Five Simulations Before Solder

The entire premise of Timbre rests on a handful of claims that no one has tested in this specific combination. Self-oscillating switched-capacitor blocks as a primary synthesis engine. Mid-note topology switching between fundamentally different oscillation modes. A clock noise floor manageable enough to produce a musical instrument rather than a science experiment. These are claims that sound reasonable on paper and in the Voice Engine writeup, but “sounds reasonable” is not evidence. Before a single CY8C29466 gets soldered to a breakout board, the physics needs to agree.

So I built five LTspice simulations - each one designed to answer one question, each answer informing the next question. The campaign took the project from “I think this works” to “here are the waveforms, here are the numbers, here is the output filter design.” Every simulation is published as an interactive SpiceBook notebook with full schematics and waveform data.

Does the biquad actually oscillate?

The foundational question. The Voice Engine page describes bandpass self-oscillation as the primary synthesis mode - a two-integrator-loop biquad driven past its stability threshold. The theory is well-established: increase Q until the loop gain exceeds unity, and the filter becomes an oscillator. But “well-established theory” and “works in switched-capacitor fabric on a commodity microcontroller” are separated by a lot of implementation detail.

The first simulation starts with the continuous-time equivalent circuit - ideal components, no switching, no clock. Three parametric runs sweep the damping conductance from well-behaved (Q of roughly 1) through ringing (Q around 10) to self-oscillating, where the damping term flips sign and the biquad sustains indefinitely. The transition is clean: at a damping conductance of +2 microsiemens, the circuit locks into stable oscillation at 1592 Hz - exactly the frequency predicted by the component values.

What matters here is not just that it oscillates, but how. The waveform clips symmetrically against the supply rails, producing odd-harmonic content that gives it a hollow, clarinet-like character. This is the same harmonic signature that made self-oscillating Moog filters musically distinctive - the symmetric saturation produces odd harmonics while suppressing even ones. And because the oscillation frequency and the filter characteristics are literally the same circuit, adjusting Q morphs the waveform continuously from near-sinusoidal (just above the oscillation threshold) to hard-clipped square (high positive feedback). A single register controls this entire range.

Does switching change the answer?

Continuous-time equivalents are useful for validating topology, but Timbre’s fabric is switched-capacitor. The actual CY8C29466 blocks use MOSFET switches cycling at hundreds of kilohertz, alternately connecting and disconnecting capacitors to build integrators from discrete charge packets rather than continuous current. The question is whether the switching process itself disrupts the self-oscillation mechanism.

The second simulation replaces the ideal components with real MOSFET switches and a 500 kHz two-phase non-overlapping clock. The dataset is dense - 938,690 data points capturing every switching transient. In the linear region, the staircase waveform is clearly visible: the output advances in discrete steps synchronized to the clock, each step a capacitor dumping its charge packet.

The answer is yes, it still oscillates. The same topology, the same frequency, the same odd-harmonic character. THD measures 4.59%, with odd harmonics dominant - matching the continuous-time result. The switching process adds its own signature: a -37 mV DC offset from charge injection asymmetry (the MOSFET switches don’t turn on and off with perfect symmetry, and the residual charge from each switching event accumulates as a small DC bias). This offset is a known switched-capacitor artifact and is straightforward to null with a DC-blocking capacitor or offset trim.

The important result is what didn’t change. The oscillation mechanism survived the transition from ideal components to clocked switches. The SC domain adds its character - the staircase waveform, the charge injection offset, the sampled-data texture - but the fundamental physics of self-oscillation is preserved. This is the validation that the Voice Engine concept requires.

Can the same fabric do something fundamentally different?

A synthesizer with one oscillation mode is a curiosity. Timbre’s architecture promises that the same twelve analog blocks can be reorganized into different topologies - not just different parameter settings of the same circuit, but genuinely different oscillation mechanisms. The third simulation tests this by building a relaxation oscillator from the same SC fabric.

The topology is minimal: one SC integrator charging a capacitor, one continuous-time Schmitt trigger detecting the voltage threshold crossings and resetting the integrator. Two of twelve available analog blocks. The circuit produces a clean triangle wave at the integrator output (plus or minus 0.989 V) and a rail-to-rail square wave at the Schmitt trigger output (plus or minus 4.5 V). Three parametric runs demonstrate octave-spaced frequency control by changing the SC clock ratio - 500 kHz, 1 MHz, 2 MHz - confirming that pitch tracks the clock with the same mechanism as the biquad mode.

The musical significance is that this is a completely different oscillation topology from the biquad. The biquad produces a near-sinusoidal tone that clips into odd harmonics. The relaxation oscillator produces a triangle/square pair with a full harmonic series. Different waveforms, different spectra, different character - from the same physical silicon. And because the relaxation oscillator uses only two blocks, ten remain available for filtering, waveshaping, or additional oscillation modes running simultaneously within a single voice.

The big one: mid-note topology switching

This is the core claim that separates Timbre from everything in the Lineage. The Oberheim Xpander could select from fifteen filter modes per patch. The 2024-25 instruments can morph between predefined modes under CV control. Timbre claims the ability to reorganize the analog fabric from one oscillation topology to another while a note is sustaining - in under twelve microseconds, as described in Reconfiguration.

The fourth simulation tests exactly this: a biquad self-oscillating at steady state, then a topology switch to relaxation mode, with the integration capacitor bridging both configurations to maintain signal continuity.

The first attempt failed. I used the same SW switch models from the biquad simulation, and the solver ran for 120 seconds before timing out with voltages spiraling to 900 V. The switch models’ parasitic capacitances and the abrupt topology change created a numerical singularity that SPICE could not resolve. This is worth documenting honestly - not every approach works on the first try, and the failure mode (numerical instability from parasitic interactions during a discontinuous topology change) is itself informative about what the real hardware will encounter.

The second attempt replaced the switch-level models with behavioral conductances - ideal voltage-controlled resistors that capture the switching function without the parasitic detail. The simulation completed in 5.4 seconds on the first run. The topology transition occurs in 12 microseconds: the biquad switches off, an 8-microsecond dead zone passes while the configuration registers update, and the relaxation oscillator starts. During that 8-microsecond dead zone, the charge stored on the bridging integration capacitor decays by 0.08%. The note sustains through the transition.

And then the simulation revealed something I did not predict.

The elongated first cycle

When the relaxation oscillator starts, it inherits the voltage sitting on the integration capacitor from the biquad’s last cycle. That voltage - roughly +4.5 V from the biquad’s rail-clipped oscillation - is well outside the relaxation oscillator’s normal switching thresholds of plus or minus 0.987 V. The integrator has to charge all the way from +4.5 V down to -0.987 V before the first Schmitt trigger transition occurs.

The result is a first half-cycle that is 2.75 times longer than the steady-state period. By the second cycle, the relaxation oscillator has locked to its predicted frequency (1139 Hz measured, 1136 Hz predicted). But that elongated first cycle produces a brief downward pitch scoop - a transient that sounds like the attack of a brass instrument, where the lip buzz starts wide and the standing wave in the bore pulls it into tune.

This is not a defect. It is a phase-dependent, performable articulation. The length of the scoop depends on where in the biquad’s cycle the switch occurs - interrupt at the positive peak and the scoop is long; interrupt near zero crossing and it is minimal. A performer controlling the switch timing via velocity, aftertouch, or a mod wheel would have direct control over this attack character. The simulation turned up a musically useful artifact that was not part of the original design intent.

What about the clock noise?

Every discussion of switched-capacitor audio hits the same wall: clock feedthrough. The Voice Engine page cites the conventional concern - roughly 10 mV peak-to-peak at the clock frequency leaking into the audio path. For a 500 kHz clock this is well above audio, but aliasing products and imaging artifacts could fold back down. The literature on SC filters in audio applications is cautious to the point of discouragement, and this caution is a significant reason no major synthesizer manufacturer ever used SC filters as primary musical VCFs.

The fifth simulation measures the actual clock feedthrough from the switch-level biquad and designs an output reconstruction filter. The filter is a second-order Sallen-Key Butterworth lowpass set at 39.7 kHz - transparent to audio (less than 0.1 dB of attenuation at 1.5 kHz, roughly 1 to 2 dB at 20 kHz) while rolling off the clock frequency range.

The result upended an assumption I had carried through the entire design process. The raw SC output at 500 kHz is already -61 dB below the fundamental. Not after filtering - before filtering. The clock artifacts are present as broadband sampled-data imaging, not as a discrete tone, and their aggregate energy is far lower than the 10 mV peak-to-peak figure cited in the general SC literature.

The reason, in retrospect, is the clock-to-signal frequency ratio. At 500 kHz clock and a 1.5 kHz fundamental, the ratio is over 300:1. The SC literature’s noise figures are typically characterized at much lower ratios - 50:1 or 100:1 - where the aliasing products are closer to the signal band and harder to separate. At 300:1, the imaging artifacts are so far above audio that even the stray capacitances and charge injection of real MOSFET switches cannot couple significant energy back down.

This means the simple second-order Sallen-Key filter is more than adequate. A first-order RC might even suffice. The “SC noise problem” that discouraged forty years of synthesizer designers from using switched-capacitor filters for musical purposes is, at this clock ratio, a solved problem before the filter is even applied.

What this means

Five simulations, five questions answered. The biquad self-oscillates musically (Sim 1). The switching process preserves the oscillation (Sim 2). The same fabric supports fundamentally different topologies (Sim 3). Topology switching works mid-note with signal continuity and produces musically useful articulation artifacts (Sim 4). And the clock noise floor is dramatically better than the literature suggested (Sim 5).

Every claim that the Voice Engine and Reconfiguration pages make about the SC fabric’s capabilities is now backed by simulation data. The numbers are published, the schematics are viewable, and the SpiceBook notebooks make every result independently reproducible.

The next step is hardware. Phase 1 of the Roadmap calls for a single CY8C29466 on a breakout board, connected to an ESP32 over I2C, producing its first MIDI-triggered tone. The simulations say it will work. The soldering iron is warming up.

Simulation	Question	Key Result
Sim 1 - CT Biquad	Does the biquad self-oscillate?	Yes, 1592 Hz, clarinet-like odd-harmonic character
Sim 2 - SC Biquad	Does switching preserve oscillation?	Yes, same THD (4.59%), -37 mV DC offset from charge injection
Sim 3 - Relaxation	Can the fabric do a different topology?	Yes, triangle/square from 2 of 12 blocks, octave-spaced clock control
Sim 4 - Topology Switch	Can you switch mid-note?	Yes, 12 us transition, 0.08% charge decay, elongated first cycle as musical artifact
Sim 5 - Clock Noise	Is clock feedthrough manageable?	-61 dB raw (before filtering), 2nd-order Sallen-Key is more than sufficient