LCR Measurements

Mmm... are you sure this isn't a homework question?

Take the measurement you have (magnitude and angle) and express it in rectangular coordinates, Z=R+jX. R is the resistance, and then knowing that X=2*pi*L or -1/(2*pi*C), you can solve for C. (If X is positive, you have an inductor, otherwise it's a capacitor, of course.)

No.... it's not a homework question. jX will indicate if the circuit is capacitive or inductive. However, I have a series RLC circuit and would like to calculate the R,L, and C from the lcr data. The part I'm having a problem with is extracting the L and C values individually.

Ah, OK. This is impossible to do if you measure the impedance at only one frequency (since you have three unknowns -- R, L, and C -- but only two equations, Re(Z) and Im(Z) ). What you do instead is:

1) Measure the impedance at two (or more) frequencies, set up a system of equations and solve (use, e.g., least-squares fitting if you use more than two equations). Most LCR meters will let you choose at least two different test frequencies. 2) (The way people usually do this...) Use an adjustable frequency generator, connect your circuit to its output, and sweep the frequency until you maximize the current through the circuit (this corresponds to the minimum |Z|). The idea here is that a current maximum is reached at resonance, at which point f*L=1/(f*C), and now that you have enough information to solve for all the unknowns. 3) (Seemed to be a popular lab exercise in school...) Similar to #2, you find the 3dB points of the impedances response as well as the resonant frequency, then you compute Q, and since you can reasure the resistance directly from Q and R you can compute L or C from Q~=2pi*fL/R or Q~=1/(2pi*fC*R). I believe the idea is that this approach tends to be a little more accurate than (2) since by measuring both 3dB points you're doing a bit of averaging and are somewhat out from resonances where, if you have a high-Q circuit, measurement accuracy is often compromised.

If you're lucky enough to have access to a network analyzer, you just tell it to measure S_{11} over some frequency range and it'll then find the minimum |Z| for you and read out the R, L, and C directly at that point. :-) The network analyzer approach is also useful to give you some idea of how accurate a simple series RLC model is for your particular circuit.

---Joel

Thanks for your help!

I am not expert but if measures the answer to an impulse you do not succeed to go back to the transfer function and to calculate poles and zero then and knowing the structure of the net to go back to the values? aspect answers from who is more expert than me