Calculating impedance, real and imag part

[samson07]

Hi people~
My name is Sam, a student just trying to work something out and failed. A little help please

I've drawn it and attached the figure here and if you take a look I have a series ciruit with PZT (some material) and resistor.

I need to work out the real and imaginary part of impedance since impedance is complex.

I figured out that the impedance can be calculated using the formula that I've drawn by inputting the measured values of Vin, Vout and R, no complex numbers here(Ztotal = R*Vin/Vout), but I have no idea how to work out Real part and Imaginary part.

As you can see that I've written down the formula for Real and Imag(told by one of my friends), but when I put some figures in there, I can tell that its wrong...

I can measure Vin, Vout and the phase difference between the two (all single value, no complex number)and someone told me that i can get both the real part and imag part by just using these 3 parameters.

please help a poor guy out, I've been stuck with this question for over 2 months...

 

[darkys]

Hmmm, that's a tricky one. The way I understand it is that the real part of the impedance is simply R*Vin/Vout, since you already have the formula for that. The imaginary part is a bit more tricky because you have to take into account the phase difference between Vin and Vout. You can calculate the imaginary part by taking the sin of the phase difference multiplied by the real part of the impedance. So, your formula should look something like this: Imaginary Part = (sin(Phase Difference))*(R*Vin/Vout). Hope this helps!