PHYS341/2024/Project5

Physics of Distortion in Guitar Amplifiers

Distorted guitar has become a key element in various genres of music, from early blues and swing to modern rock, punk, and heavy metal. An effect that started as the result of technological limitations and malfunctions is now a highly desired sound that can be produced and shaped in numerous ways.

History

Due to the low fidelity of early audio equipment, guitar amplifiers would often produce distortion if the volume/gain was increased beyond a certain limit. Guitarists in the 1930s and 40s began taking advantage of this effect, and distorted guitars became increasingly prominent in early blues and rock music. Some guitarists would intentionally manipulate their amps to achieve this distorted tone. Link Wray famously punctured the speakers of his amplifier to produce the distorted tone which can be heard on his classic record "Rumble".

Eventually, recording engineers figured out how to produce harsh distorted tones without having to manipulate their expensive equipment, leading to the creation of standalone effects units such as the Maestro FZ-1 Fuzz-Tone and the Electro-Harmonix Big Muff Pi. Alongside this, the quality of the guitar amps themselves increased throughout the 60s and 70s allowing them to be louder with more control over the distortion.

What is Distortion?

Before looking at what distortion looks like on a physical level, it is important to understand the fundamental principles on which amplifiers function.

Amplifiers generally consist of two components: a preamplifier and a power amplifier. The main purpose of the preamplifier is to boost the weak input signal so that it drives the power amplifier. This function is usually controlled using the "gain" or "volume" knob on the amp (the labelling of these controls can vary depending on the model of amplifier). The purpose of the power amplifier is to boost the incoming preamp signal so that it drives the loudspeakers. This function is usually controlled using the "master" knob on the amplifier (again, the labelling can vary). Both amplifier sections work by boosting the voltage of the input signal.

The amplitude response of an ideal amplifier is linear, and the ratio of the output voltage to the input voltage is called the gain. For example, an amplifier with a voltage gain of 2 will boost a 4 V input signal to an 8 V output. This process is sometimes called linear distortion. However, any amplifier will have a maximum output level known as its saturation level. Additionally, the amplitude response leading up to the saturation level becomes non-linear after a certain point, meaning that an input voltage in this range will be amplified at a ratio less than the voltage gain of the amplifier. This process is called nonlinear distortion, and is generally what is being referred to when discussing "distortion".

Here is a more detailed example to demonstrate how such an amplifier might work. Using the same hypothetical amplifier mentioned previously, let's say the saturation level is 10 V. The amplitude response is linear for all input voltages up to 4 V and thus all output voltages up to 8 V. For input voltages between 4 V and 7 V, the response is non-linear, so the output voltage may range from 8 V to the saturation level of 10 V. For any input voltage above 7 V, the output voltage will always be 10 V.

Soft vs. Hard Clipping

Linear distortion preserves the waveform shape while only increasing the amplitude. In other words, the loudness increases, but the tone quality stays the same. Nonlinear distortion results in what is called clipping, where the peaks and troughs of the sound wave are "clipped" such that the maximum voltage stays below the saturation level. The simplest demonstration of this is with a sine wave. When a sine wave is amplified through linear distortion, the output will look like the exact same sine wave just with a greater amplitude. When a sine wave is amplified with nonlinear distortion, the output will start to resemble a square wave, as the peaks of the wave are clipped and additional harmonics are added to the wave.

The extent to which the wave is clipped can be described as being "soft" or "hard". A sound wave that undergoes soft clipping will still generally resemble the input signal, with the peaks and troughs flattened but still rounded. This results in what is sometimes referred to as a "warm" distortion sound, due to the addition of harmonics. A sound wave that undergoes hard clipping will look more like a square wave, with the peaks and troughs flattened down. This results in a more "gritty" or "harsh" distortion sound, due to the addition of inharmonic frequencies on top of the harmonics.

Types of Distortion

Distortion can occur at any step in the audio signal chain. The primary method that guitarists and producers use to achieve distortion nowadays is overdriving the preamplifier section of the guitar amplifier, which can be done simply by turning up the gain on the amp until the preferred level of distortion is achieved. This can also be done to a similar effect using effects pedals placed before the amp.

When discussing different types of distortion in guitar amplifiers, it is common to distinguish between two categories of amps: tube amps and solid-state amps.

Tube amps use vacuum tubes (or valves, as they are called in the UK) to amplify the guitar signal. Vacuum tubes used in guitar amplifiers consist of a hot cathode that emits electrons and an anode that receives the electrons. Between these is a third electrode, a control grid, which, based on the incoming guitar signal, has the potential to amplify the flow of electrons.

Solid-state amps use semiconductor devices such as transistors to amplify the guitar signal. Transistors use the properties of semiconductor materials such as silicon to amplify a signal in a much more efficient, small-scale manner.

The invention of the transistor in 1947 led to solid-state electronics replacing vacuum tubes in almost every application, but many guitarists still prefer tube amps due to the characteristic distortion sound they produce. Specifically, tube amps are more often associated with the "warm" distortion sound produced by soft clipping, whereas solid-state amps clip the signal harder.

Test

The frequency spectrum for a tube amplifier model

The frequency spectrum for a solid-state amplifier model

This section will examine the differences between tube and solid-state distortion by looking at the frequency spectrums and waveforms they produce. Because guitar amps can be quite expensive (and I don't own any physical amps) I opted to use digital amp models to perform this test. The question of how accurately virtual amps can replicate the actual sound of the amps they model is one for another article, but perhaps this software can still provide some insight on the different ways distorted guitar tones can be produced.

The amplifiers I used for this test are the Mesa Boogie Dual Rectifier tube amp and the Fender MH-500 Metalhead solid-state amp. Both models are officially certified by their respective manufacturers for the amp simulator software AmpliTube 5.

I put the same recording through both amps and increased the gain on the amps over time.

Waveforms of tube distortion (top) vs. solid-state distortion (bottom)