I am sending a sine wave through a unknown RC circuit. At the other side I have a current-to-voltage converter (transimpedance amplifier) measuring the current indirectly as voltage.
I am using IQ demodulation technique and get the Real and Imaginary part of the voltage representing the current.
I want to calculate the admittance, impedance, conductance, resistance, susceptance and reactance.
First of all the values Iv and Qv (Iv and Qv is the voltage representing current) need to be converted to current:
Ii = Iv / Rf Qi = Qv / Rf
where Rf is the transimpedance amplifier feedback resistor.
Since I am exciting with voltage and reading the current I assume I have a ratio of current to voltage which is admittance.
If the excitation voltage is Vex admittance Y is then given as:
Y = G + jB = (Ii/Vex) + (jQi/Vex)
The amplitude is given as:
|Y| = sqrt(G^2 + B^2)
By using complex number one can derive the relationship between conductance and resistance:
R = ( G / (G^2 + B^2) )
and reactance and susceptance:
X = -j * ( B / (G^2 + B^2) )
Impedance is then:
Z = R + jX
|Z| = sqrt(R^2 + X^2)
Do I convert to current correctly? Do I find conductance and susceptance correctly? Did I understand correctly that the values I measure is admittance? Is the Z, R, X conversions correct?
Lets say that the unknown RC circuit was only a 1000 Ohm resistor. I would then find out that Z = R = 1000 right?