Sine Waves, Frequency and Period
The sine wave is the most fundamental shape in all of electronics and radio. Every AC signal — from the 50 Hz current in your power supply to the 14 MHz signal from your HF transmitter — either is a sine wave or can be built from a combination of sine waves. Understanding its characteristics is essential before you can understand any RF circuit, modulation scheme or antenna system.
What Is a Sine Wave
A sine wave is the graph of the mathematical sine function. It starts at zero, rises smoothly to a maximum (positive peak), falls back through zero, continues to a minimum (negative peak), then returns to zero — completing one cycle. This is exactly the shape of the voltage produced by a rotating generator. It is also the shape of the voltage across a capacitor or inductor driven by a single-frequency AC source.
Any periodic waveform — a square wave, sawtooth or triangle wave — can be decomposed into a sum of sine waves at different frequencies. This is the basis of Fourier analysis, and it is why the sine wave is treated as the fundamental building block of all AC signals.
A labelled sine wave showing amplitude, period (T), peak voltage (Vpeak), peak-to-peak voltage and RMS voltage.
View LargerAmplitude and Peak Values
The amplitude of a sine wave is the maximum displacement from zero. This is often called the peak value. Several related terms are used in electronics:
- Peak voltage (Vpeak or Vmax): the maximum positive or negative voltage reached in one cycle.
- Peak-to-peak voltage (Vpp): the total swing from the most negative to the most positive value. Vpp = 2 × Vpeak.
Period and Frequency
Period (T) is the time taken to complete one full cycle. It is measured in seconds (s).
- A 50 Hz line voltage wave has T = 1/50 = 0.02 s = 20 ms.
- A 14 MHz radio signal has T = 1/14,000,000 ≈ 71.4 ns (nanoseconds).
Frequency (f) is the number of complete cycles per second. The unit is the hertz (Hz), named after Heinrich Hertz (1857–1894), who first demonstrated the existence of radio waves. 1 Hz means one cycle per second.
Common frequency prefixes used in radio:
- kHz — kilohertz — 1,000 Hz
- MHz — megahertz — 1,000,000 Hz
- GHz — gigahertz — 1,000,000,000 Hz
High-frequency signal (left) with short period versus low-frequency signal (right) with long period. Frequency and period are reciprocals.
View LargerThe f = 1/T Relationship
Frequency and period are reciprocals of each other:
Working through the key examples you will encounter throughout this course:
| Signal | Frequency | Period |
|---|---|---|
| UK utility power | 50 Hz | T = 1/50 = 0.02 s = 20 ms |
| Audio tone | 1 kHz | T = 1/1,000 = 0.001 s = 1 ms |
| 14.2 MHz SSB carrier | 14.2 MHz | T = 1/14,200,000 ≈ 70.4 ns |
| 2.4 GHz Wi-Fi | 2.4 GHz | T = 1/2,400,000,000 ≈ 417 ps |
Frequency/Period Calculator
Frequency ↔ Period Converter
Enter a frequency to calculate the period, or enter a period to calculate the frequency. Use f = 1/T and T = 1/f.
The RMS Value
RMS stands for Root Mean Square. It is the effective value of the AC signal — the equivalent DC voltage that would deliver the same power to a resistive load. The process: square the waveform at every instant, average those squared values over a full cycle, then take the square root of that average.
For a pure sine wave, the result is:
Vpeak = Vrms × √2 ≈ 1.414 × Vrms
Why this matters in practice:
- When a power outlet is rated "120 V AC" or "230 V AC", that is the RMS value. The actual peak voltage is 170 V or 325 V respectively.
- A multimeter set to AC voltage mode always displays the RMS value (assuming a pure sine wave).
- Power formulas — P = V²/R and P = VI — use RMS values when applied to AC circuits. Using peak values instead is a common mistake.
Sine Waves in Ham Radio
The sine wave appears throughout amateur radio operation in both obvious and less obvious ways:
- Voice SSB transmission: when you speak into a microphone, the audio output is a complex mixture of sine waves at different frequencies (roughly 300–3000 Hz). Each frequency component becomes a separate sine wave offset from the carrier frequency. A single 1000 Hz tone produces a single sine wave 1000 Hz from the suppressed carrier.
- CW (Morse code): a pure sine wave at the transmitter frequency is switched on and off at the keying speed. The cleaner the sine wave, the narrower the signal bandwidth and the less interference to adjacent frequencies.
- Power supply ripple: a poorly filtered power supply superimposes an unwanted sine wave (at 100 Hz for full-wave rectified 50 Hz line voltage, or 120 Hz for 60 Hz line voltage) on the DC rail. This ripple can be heard as an audio hum in the received signal.
- RF oscillators: the VFO (variable frequency oscillator) and crystal oscillator at the heart of a transceiver both generate a sine wave at a precise frequency. The purity of this sine wave determines how clean the transmitted signal is.
- Audio frequency response: the human voice produces a range of sine waves. The voice frequency range is approximately 80 Hz to 8 kHz, though SSB filters restrict this to 300–3000 Hz for efficient use of spectrum. Radio frequencies are far above the range of human hearing.
Frequently Asked Questions
What is the difference between frequency and pitch?
Pitch is the subjective perception of frequency in sound. A higher frequency produces a higher pitch. The two terms are often used interchangeably, but frequency is the objective, measurable quantity (cycles per second), while pitch is the human perceptual experience. In electronics, we always use frequency. Middle A on a piano is 440 Hz. The lowest note on a bass guitar is about 41 Hz. The highest frequency most adults can hear is about 15–20 kHz. Radio frequencies are far above the range of human hearing, which is why you cannot hear a 14 MHz signal directly.
Why do we use sine waves rather than square waves for radio?
Sine waves are used because they contain energy at only one frequency. A square wave contains the fundamental frequency plus all odd harmonics (3rd, 5th, 7th, and so on) at decreasing amplitudes. Transmitting a square wave on a radio channel would therefore cause interference at all those harmonic frequencies — potentially violating regulations and interfering with other users. Transmitters are designed to produce as pure a sine wave (or sine-wave-based modulation) as possible, with output filters to suppress any harmonics that do appear.
What is angular frequency?
Angular frequency (ω, omega) expresses frequency in radians per second rather than cycles per second: ω = 2πf. One complete cycle equals 2π radians (360°). At 50 Hz: ω = 2π × 50 = 314 rad/s. Angular frequency appears in the mathematical description of sine waves: v(t) = Vpeak × sin(ωt + φ), where φ is the phase angle. You will encounter ω throughout this course in filter equations, resonance formulas and impedance calculations.
What is harmonic distortion?
An ideal amplifier or oscillator produces a perfect sine wave output. Real circuits are not perfectly linear and introduce small amounts of signal at harmonic frequencies (2×, 3×, 4× the fundamental). This harmonic distortion is expressed as a percentage of the fundamental or in dB below it. A 1% total harmonic distortion (THD) amplifier is considered quite clean for audio use. For RF transmitters, regulations typically require harmonics to be 40–60 dB below the fundamental. Well-designed output stages minimize distortion; low-pass filters remove what remains.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.