Frequency vs. Phase: Understanding the Relationship and Measurement

This article explains the difference between frequency and phase, highlighting their relationship. It also touches upon how these concepts relate to signal generation and measurement.

A crystal oscillator is commonly used to generate a sine wave signal. This sine wave can then be converted into other waveforms like square waves or rectangular waves.

The figure above illustrates a signal completing one cycle within one period.

• Frequency: Frequency is simply the inverse of the time period required for one complete cycle of a waveform. Think of it as how many cycles occur per second.
• Phase: Phase refers to the position of a point in time (an instant) on a waveform cycle. A complete cycle encompasses 360 degrees, which is equivalent to 2π radians. Each instant in the wave will have a different phase value.

Measuring Frequency Offset

Frequency offset, the deviation from a nominal frequency, can be measured in both the frequency domain and the time domain.

Frequency Domain Measurement

In the frequency domain, the frequency offset is directly measured using a frequency counter. The formula is:

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

Where:

• F nominal is the specified output frequency of the oscillator, found on its nameplate.
• F measured is the frequency reading obtained from the frequency counter.

Time Domain Measurement

In the time domain, we measure frequency offset by comparing the phase of the Device Under Test (DUT) with a reference signal. This is typically done using an oscilloscope.

The oscilloscope displays both sine waveforms. If the DUT and reference signals have the same frequency, there will be a zero phase shift between them, and the waveforms will appear stationary on the display.

However, if the DUT’s frequency is lower than the reference, the phase shift difference will increase over time. A changing time interval between the two signals signifies different frequencies, and the rate of this change is the frequency offset.

For measuring high-frequency signals, specialized instruments often use mixers. Mixers downconvert the high frequency to a lower, more manageable frequency for measurement purposes.

Expressing Frequency Offset

Frequency offset can be expressed as:

F(offset) = -Δt/T

Where:

• Δt = amount of phase deviation
• T = measurement period

For example, a phase deviation of 1 µs per day results in a frequency offset of approximately -1.16 x 10^-11.