BiasGate

Tier: Color | ComponentType: 24 | Params: 5

Transistor bias/starve simulation with splutter gating -- models a transistor operating near its cutoff point with randomized threshold instability.

Overview

BiasGate simulates the behavior of a transistor circuit that has been starved of bias current to the point where it intermittently cuts off. When a transistor's bias point is set near its conduction threshold, small signals may not be strong enough to turn it on, creating a natural gating effect. The "splutter" parameter adds random variation to this threshold, causing the gate to fire erratically -- the characteristic sputtering, dying-battery sound of a nearly dead fuzz pedal.

The bias point parameter shifts the entire input signal up or down before the gate decision. With a positive bias, the signal sits higher on the transfer curve and the transistor stays on more of the time. With a negative bias, the signal is pushed below the conduction threshold and more of it gets gated out. At zero bias, the gate responds symmetrically to positive and negative signal excursions.

The gate envelope uses a fast attack (~1 ms) so the transistor turns on almost instantly when signal exceeds the threshold, and a configurable release time that controls how quickly the signal decays to silence when it drops below threshold. Short release times create choppy, staccato gating. Long release times create a smoother fade that sounds more like a dying amplifier losing power. A DC blocker follows the gate to remove the offset introduced by the bias, and a makeup gain stage compensates for the level loss from gating.

File Locations

	Path
Header	`Sources/FolioDSP/include/FolioDSP/Color/BiasGate.h`
Implementation	`Sources/FolioDSP/src/Color/BiasGate.cpp`
Tests	`Tests/FolioDSPTests/BiasGateTests.swift`
Bridge	`Sources/FolioDSPBridge/src/FolioDSPBridge.mm` (BiasGateBridge)

Parameters

Index	Name	Description	Min	Max	Default Min	Default Max	Default	Unit
0	Bias Point	DC offset added to signal before gate -- shifts operating point	-1.0	1.0	-0.5	0.5	0.0
1	Threshold	Signal level required to turn on the transistor	0.001	0.5	0.01	0.2	0.05
2	Splutter	Random threshold variation -- higher values = more erratic gating	0.0	1.0	0.0	1.0	0.0
3	Gate Release	Envelope release time when signal drops below threshold	1	1000	5	200	50	ms
4	Makeup Gain	Output gain to compensate for level loss from gating	0	40	0	20	0	dB

Processing Algorithm

The process() function executes these steps for each input sample:

1. Bias Offset

A DC offset shifts the signal's operating point relative to the gate threshold:

\[x_b = x + \text{bias}\]

2. Splutter Threshold

The gate threshold is randomized per-sample using a xorshift32 PRNG:

\[T_{\text{eff}} = T \cdot (1 + S \cdot r)\]

Where \(T\) is the base threshold, \(S\) is the splutter amount (0--1), and \(r \in [0, 1)\) is a uniform random value. At \(S = 0\), the threshold is deterministic. At \(S = 1\), the effective threshold ranges from \(T\) to \(2T\).

3. Gate Decision

The transistor is considered "on" when the absolute biased signal exceeds the effective threshold:

\[\text{on} = |x_b| > T_{\text{eff}}\]

4. Gate Envelope

A one-pole smoother creates the gate envelope with fast attack and configurable release:

\[\alpha_a = 1 - e^{-2\pi / (1.0 \cdot f_s / 1000)}\]

\[\alpha_r = 1 - e^{-2\pi / (R \cdot f_s / 1000)}\]

\[g_{\text{target}} = \begin{cases} 1.0 & \text{if on} \\ 0.0 & \text{if off} \end{cases}\]

\[\alpha = \begin{cases} \alpha_a & \text{if on} \\ \alpha_r & \text{if off} \end{cases}\]

\[g_n = g_{n-1} + \alpha \cdot (g_{\text{target}} - g_{n-1})\]

Where \(R\) is the gate release time in milliseconds. The attack is fixed at ~1 ms.

5. Apply Gate

The biased signal is multiplied by the gate envelope:

\[x_g = x_b \cdot g_n\]

6. DC Blocker

A first-order highpass removes the DC offset introduced by the bias:

\[d_n = d_{n-1} + \alpha_{\text{dc}} \cdot (x_g - d_{n-1})\]

\[y_{\text{dc}} = x_g - d_n\]

Where \(\alpha_{\text{dc}} = 1 - e^{-2\pi \cdot 10 / f_s}\).

7. Makeup Gain

Output gain compensates for the level reduction caused by gating:

\[g_m = 10^{\text{makeup}_{\text{dB}} / 20}\]

\[y = y_{\text{dc}} \cdot g_m\]

Core Equations

\[x_b = x + \text{bias}\]

\[\text{on} = |x_b| > T \cdot (1 + S \cdot r)\]

\[g_n = g_{n-1} + \alpha \cdot (g_{\text{target}} - g_{n-1})\]

\[y = \text{dcBlock}(x_b \cdot g_n) \cdot 10^{M/20}\]

Snapshot Fields

Field	Type	Range	Description
Input Level	Float	0--1	Smoothed absolute input level
Output Level	Float	0--1	Smoothed absolute output level
Bias Point	Float	-1--1	Current bias parameter value
Gate Gain	Float	0--1	Current gate envelope level
Splutter	Float	0--1	Effective splutter threshold (after randomization)
Transistor On	Bool	0--1	Whether the transistor is currently conducting
Eff. Bias	Float	-2--2	Effective biased signal value (input + bias)

Implementation Notes

DC blocker uses a one-pole highpass at 10 Hz with coefficient \(\alpha = 1 - e^{-2\pi \cdot 10 / f_s}\). This is essential because the bias parameter introduces a DC offset that would otherwise propagate through the signal chain.
xorshift32 PRNG: The random number generator uses the xorshift32 algorithm (shifts 13, 17, 5) for real-time-safe random values. The output is mapped to \([0, 1)\) by dividing by \(2^{32}\).
Gate initialization: On reset, the gate starts fully open (gateGain_ = 1.0, transistorOn_ = true) so the signal passes through immediately.
Test consideration: Tests must use AC signals (sine waves), not DC, because the DC blocker correctly removes constant inputs.
Level tracking uses exponential smoothing with coefficient 0.01 for display-rate visualization.
Snapshot emission is decimated to ~60 fps (every 735 samples at 44.1 kHz).

Equation Summary

y = gate(x + bias) · makeup