## Accuracy of phase shift measurement

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semamina
Newbie
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Joined: Wed Jun 26, 2024 2:09 pm

### Accuracy of phase shift measurement

Dear all

I am trying to buy a new USB Picoscope (possibly 3000 or 5000 series).
I would like to do precise phase shift measurements between 2 AC signals of 2 channels.

I need to measure around 0.5° of difference on a bit less.

Could you please advice me how to be sure of that ? should i check only the sampling rate of the scope for that? and will be possible to measure at that range?

Many thanks

Gerry
PICO STAFF
Posts: 1158
Joined: Mon Aug 11, 2014 11:14 am

### Re: Accuracy of phase shift measurement

This question was answered on our Help Desk, so I've added the response here (although I've had more time to re-write it, to add more detail and clarity). There's a summary at the bottom for a quick answer.

The precision of a Phase Measurement and Phase Calculation, Math Channel (i.e. the smallest distance that can be resolved between 2 points, at the same relative location of 2 waveforms) is determined by the Amplitude and Frequency Resolution of the data. So, the following should be done, for maximum precision:
1/ Use the most suitable Input Range, so that the pk-pk amplitude of the waveform extends across most of the Scale.
2/ Use the highest Vertical Resolution (Number of Bits) and highest horizontal resolution (Sample Rate) (or best combination of them for Flexible Resolution Scopes).
3/ Minimise the Noise.
The Precision of the Phase Measurement and Phase Calculation, Math Channel can be demonstrated with an example. I don’t have a suitable capture in a 3000/5000 series PicoScope, however, I do have a capture of 1kHz waveforms in a PicoScope 4262, which shows that, for Phase, you can actually measure down to 0.1° precision. To demonstrate this I have created the following:

1/ A data file, with 2, almost identical 1kHz frequency, sine waves that have a delay between them.
2/ A Math Channel of Phase (A, B), which is also plotted as a fixed value,and then measured.
3/ An automatic measurement of Phase between A and B, to compare with the precision of the manually measured Phase() Math Channel.

You can see how the precision of the Phase() Math Channel, compares with the Automatic measurement in the Image of the data file below:
(unfortunately, there is no data file as it's too big for the post)
The capture actually uses 2 waveforms that are extremely close in frequency (so that they are both measured as 1kHz), but not identical. So, when zoomed into the math Channel values, you notice that the measurement of each cycle has different discrete values that follow a sinusoidal looking pattern across the capture period, as shown below:
This gives us the variance of the precision, due to interaction of the slightly varying frequencies and the resulting distance between the 2 points at each measurement point.

So, you could achieve this 0.1° precision, with a variance of <0.01°, in a PicoScope 4262 calculating the phase difference between two 1kHz waveforms with a Math Channel.

The Noise performance of the PicoScope 4262 is the best in the Range of PicoScope models that we have. We can minimize the noise variance without affecting the shape of the waveform, by using 2.5 bits or Resolution Enhancement (or a moving average filter of width 2^5), as shown by the Pink Waveform below:
So, looking at the effect that the noise reduction has for the Phase calculation & measurement:
we only get a 1/3 improvement in the variance of the Phase measurement, but this would be considerably more effective for other PicoScopes that have more noisy performance.

Summary
So, to answer the original question, whether or not you can achieve 0.5° precision, or better still, the 0.1° precision and <0.01° Variance in the Precision shown here, for the waveforms that you want to calculate the Phase difference for, in the PicoScope that you would like to purchase, will depend upon a number of factors. These are, the PicoScope model, the Frequency of the waveforms, how you capture them (i.e. how you maximise the Input Range, Vertical Resolution and Sample Rate you are using) and how much of a factor the noise and its reduction will be (which depends upon the Input Range being used, although for the 5000 Series PicoScopes, noise reduction will be a required, even for larger Input Ranges).

Regards,

Gerry
Gerry
Technical Specialist