Harmonic Frequency
f_n = n × f_sw
Quick answer
This calculator solves f_n = n × f_sw for Harmonic Frequency. With Harmonic Number 0.5, Switching Frequency 100 kHz, the result is 50 kHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Any periodic switching waveform generates harmonics at integer multiples of the fundamental switching frequency. In EMC analysis, these harmonics are the primary source of conducted and radiated emissions from switch-mode power supplies, motor drives, and digital clocks. Odd harmonics dominate in symmetric waveforms (50% duty cycle square waves), while even harmonics appear with asymmetric duty cycles. The amplitude of the nth harmonic of an ideal square wave falls off as 1/n, but parasitic ringing can cause certain harmonics to exceed this envelope.
Variables
- f_n — Frequency of the nth harmonic (Hz)
- n — Harmonic number (integer, dimensionless)
- f_sw — Fundamental switching frequency (Hz)
Practical Notes
EMC standards like CISPR 32 and FCC Part 15 specify emission limits from 150 kHz to several GHz. A 100 kHz switching converter has harmonics at 200 kHz, 300 kHz, etc., with significant energy extending to 30-50 MHz depending on edge rates. Spread-spectrum clocking reduces peak harmonic amplitudes by spreading energy across a wider band.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| fn | Harmonic Frequency | MHz | Hz, kHz, MHz, GHz |
| n | Harmonic Number | — | — |
| fsw | Switching Frequency | kHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Harmonic Number 0.5, Switching Frequency 100 kHz
- 2. The relation: f_n = n × f_sw
- 3. Substitute: n = 0.5, fsw = 100 kHz
- 4. Result: Harmonic Frequency = 50 kHz
Worked examples
Minimum range
Given: Harmonic Number 0.025, Switching Frequency 100 Hz
Result: Harmonic Frequency = 2.5 Hz
Low range
Given: Harmonic Number 0.25, Switching Frequency 1 kHz
Result: Harmonic Frequency = 0.25 kHz
Typical
Given: Harmonic Number 0.5, Switching Frequency 100 kHz
Result: Harmonic Frequency = 50 kHz
High range
Given: Harmonic Number 0.8, Switching Frequency 0.5 MHz
Result: Harmonic Frequency = 0.4 MHz
Maximum range
Given: Harmonic Number 8, Switching Frequency 5 MHz
Result: Harmonic Frequency = 40 MHz
Solving for each variable
Solve for Harmonic Frequency
Harmonic Number 0.025, Switching Frequency 100 Hz → 2.5 Hz
Solve for Harmonic Number
Harmonic Frequency 100 kHz, Switching Frequency 100 Hz → 1000
Solve for Switching Frequency
Harmonic Frequency 100 kHz, Harmonic Number 0.025 → 4 MHz
How Harmonic Frequency changes with Harmonic Number
| Harmonic Number (input) | Harmonic Frequency (result) |
|---|---|
| 0.05 | 5 kHz |
| 0.125 | 12.5 kHz |
| 0.25 | 25 kHz |
| 0.375 | 37.5 kHz |
| 0.5 | 50 kHz |
| 0.75 | 75 kHz |
| 1 | 100 kHz |
| 2 | 0.2 MHz |
| 3.5 | 0.35 MHz |
| 5 | 0.5 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 50000 |
| kHz | 50 |
| MHz | 0.05 |
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<p><a href="https://vbatpower.com/formulas/harmonic-frequency/">Harmonic Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Harmonic Frequency?
Use f_n = n × f_sw. With Harmonic Number 0.5, Switching Frequency 100 kHz, Harmonic Frequency works out to 50 kHz.
What is the formula for Harmonic Frequency?
The formula is f_n = n × f_sw. Any periodic switching waveform generates harmonics at integer multiples of the fundamental switching frequency.
How do you find Harmonic Number when you know the other values?
Rearrange for Harmonic Number: with Harmonic Frequency 100 kHz, Switching Frequency 100 Hz, Harmonic Number is 1000.
How do you find Switching Frequency when you know the other values?
Rearrange for Switching Frequency: with Harmonic Frequency 100 kHz, Harmonic Number 0.025, Switching Frequency is 4 MHz.
What units does Harmonic Frequency use?
Harmonic Frequency is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All EMC / EMI formulas →Need more features?
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