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Interactive Voltage Controlled Oscillator (VCO) Simulator


VCO Module v1.0 (Simple)

Inputs & Controls

Oscilloscope

Output Frequency: 220 Hz

Equation: f = Base + (CV × Tracking)

Advanced VCO (1V/Oct)
CONTROL VOLTAGE 0.00 V
BASE FREQUENCY 261.63 Hz
WAVEFORM
FM Synthesis (Modulation)
MOD DEPTH (Cents) 0
MOD RATE 5 Hz
TIME DOMAIN (OSCILLOSCOPE)
FREQUENCY DOMAIN (SPECTRUM ANALYZER)

Mathematical Background

In Digital Signal Processing (DSP), the output of a Voltage Controlled Oscillator (VCO) undergoing frequency modulation is defined by the following time-domain equation:

y(t) = A sin( 2π fct + β sin( 2π fmt ) )

Variable Mapping

To relate this mathematical model to the hardware simulator controls, we map the parameters as follows:

  • 1. fc (Carrier Frequency) = "Base Frequency"

    This is the center pitch (e.g., 440Hz). In the absence of modulation, this is the fundamental frequency produced by the oscillator.

  • 2. fm (Modulating Frequency) = "Mod Rate"

    Defines the speed of the modulation. If fm is 5Hz, the pitch completes a full cycle (up and down) five times per second.

  • 3. Δf (Frequency Deviation) = "Mod Depth"

    The maximum shift away from the carrier frequency.
    Example: If fc = 440Hz and Δf = 50Hz, the VCO swings between 390Hz and 490Hz.

  • 4. β (Modulation Index) = "The Secret Sauce"

    The ratio of deviation to modulation frequency. This determines the harmonic complexity (timbre) of the sound.

    β = Δf / fm

Lab Mapping Summary

Simulator Label Math Symbol Physics Designation
Base Frequency fc Carrier Frequency
Mod Rate fm Modulator Frequency
Mod Depth Δf Peak Frequency Deviation
Calculated Value β Modulation Index
Why it matters: The Modulation Index (β) is a multiplier for the wiggling effect. Increasing Mod Depth makes the sound harsher by increasing β. Increasing Mod Rate while keeping depth constant actually decreases β, which can make the sidebands thinner.

Live Parameter Calculator

Current Modulation Index (β) = 10.00

Status: Low-frequency modulation (Vibrato).

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