I have the following bode plot of some unknown circuit:
(The lines denote the -3dB frequencies, f_low and f_high.) I'm guessing it's a high-pass resonant filter. I don't have phase information, other than that:
theta = -135 deg at f_low
theta = -80 deg at f_0 (resonant frequency)
theta = -31 deg at f_high
I know for certain that it contains between 2-3 circuit elements including inductors, capacitors, and resistors, and I know that it's passive. My guess is that it's a second-order high-pass filter. I've worked out that the transfer function for such a circuit should be:
H1(s) = (A*(s/w_0)^2) / (s^2 + s*(w_0/Q) + (w_0)^2)
where w_0
is the resonant frequency in rad/s, Q
is the quality factor, and A
is the high-frequency gain. In this case, A = 1
, w_0 = 2*pi*f_0
, and `Q = (f_0)/(f_high - f_low)'.
From here, I should be able to come up with a predicted transfer function given what I believe the circuit to be, which will contain R
,L
, and C
as coefficients, and use the transfer function H1(s)
to find R
,L
, and C
. A fitting circuit, by my guess, would be:
which would have transfer function:
H2(s) = (sL) / (R + 1/(sC) + sL)
which I could rearrange to the form of H1(s)
, and from there I could match the coefficients in each transfer function H1(s)
and H2(s)
to find appropriate values of R
,L
, and C
.
But that gives me
R/L = w_0/Q
and
1/LC = w_0*Q
Is there any way other than plugging in values and using guess & check to find specific values of R
,L
, and C
?