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Signals7 min read
Frequency & Phase
Connect period, frequency and phase to what you actually see on an oscilloscope.
Mental model
Frequency is how often a wheel completes a turn. Phase tells you where on that turn the wheel is compared with another wheel.
Frequency controls how often a cycle repeats; phase and sampling control where observations occur in time.UNDERSTAND THE BEHAVIOR
01
A periodic waveform repeats after one period T. Frequency is simply the number of repeats per second, so short periods correspond to high frequencies.
02
Phase compares two signals of the same frequency. A quarter-period delay is 90°, half a period is 180°, and a full period is 360°. Phase is therefore a relative timing measurement, not a fixed property of one isolated waveform.
03
On an oscilloscope, measure the horizontal time difference between equivalent points such as rising zero crossings. Using peaks can be unreliable when signals are noisy or distorted.
Why it matters
Timing and phase explain delay, power factor, filter behavior, stability and communication signals.
Core ideas
Frequency counts cycles per second in hertz.
Period is the time taken by one complete cycle.
Phase shift compares the horizontal timing of two waves.
Key equationsf = 1 / TPhase (°) = 360° × Δt / T
EXAMPLE
Worked example — oscilloscope timing
1One cycle occupies 2 ms, so f = 1/0.002 = 500 Hz.
2A second waveform is delayed by 0.5 ms.
3Phase delay = 360° × 0.5/2 = 90°.
4The second waveform lags the first by 90°.
Common mistake
Do not use the phase formula when the two signals have different frequencies; their relative phase then keeps changing.
RememberFrequency counts cycles per second in hertz.
DEEPER EXPLANATION
How do timing measurements become frequency and phase?
Measure the time between matching points of successive cycles, for example rising zero crossings. This is the period T. Frequency f = 1/T counts the number of periods in one second. Units must be converted first: 2 ms is 0.002 s, so it corresponds to 500 Hz, not 0.5 Hz.
Phase compares the position of two periodic signals at the same frequency. A full period is 360°. If the second signal arrives a quarter-period later than the first, it lags by 90° and its phase relative to the reference can be written −90°. Divide measured delay by the full period before multiplying by 360°.
A time delay is not a single fixed phase for every frequency: φ = −360° f Δt for a delayed sinusoid. Doubling frequency while keeping the same delay doubles phase shift. If the signals have different frequencies, their relative phase changes over time; one constant phase difference does not describe them.
Walk through another example
An oscilloscope shows one cycle every 0.5 ms. Converting to seconds gives 0.0005 s, so f = 2000 Hz.
A second 2 kHz wave peaks 0.125 ms later. Delay/period = 0.125/0.5 = 0.25.
Its relative phase is −360° × 0.25 = −90°. Confirm that both peaks refer to the same repeating cycles.
Check your intuition
Double the period from 0.5 ms to 1 ms and the frequency halves from 2 kHz to 1 kHz.
Where this model can mislead you
Do not use a millisecond value as seconds, or describe two unrelated frequencies by one constant phase offset.
TEST YOUR UNDERSTANDING
Three quick checks
Choose one answer per question, then check your work. Each answer includes an explanation.
Practice and check your understanding
Try each question before opening the worked answer.
1. A waveform repeats every 250 μs. Find its frequency.
Show answer and reasoning
Convert to seconds: T = 0.00025 s. Then f = 1/T = 4000 Hz = 4 kHz. Forgetting the microsecond conversion gives an incorrect result.
2. At 1 kHz, a second sinusoid is delayed by 0.25 ms. What is its phase relative to the first?
Show answer and reasoning
T = 1 ms. The delay is one quarter of a cycle: 360° × 0.25/1 = 90°. Because the second waveform is delayed, its relative phase is −90°, or a 90° lag.
A related calculation tool, not a complete simulation of the circuit. Check its model and units.
Continue learning
Bode Plots — Read gain and phase across frequency without treating the graph as a mysterious set of slopes.
Fourier Transform — Understand how a waveform can be described as a combination of frequencies and how to read an FFT without confusing bins with physical components.
ADC Sampling & Aliasing — Understand how a continuous signal becomes numbers, why sampling rate matters and how aliasing creates false frequencies.