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Amplitude ratio and phase shift of two signals

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Eugen_E

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Hello,

I need to measure the phase difference and amplitude ratio of 2 signals of equal frequency (~1kHz), afected by noise and harmonics. The signals are sampled by soundcard on channels L and R, then filtered by a few bandpass biquad cells at 1 kHz.
I imagined 2 methods for measuring this:

1. Shifting a signal by 90°, multiplying with the other signal and obtaining the I and Q components, then filtering and computing the phase difference. The amplitude ratio can be estimated?

2. Doing a sine fit on both filtered signals, then obtaining the amplitude ratio and phase shift.
I never did this before but I found references on sine fitting for ADC characterization (only papers, no sample code :( ), and the joint fitting of the signals seems difficult.

What is your oppinion about these methods regarding speed and precision, low SNR performance... ? 2. has a big advantge?

Thanks
 

FvM

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The answer depends on the nature of the input signal, I think. If it has exactly stationary frequency and phase, the "sine fit" promises better SNR due to a lower noise bandwidth. The joint fitting is estimating one frequency and two phase values and shouldn't involve problems.
 

Eugen_E

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Thanks for your answer

This is for impedance measurement, first I will test at 1 kHz, so the signal is quite stable and has low phase noise.
If it works I plan to use 2 VCOs (1-10MHz), one feeding the impedance tested through a current probe. The second VCO - feeding a mixer, will downconvert the voltage and current proportional signals to 1 kHz. Those VCOs will have higher phase noise, but will be controlled by PLL to be at 1kHz difference in frequency. A fast response is preferred.

For sine fitting do you know of a C code freely available, or some examples? I could try to do a gradient least squares optimization, but I don't know if it's good enough and efficient.
Also I couldn't find some theory regarding the number of samples to be processed.
 

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I don't understand the two oscillators concept. Usually impedance measurement is performed using synchronous demodulation with a reference from the generator signal. This avoids any need for a "sine fitting" or other kinds of frequency measurement or estimation methods. Sounds like you are complicating a simple thing.

For a digital implementation of a vectrial impedance measurement it's interesting to review the ADI AD5933 concept.
 

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