Waveform Mixer | Sine Waves, RMS and Spectrum

Waveform Components

Component 1 Enable

Amplitude A

Frequency f (Hz)

Phase φ (°)

Component 2 Enable

Amplitude A

Frequency f (Hz)

Phase φ (°)

Component 3 Enable

Amplitude A

Frequency f (Hz)

Phase φ (°)

Component 4 Enable

Amplitude A

Frequency f (Hz)

Phase φ (°)

Composite Waveform Stats

Results

—

RMS

—

Peak

—

Crest Factor

—

THD (%)

Time-domain waveform & frequency spectrum (DFT)

Time

Theory & Key Formulas

Square: $\dfrac{4A}{\pi}\sum_{n=1,3,5...}\dfrac{1}{n}\sin(n\omega t)$
Triangle: $\dfrac{8A}{\pi^2}\sum_{n=0}^{\infty}\dfrac{(-1)^n}{(2n+1)^2}\sin((2n+1)\omega t)$
Sawtooth: $\dfrac{2A}{\pi}\sum_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{n}\sin(n\omega t)$

Model and scope

The time record has 512 samples over two periods of the lowest enabled frequency. Square and triangle waves use 20 odd harmonics; sawtooth uses 20 harmonics. The spectrum uses a 64-point DFT after 8:1 decimation. Approximate THD takes the strongest component as its reference and checks multiples 2–8.

Questions and answers

Why is the amplitude input different from A?

The input uses a factor-of-ten scale: 10 means A=1.0 and 100 means A=10.0. No physical amplitude unit is imposed. If interpreting it as voltage, use that same unit for the waveform and RMS.

Why does a square-wave peak exceed A?

A finite harmonic series approximates a discontinuity with overshoot. The sampled approximation therefore need not have the ideal square wave's peak or RMS.

Why can high-frequency components appear in the wrong place?

Spectrum decimation has no antialiasing filter, so harmonics can fold back. The plot is also limited to 600Hz. Do not treat it as a precision spectrum analyzer or THD measurement.

Can I combine frequencies that are not integer multiples?

Yes, but components containing a noninteger number of cycles in the observation window produce spectral leakage. Phase and window length affect the sampled metrics. Start with integer multiples to understand the display.

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