Frequency is the number of complete cycles of a periodic quantity per second, measured in hertz (Hz); period is the duration of one complete cycle, measured in seconds. For any periodic waveform the two are exact reciprocals, f = 1/T.
Learning objectives
- Convert between frequency and period using f = 1/T
- Express frequency in hertz, kilohertz and megahertz correctly
- Calculate angular frequency and use it in reactance formulas
- Relate a phase shift in degrees to a time delay
- Explain why frequency affects capacitive and inductive behaviour
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
Frequency does not describe how fast electrons move or how large the voltage is: it describes how often the pattern repeats. Electrical frequency is measured from a voltage or current waveform, for example with the hertz range of a multimeter.
Intermediate How it behaves in a circuit
Frequency also sets reactance. Inductive reactance XL = 2πfL rises with frequency, while capacitive reactance XC = 1/(2πfC) falls. A capacitor is nearly an open circuit at low frequency and nearly a short circuit at high frequency.
Advanced Limits, assumptions, engineering detail
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Frequency | f | hertz (Hz) |
| Period | T | second (s) |
| Angular frequency | ω | radian per second (rad/s) |
| Phase angle | φ | degree (°) or radian (rad) |
Worked examples
Period of a 50 Hz supply
Problem. A supply has a frequency of 50 Hz. What is the duration of one cycle?
Solution. T = 1 / f = 1 / 50.
Frequency of a 16.67 ms cycle
Problem. An oscilloscope shows one complete cycle lasting 16.67 ms. What is the frequency?
Solution. f = 1 / T = 1 / 0.01667.
Angular frequency
Problem. Calculate the angular frequency of a 50 Hz voltage.
Solution. ω = 2πf = 2 × 3.1416 × 50.
Practical applications
- Mains frequency verification
- Variable-frequency drive speed control
- Filter and resonant circuit design
- Audio and signal generation
- Digital clock and communication timing
- Speed measurement from pulse trains
Automotive applications
Engine speed is often transmitted as a frequency: a tachometer counts ignition or crankshaft pulses and converts them to rpm. CAN bus signals and wheel-speed sensors also carry timing information, and the frequency of an alternator phase rises with engine speed.
Industrial applications
The speed of an induction motor is set mainly by the supply frequency, which is why variable-frequency drives change frequency to control speed. Power-quality analysers record frequency excursions to detect an imbalance between generation and load.
Measurement procedure
- Use the Hz function of a multimeter; for low frequencies, measure the period on an oscilloscope and compute f = 1/T.
- Check the meter frequency range and the minimum signal amplitude it can count.
- Average several readings when the signal is noisy or modulated.
- Remember that the meter measures the frequency of the voltage it sees, which may differ from the intended drive frequency.
Common mistakes
- Confusing hertz with milliseconds: 50 Hz corresponds to a 20 ms period.
- Using ω = 2πf where the formula requires f in hertz.
- Assuming a frequency reading is stable when the signal is distorted or intermittent.
- Treating period and frequency as proportional rather than reciprocal.
Safety considerations
- Measuring mains frequency still means contacting live conductors; use the correct CAT rating and rated probes.
- Do not connect a frequency counter to a circuit whose voltage exceeds its input rating.
- Isolate equipment before attaching probes where terminals are exposed.