutzer

2. ### Don PearceGuest

The impedance should be R + jwL + 1/(jwC)

d

_____________________________

http://www.pearce.uk.com

4. ### Diego StutzerGuest

WOW!! Thank you soo much. The world is sound and the laws of physics apply
again. I just confused w (omega) and f.
Best Regards
D. Stutzer

5. ### MichaelGuest

The impedance should be R + jwL + 1/(jwC)
You sure?, how do the j parts cancel at resonance if they are both added?

6. ### Tom BruhnsGuest

Which voltage and which current? Clearly the voltage across the
capacitor will always be pi/2 relative to the current in that
capacitor, and the same (but opposite sign) for an inductor. Also,
are you doing an AC or a transient analysis? If transient, are the
transients settled, are you really on the resonance frequency, and are
you simulating with sufficient time resolution? Oh, and I'm not quite
sure what you mean by "lambda/4" phase shift. Is that degrees or

Cheers,
Tom

-j/wc= 1/jwc

8. ### Reg EdwardsGuest

Multiply top and bottom of 1/jwC by j (This does not change its value) and
you get 1/jwC = minus j/wC.

Back to school with your algebra.

9. ### budgieGuest

His algebra looks perfectly fine to me. But as others have pointed
out, he's left the 2pi out.

10. ### Reg EdwardsGuest

------------------------------------------

Yes. I apologise for my remark about school. I gained the incorrect
impression from the previous replies.

The w in wC stands for omega = 2*Pi*F, the angular frequency.

11. ### Active8Guest

now that were all done playing with j...

Z = sqrt[R^2 + (jwL)^2 - (1/jwC)^2] = sqrt[R^2 + (jwL)^2 + (j/wC)^2]

this is scary shit.

mike

12. ### Active8Guest

now that were all done playing with j...

don't forget

Z = sqrt{R^2 + [(wL) - (1/wC)]^2]}

and

Z(s) = R + Ls + 1/Cs

which is just plain easier to deal with 'til you need to journey back
into time domain land. no need to leave it f(t) for this deal, though.

all that j stuff... that was scary shit. so easy to make a mistake.
swapping w and f is another good one. only works for f/f stuff.

mike

13. ### Paul BurridgeGuest

Especially so given the limited typography of this particular medium.
I suspect few of us would have a problem if we could only view these
formulae in a suitably appropriate typeface!!!

14. ### Laycock, ChristopherGuest

R + jwL + 1/(jwC)
= R + jwL -j/(wC)
so at resonance wL=1/(wC)
ie w=1/sqrt(LC)

Chris

15. ### John FieldsGuest

---
Since he calculated the resonant frequency of the circuit using

f = 1/sqrt(L*C),

his answer will always be a frequency 6.28 times higher than it should
be, so the reactance of the inductor will be greater than the reactance
of the capacitor, making the phase angle positive.

"Lambda" is usually taken to mean wavelength, so "lambda/4" would mean a
quarter wavelength; in this context, 90°, the approximate phase
difference between his simulated voltage and current.

16. ### Active8Guest

what pre tell, is a typeface that would make it hard? wing-dings?

i admit, even in HTML with arial or fixed-pitch, where you have sub and
super tags and greek letter codes, you can't do much. i tried a few free
math notation tools for HTML and wasn't happy. plus you need a plugin
for most if not all. W^3C has a standard. i'd like to see more math
capabiliies in browsers. we could attach formulae without violating the
no bianaries rule. of course microshaft and standards will probably
never be seen in the same line of code.

i still don't see why text based math legibility is font dependant. i
see i could have eliminated some clarifying parens by

- -
| 2 1 2 |
sqrt | R + ----- | or a 1/2 power instead of sqrt
| jwC |
- -
created by Andy´s ASCII-Circuit v1.22.310103 Beta www.tech-chat.de

does that also foul up?

brs,
mike

17. ### Fred AbseGuest

Improbability level now zero. Normality restored. Anything you still can't