Guitar Speakers - 14th May 2020

Intro

Guitar amp emulation is a difficult one to get right. There's all the active circuitry within the amplifier itself, followed by the behaviour of the speakers(s) at the end of the chain. Guitarists often spent time carefully choosing the speaker that best represents how they want to sound - it's clearly an important factor. In the studio, it's impractical to have every different guitar speaker on-hand to choose from, and some studios have simply moved across to software: that way, you can record the raw guitar part, and put those signals through a virtual amp + cabinet of your choosing.

When it comes to emulating a guitar speaker, the typical approach is to measure the frequency and phase response, use that (via Fourier) to create an impulse response (IR), and use that IR signal to emulate what a speaker might actually be doing.

This typical approach has often been found lacking in realism when guitarists go from an actual speaker, to one which is being emulated using IR signals.

In this investigation, I'll be taking a look at why that might be the case.

Hypothesis

My hypothesis is this: using a single frequency sweep cannot capture the behaviour of a real loudspeaker under dynamic conditions. ie, a low-level sweep doesn't tell us anything about what happens when you crank it to 11.

Testing

A sensible method to test this would be as follows: take a series of frequency sweeps at increasing levels, and see how the behaviour changes as the drive levels increase.

Setup

In order to realise that test, I used the following equipment:

- A 1x12" guitar cabinet, loaded with an Eminence Man O War 16Ohm speaker - this was to be the test subject.

- A Crown MA12000i Amplifier - a large amplifier is needed to make sure there's no clipping at high levels

- A QSC TouchMix 30 Pro Mixing Desk - used for USB I/O and high input headroom

- A Sennheiser e906 to mic the cabinet

- A laptop running REW to measure everything

- A digital multi-meter to check voltages.

I also used plenty of acoustically absorbent materials to encase the cabinet, thus reducing the amount of sound escaping into the room. This particular speaker is very efficient, so high SPLs were achieved.

Below are some photos of the setup.

Method

The method here is pretty straightforward. First, I calibrated the voltages by playing a 50Hz test tone, and adjusting the fader on the mixing desk until the voltage was exactly 4.0V. This represents 1W into this 16Ohm speaker.

Using REW, I then ran a frequency sweep at the same level as the test tone. The sweep ran from 1Hz to 24kHz, although it's possible that there would be some rolloff in the signal chain towards the very low frequencies. The sweeps were approximately three seconds long, which was a tradeoff: a longer sweep allows more "detail", particularly at low frequencies where the cone might not have completed a full cycle before the input frequency changed. However, using a very long sweep would have put severe thermal stress on the speaker, resulting in power compression etc further confounding the results.

I decided that +6dB was a useful increment, representing double the voltage (4x the power). Since it's a digital mixing desk, the QSC TM30 made it very easy to apply increments in exactly 6dB steps.

It's important to note that the SPLs reported were not calibrated, so we can only consider things relative to one another.

Results

The results are presented below. It's clear to see that, at very high power levels, the speaker was clearly compressing the signal, particularly towards the bass where cone excursions were very large. The speaker was audibly distressed at the highest drive level.

First up, here are the raw results:

Next up, a more interesting graph: I added an offset to each curve, to compensate for how much gain was being applied. By doing that, we can see how the speaker deviated from its low-power behaviour, as the drive levels went up:

This clearly shows that, at very high power levels (64V RMS), the speaker is compressing over most of the frequency range. The rest of the sweeps stay fairly close to the original, with the 32V RMS curve showing a couple of areas of compression.

Even these curves, however, don't tell the full story. Below is a gallery of frequency response curves with the harmonic distortion also included.

These curves show that, while the frequency response does change at high power levels, harmonic distortion can be high at moderate levels.

Remember, 10% distortion is -20dB, and 50% distortion is -6dB.

10% distortion is generally considered to be clearly audible, which is why amplifier manufacturers often rate their amplifiers' power outputs at 10% THD - that's the power output where the sound will have degraded noticeably.

Analysis & Conclusion

At very high levels, this speaker showed signs of compression over much of the frequency range. This is unlikely to be due to thermal build-up: the sweeps were short, and started at a low frequency, where compression was immediately apparent anyway.

It is unlikely that the short-term compression effects would show up under normal use: 64V RMS into a 16ohm (nominal) speaker results in a nominal power input of 256W - the speaker wouldn't survive long with sustained power input of that magnitude. So, I think the short-term compression can be safely ignored in the pursuit of a good speaker emulator.

The harmonic distortion rise occurred at much more sensible (ie, likely to happen under normal use) power inputs, and those should certainly be considered essential to more completely emulate the behaviour of a guitar speaker in software. NB: the harmonic distortion varied with drive level. ie, if you pick one note harder than the other, then the speaker will add more harmonic distortion to the louder note. This would be non-trivial to put into code, but computing power is ever-increasing and I'm hopeful that such effects will be incorporated in the future.

8v Distortion