## Frequency vs Phase-difference between frequency and phase

This page on frequency vs phase describes **difference between** frequency and phase.It mentions relation between them.

Crystal oscillator is used to generate sine wave signal. This sine wave signal is converted to waveform of different shapes such as square wave, rectangular wave etc.

Figure depicts one such signal having one cycle in one period.

**Frequency**: It is the inverse of the time priod equivalent to one cycle of the waveform.

**Phase**: Different instants of waveform will have different phase values.
One cycle will have total 360 degrees which is equal to 2*π radians.

Frequency offset can be measured in frequency domain and time domain.

In frequency domain, it is directly measured by measuring frequency output using frequency counter.

F_{offset} = { (F_{measured} - F_{nominal})/ F_{nominal} }

F_{nominal} is specified output frequency of oscillator on its nameplate.

F_{measured} is the reading from frequency counter.

In time domain, it is measured using a method in which phase comparison is done between
DUT and the reference. This is done using Oscilloscope equipment.

Oscilloscope displays both sine waveforms.
If both the frequencies (one from DUT and another from reference) are equal, they will have zero phase shift between them and they look
stationary on the display panel.
When phase shift difference increases over time, the frequency of DUT is lower compare to the reference.

If the two signal frequencies have different frequencies, time interval will change. Here rate of change is known as frequency offset. In order to measure high frequency signals, instruments are designed using mixers which brings down the high frequency into low frequency for measurement purpose.

Frequency offset can be expressed as follows:

F(offset) = -Δt/T

Where, Δt = amount of phase deviation

T = measurement period

Phase deviation of 1µs per day results into frequency offset of value -1.16 x 10^{-11}.

Refer Frequency Offset Estimation and Correction➤➤

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