Interactive VCO Simulator Online

UNIVERSAL VCO LABORATORY

Voltage-to-Frequency Transformation Engine

Voltage Control Unit (VCU)

Base Control Voltage ($V_{dc}$)

Static Offset 1.00 V

Modulation Amplitude ($A_m$)

Dynamic Swing 0.00 V

Modulation Rate ($f_m$)

AC Frequency 5 Hz

VCO Sensitivity ($K_v$)

Hz per Volt 100 Hz/V

Hardware Insight

Internally, the Control Voltage determines how fast an integrating capacitor charges. Higher voltage = faster charge cycle = higher frequency output.

$$ V_{in}(t) = V_{dc} + A_m \sin(2\pi f_m t) $$

Step 1: Combined Input Voltage Signal

$$ f_i(t) = K_v \cdot V_{in}(t) $$

Step 2: Instantaneous Frequency (The Control Path)

$$ s(t) = \sin\left( 2\pi \int_{0}^{t} f_i(\tau) d\tau \right) $$

Step 3: VCO Output Waveform (Time Domain)

$$ S(f) = \mathcal{F}\{s(t)\} $$

Step 4: Spectral Result (Frequency Domain)

Simulator Workflow & Mathematical Pipeline

1

Input Generation

We begin with the Control Voltage ($V_{in}$). Depending on the mode, this is either a flat DC line (for a stable pitch) or a fluctuating AC sine wave (for FM).

Logic: If Mode=FM, enable AC component.

2

Signal Processing

The voltage is scaled by the Sensitivity ($K_v$). This maps Volts to Hertz. In hardware, this corresponds to the speed at which the capacitor charges.

Formula: $f_i = K_v \times V_{in}$

3

Core Transformation

This is the Phase Accumulator. We integrate the instantaneous frequency over time to ensure Phase Continuity, preventing clicks or pops in the audio.

Process: $\sum 2\pi f_i \Delta t$

4

Resultant Waveform

The accumulated phase is passed through a trigonometric function to generate the final waveform. We then perform an FFT to visualize the spectral sidebands.

Final: $s(t) = \sin(\theta)$

Engineering Insight: The 1V/Octave Standard

While this simulator uses a linear Hz/Volt relationship for simplicity, many practical musical VCOs follow an Exponential relationship (1 Volt per Octave). This means that for every 1V increase, the frequency doubles ($f = f_0 \cdot 2^{V_{in}}$), mapping perfectly to how the human ear perceives musical pitch.

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