How Do You Calculate the Frequency for a 90 Degree Phase Shift in Coils?

[Jdo300]

Hello All,

I did an experiment recently involving two coils in series with a high frequency signal running through them. My goal was to determine at what frequency the signal in one coil would be phase shifted by 90 degrees with respect to the first coil. I was able to experimentally determine the right frequency but I am wondering how one would calculate the frequency that would give you a 90 degree phase shift in voltage knowing the inductance of the coil.

Thanks,
Jason O

 

[antonantal]

That's weird. Theoretically you shouldn't have a phase shift between the two coils. Even if we consider the series resistances of the coils, there could only be a very small phase shift between the signals measured at the terminals of the two coils. This very small phase shift would exist if the phases of the complex impedances of the two coils (each modeled as an inductance in series with a resistance) would differ.

Anyway, what was the frequency that you measured?

 

[Jdo300]

Hi,

I think the reason I got the phase shift is because I was driving the coils close to their natural resonant frequency. I got the 90 degree shift when I drove the coils at about 9 MHz. They are not very large coils either, only about 50 turns each around a styrofoam core that is about 1.5 inches in diameter.

 

[antonantal]

From what you sad I understood that the two coils are identical, right? This means that no matter what frequency you apply the phase shift should be (close to) zero.

You might get a phase shift of 90 degrees if you choose the two coils so as the self-resonance frequency of one of them is much below the applied frequency and the self-resonance frequency of the second is much above the applied frequency.

Now, back to your question, you can calculate the frequency that will give you a phase shift of n degrees, but you must measure the inductances, the parasitic capacitances and the series resistances of the coils. Then, you calculate the complex impedance of each coil (X_{L}+R)||X_{C} and see at what frequency the phase shift between the two impedances is n degrees.

 

[Jdo300]

Ahh thanks for the clarification. I haven't learned those equations (using complex numbers) yet. Could you give me a general example that I can use once I determine the Inductance and capacitance of my coils?

Thanks,
Jason O

 

[antonantal]

Ahh thanks for the clarification. I haven't learned those equations (using complex numbers) yet. Could you give me a general example that I can use once I determine the Inductance and capacitance of my coils?

Thanks,
Jason O

There's no point in using formulas that you don't understand. Here is a good website which covers AC theory from scratch, and has very practical explanations: http://www.ibiblio.org/obp/electricCircuits/AC/index.html