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# Does they really need to be same frequency to compare phase?

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#### cherishnguyen

##### Newbie level 5
Hi all,

Can anyone please explain to me that is it possible to compare phase difference b/t 2 signals which are at different freq, or we firstly have to convert them into the same freq and then compare their phase together?

Re: Does they really need to be same frequency to compare ph

Hi cherishnguyen,

the phase difference between two sinusoids (or complex exponentials) of different frequency is
Δθ = θo + Δω×t
It increases in time without bound.
Normally, phase difference is defined and measured for signals of the same frequency.
One (or both) of the signals can be modulated in phase. In that case the phase difference is time-varying, but bounded if the carrier frequency is the same
Regards

Z

Re: Does they really need to be same frequency to compare ph

zorro said:
Hi cherishnguyen,

the phase difference between two sinusoids (or complex exponentials) of different frequency is
Δθ = θo + Δω×t
It increases in time without bound.
Normally, phase difference is defined and measured for signals of the same frequency.
One (or both) of the signals can be modulated in phase. In that case the phase difference is time-varying, but bounded if the carrier frequency is the same
Regards

Z

Thanks for your help. I agree with you that "Normally, phase difference is defined and measured for signals of the same frequency". Just one thing i still confused when there are 2 signals, for ex. 2 sinusoids A and B, where freq of B is twice freq of A.
How are they considered as in-phase, is it because they are started at the same initial time t=0 (same θo), even at another time t≠0, their phase are different (because their ω are not the same)? I drew them on paper but cannot explain, maybe i misunderstand something. I really need your advise to make clear these stuff.

Thx very much.

Re: Does they really need to be same frequency to compare ph

That is a good question Cherishnguyen.

Perhaps we should redefine 'in-phase' as meaning the same point in the two waveforms align with each other at fixed intervals. That interval being a multiple of the cycle lengths.

If we only consider signals of the same frequency it implies that PLL frequency multiplying is not possible!

Brian.

Re: Does they really need to be same frequency to compare ph

Hi,

The concept of "to be in phase" between two signals is defined when they are sinusoids of the same frequency.
For other signals, we can speak about "instantaneous phase" between them. For example, the instantaneous phase between a carrier and a phase-mudulated signal (with the same carrier) follows variations according to the modulating signal.
The concept can be extended to any two signals. Consider the phasors representing them: The angle between them is the instantaneous phase between them. Occasionally their phase difference is zero, but we can not say that they are "signals in phase".

cherishnguyen said:
Just one thing i still confused when there are 2 signals, for ex. 2 sinusoids A and B, where freq of B is twice freq of A.

In that case, one phasor is rotating at twice the speed of the other.
We could adopt a convention: say they are in phase if they coincide when they are on the real axis (i.e., if they pass by their maximum at the same time). But this would be just a convention.

betwixt said:
If we only consider signals of the same frequency it implies that PLL frequency multiplying is not possible!

I don't agree. The two signals entering the phase comparator must have the same frequency with fluctuations in their instantaneous phase. But if the frequencies are "substantially" different, the PLL is not locked.
It is possible that in a PLL the two frequencies are harmonically related (harmonic lock), but in that case they have a common harmonic, and the phase comparator compares the phase between those components (same frequency).

Regards

Z

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