Hello!
I have some problems when calculating on a special RLC-circuit. The circuit looks like this:
1 inductor (50nH) in series with a RLC-circuit that consists of 1 inductor (50nH), 1 capacitor (variable) and 1 resistor (139 ohms) all paralell-connected.
The resonant frequency is at 90 MHz, and the question is how much the inimpedance is then?
I found that the circuit has two resonances, one series resonant and one parallel resonant. Continued then with defining the resonance circuit from Im(Y) = 0, where Y is the parallel resonant circuit Y = jwL1 + 1/(jwL2) + jwC + 1/R. Am I on the right way?
I can draw a picture of the circuit if it is needed!
At resonance, the RCL parallel circuit should appear as pure resistance with a value of 139 ohms (the inductive and capacitive reactances cancel each other at resonance). At this same frequency, the inductive reactance of the series inductor is 28.274 ohms. Slapping those two into the "square root of the squares" equation gets you 141.875 ohms impedance without all the engineering "j" factors.
Lessee if there's any disagreement out there. Odds are, there is!
Dean
|--^^R^^--|
A x-----~~L1~~--|--| C |--|-----x B
|-~~L2~~--|
A x-----~~L1~~-----^^R^^-----x B
RadioRon said:If you define a resonant circuit as one which has a purely resistive input impedance, then this is not resonant.
L1=L2 = 50 nHCode:|--^^R^^--| A x-----~~L1~~--|--| C |--|-----x B |-~~L2~~--|
R = 139 Ohms
C = Variable
Yes, it's the input impedance i want in the circuit at resonant frequency.
RadioRon:
Oh I maybe forgot to say, but it is a one-port network, input is across A and B. I get your point
I think that the impedance 141.8 ohms is the parallel resonance. But how do I get the series resonance?
Thanks!
Okay, but what I meant was not that it has two resonances, I was a little bit unclear. I meant that there must be two different impedances, right? One with low impedance (series) and one with high impedance (parallel). I am almost sure about that.
I'll try to calculate a little and then return with some conclusions, but thanks for the help so far! It's helping me to understand this
I used LTspice, and just tried some different values of C, as well as running a parameter sweep of C.Yep, I tried to analyze and simulate it in multisim. But I can't get it working
It's the variable cap that bothers me (among others).
Is it the network analyzer you have to use btw?
I feel I suffer from mental exhaustion, but I'll try anyway. (and I haven't had the time for some calculation)
Lets see.
L1 reactance: +j28 ohms
L1 susceptance: 1/j28 ohms (?)
C susceptance (in order to cancel the two inductive susceptances that come to existence): +j2/28 ohms (or -2/(j28) ohms if you like) (?)
Am I thinking right?
Then I'm not really sure how you have calculated the series resonance. Is it by this formula:
Im(Z)=0
1/(jwL1)+jwL2+1/(jwC) = 0
?
Hmm... I did not really get Zin=133 ohms, rather 141.8 ohms (as mentioned in a earlier post.)
Isn't it: Z=R+jwL = 141.8 ohms (@ 11.5 degrees)
As I said, slight risk of mental exhaustion!
MrAl, if you are saying that the phase of the impedance in this circuit is never zero, that's wrong.BTW, the imaginary part only goes away in some circuits, not all, and not this one in particular.
You appear to be defining resonance as the minima and maxima of impedance. H3rroin and RadioRon are defining it as the frequencies where the impedance is purely resistive (phase angle is zero).You can find all the resonances by finding d|Z|/dF and
setting it equal to zero:
dZ/dF=0
MrAl, if you are saying that the phase of the impedance in this circuit is never zero, that's wrong.
Well, i assure you that i not only appear to be defining resonance in thisYou appear to be defining resonance as the minima and maxima of impedance. H3rroin and RadioRon are defining it as the frequencies where the impedance is purely resistive (phase angle is zero).
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