Interactive Voltage Controlled Oscillator (VCO) Simulator

VCO Module v1.0 (Simple)

Inputs & Controls

Control Voltage (V) 0.00 V

Tracking (Hz per Volt) 100 Hz

Base Frequency (Offset) 220 Hz

Waveform Sine Square Sawtooth Triangle

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

SAWTOOTH (RICH HARMONICS) SQUARE (ODD HARMONICS) TRIANGLE (SOFT) SINE (PURE)

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 f_ct + β sin( 2π f_mt ) )

Variable Mapping

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

• 1. f_c (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. f_m (Modulating Frequency) = "Mod Rate"

  Defines the speed of the modulation. If f_m 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 f_c = 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 / f_m

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

Carrier (f_c) Hz

Mod Rate (f_m) Hz

Mod Depth (Δf) Hz

Current Modulation Index (β) = 10.00

Status: Low-frequency modulation (Vibrato).

LOW-FREQUENCY BFSK VISUALIZATION (VCO MODEL)

Demonstrating spectral transitions at visible frequencies (5Hz–30Hz) for waveform analysis.

Symbol Duration (T_b)

Slow BitrateFast Bitrate

Modulation Depth (Frequency Swing)

Logic '0': 5 Hz | Logic '1': 20 Hz

10101100

BASEBAND $m(t)$

MODULATED $s(t)$ (Phase Continuous)