## 1 Introduction  
Nonlinear waveshaping is a technique used in sound synthesis to generate complex harmonic spectra. It consists of processing a signal with low harmonic content (typically a sinusoid) using a nonlinear mapping function designed to introduce harmonic overtones to the output signal [1]. The first documented use of waveshaping in the digital domain can be traced back to 1969, when [PERSON] emulated the sound of a clarinet by distorting a sinusoid with a clipping function [2]. Waveshaping techniques were extensively researched within the context of computer music in the 1970s, with several authors exploring the use of Chebyshev polynomials in particular, as an accurate and computationally cheap alternative to additive synthesis [1; 3; 4; 5]. The underlying principles behind waveshaping synthesis are closely related to other well-known synthesis techniques, such as frequency modulation (FM) and phase distortion (PD) synthesis [6; 7]. These two techniques rely on distorting the frequency and phase, respectively, of sinusoidal oscillators. Recent research on the topic of distortion-based synthesis has explored the use of logic operators in lieu of traditional polynomial waveshapers [8], and proposed extensions to both FM and PD synthesis [9; 10]. The use of waveshaping in the analog domain began in the 1950s, when guitar players started deliberately overdriving their tube amplifiers to alter the timbre of their instrument [11]. In 1961, Gibson released the \"Maestro FZ-1 Fuzz Tone\", the first commercially available fuzz distortion pedal, which exploited the saturating behavior of transistors to introduce harmonic distortion [12]. Most guitar distortion pedals, including popular designs such as the Ibanez Tube Screamer and Electro-Harmonix Big Muff Pi, operate under this same basic principle [13; 14]. In analog synthesizers, the use of distortion-based methods is one of the cornerstones of \"West Coast\" synthesis, a paradigm pioneered by California-native [PERSON] during the 1960s. [PERSON]'s instruments focused on timbre manipulation at oscillator level by employing a variety of techniques such as nonlinear waveshaping, oscillator synchronization and pitch modulation [15; 16; 17]. This approach to sound synthesis contrasts that of traditional subtractive synthesis, where timbre is typically controlled by filtering harmonically-rich oscillator waveforms, like sawtooth and square waves, using resonant filters [18]. In recent years, West Coast synthesis has become increasingly popular, with contemporary manufacturers such as Make Noise and Verbos Electronics releasing their own takes on classic [PERSON] circuits. This study presents virtual analog (VA) models for two analog synthesizer circuits: the Lockhart wavefolder and the wavefolder used in the middle section of the Serge Wave Multipliers. Wavefolding is a type of nonlinear waveshaping common in West Coast synthesis where portions of the input signal that exceed certain threshold are inverted or \"folded back\", hence the name of the effect. The two circuits considered in this study were chosen because of the strong similarities between their general behavior. In a similar way to guitar distortion pedals, both wavefolders exploit the saturating behavior of semiconductor p-n junctions (i.e., transistors/diodes) to implement a folding function. Wavefolders are amongst the most emblematic building blocks of West Coast synthesis. In spite of that, they have been mostly overlooked by both VA and digital waveshaping research. We have recently begun to fill this research gap in [17], which presents a VA model of the wavefolder circuit in the seminal Buchla 259 module. Previous work on circuit-based VA modeling has researched the filters found in vintage synthesizers such as those produced by Moog [19; 20; 21; 22], Electronic Music Studios (EMS) [23; 24], Korg [25; 26] and Buchla [16].