Calculator Inputs
Example Data Table
| Harmonic Order | Frequency at 60 Hz | Voltage | Type | Phase | Meaning |
|---|---|---|---|---|---|
| 1 | 60 Hz | 120 | RMS | 0 deg | Main sine component |
| 3 | 180 Hz | 8 | RMS | 15 deg | Third harmonic component |
| 5 | 300 Hz | 5 | RMS | -20 deg | Fifth harmonic component |
| 7 | 420 Hz | 2.5 | RMS | 30 deg | Seventh harmonic component |
Formula Used
Total RMS voltage with DC offset and orthogonal harmonic components is calculated as:
VRMS,total = sqrt(VDC2 + V12 + V22 + ... + Vn2)
When input is peak voltage, the calculator converts it with VRMS = Vpeak / sqrt(2).
When input is peak-to-peak voltage, it uses VRMS = Vpp / (2 sqrt(2)).
Total harmonic distortion is calculated as:
THD = sqrt(V22 + V32 + ... + Vn2) / V1 x 100%
Phase is used for waveform sampling and peak estimation. Exact harmonic RMS addition does not depend on phase when orders are integer multiples.
How to Use This Calculator
- Enter the DC offset. Use zero when the waveform has no DC component.
- Enter the fundamental frequency. This is used for frequency labels and waveform sampling.
- Select the voltage unit and the default value type.
- Add harmonic rows using order, voltage, value type, and phase.
- Click Calculate to view total VRMS, THD, peak estimates, and contribution values.
- Use the CSV or PDF buttons to export the current calculation.
Understanding Harmonic RMS Voltage
A pure sine wave has one frequency. Real supplies, drives, inverters, and audio circuits often carry more. These added sine waves are harmonics. They occur at whole number multiples of the fundamental frequency. A third harmonic is three times the base frequency. A fifth harmonic is five times the base frequency.
Why Total VRMS Matters
Meters, insulation checks, transformer loading, and heat estimates depend on RMS voltage. RMS describes the equivalent heating value of a varying waveform. When harmonics are present, the total value is not found by simple addition. Each harmonic contributes energy. The squared RMS values must be added, then the square root is taken. A DC offset is also squared and included.
Practical Example
Assume a waveform has 120 V RMS at the fundamental. It also has 8 V RMS at the third harmonic, 5 V RMS at the fifth harmonic, and 2.5 V RMS at the seventh harmonic. The total VRMS is the square root of 120 squared plus 8 squared plus 5 squared plus 2.5 squared. The result is about 120.40 V RMS. The value only rises slightly because the fundamental is much larger.
Distortion View
Total harmonic distortion compares all harmonic RMS values above the first order against the fundamental RMS value. It helps describe waveform purity. A lower percentage means the waveform is closer to a pure sine wave. A high value can indicate nonlinear loads, switching devices, saturation, or poor filtering.
Phase and Waveform Sampling
Phase usually does not change the analytical RMS total when harmonic frequencies are exact integer multiples. Yet phase can change waveform peaks. This calculator uses phase to sample the waveform and estimate peak voltage, crest factor, average rectified voltage, and form factor. Those figures help when checking device stress.
Using Results Carefully
The calculator is useful for classroom examples, lab reports, and preliminary engineering checks. Always confirm critical designs with calibrated instruments and applicable standards. Enter realistic harmonic data from a spectrum analyzer, simulation, or trusted measurement. More sample points improve peak estimation, but they also increase calculation time slightly. Keep records of assumptions, units, and harmonic sources. Clear notes make repeated tests easier and reduce reporting errors later significantly.
FAQs
What is VRMS with harmonics?
It is the total effective voltage of a waveform containing a fundamental sine wave plus harmonic sine components. It represents heating equivalent voltage.
Do I add harmonic voltages directly?
No. Square each RMS component, add those squares, include DC if present, then take the square root.
Does phase change total RMS?
For exact integer harmonics over a full period, phase does not change analytical RMS. It can change peak voltage and crest factor.
What does THD mean?
THD means total harmonic distortion. It compares all RMS harmonics above the first order against the fundamental RMS voltage.
Can I enter peak values?
Yes. Choose Peak as the value type, or write peak in the row. The calculator converts peak voltage to RMS automatically.
What is the DC offset used for?
DC offset is a steady voltage added to the alternating waveform. Its square contributes to total RMS voltage.
Why is sample RMS shown?
Sample RMS checks the waveform numerically. It also supports peak, rectified average, crest factor, and form factor estimates.
Is this suitable for final equipment design?
Use it for study, estimates, and reports. For final design, verify values with calibrated instruments and required engineering standards.