The Inverse Relationship

The more gain you apply, the more unstable the system becomes.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

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If you want to louse up the sound of a PA system without actually damaging any components, there’s a really quick way to go:

1) Plug in some microphones.

2) Keep the PA and the microphones in the same room.

3) Apply enough gain to the microphones such that they actually become useful for sound reinforcement.

In other words, just go ahead and use the PA as you would normally expect to use it. As you add more gain to the system, the system’s sound quality will degrade progressively. If you want to avoid this degradation, don’t use the PA for anything except playback – not turntable playback, though! Those tone arms are sensitive to environmental vibration. Use a media player, or a phone with the right software.

Okay, so I’m kinda “winding you up” with this. To be practical, we have to use PA systems in the same room as the microphones they’re amplifying. We do this all the time. We tend not to agonize over the loss of sound reproduction quality, because it just isn’t worth it. The issue is just inherent to the activity.

The reason to present this in such a stark fashion, though, is to get your attention – especially if you’re new to live audio. There are plenty of inescapable facts in this business, but one of the most important bugaboos is this:

In any audio system that involves a closed or partially closed loop from the input to the output, the system’s stability decreases as the applied gain increases. Further, to use such a system means that the assemblage is at least partially destabilized as a matter of necessity.


We spend a lot of time working with and talking about “gain” in pro-audio, but we don’t usually try to formally define it very often. Gain is a multiplier applied to a signal’s amplitude. Negative gain is a multiplier that is less than one, and positive gain is a multiplier that is greater than one. A gain of exactly one (the multiplicative identity) is “unity,” where the input signal and the output signal amplitudes are the same.

For convenience, we usually express gain as the ratio of the input signal to the output signal in decibels. Unity gain in decibels is zero, because 0 dB relative to a given amplitude is that same amplitude.

Because our systems work in partially closed loops, we can also talk about concepts like “loop gain.” Loop gain is the ratio between the system output and system input, where the output is at least partially connected to the input. A system with a loop gain greater than one is in the classic “hard feedback” scenario, where an unwanted signal aggressively self-reinforces until it can no longer do so – or somebody fixes the problem. A loop gain of exactly one is still a huge problem, because a signal just continues to repeat indefinitely. The sound may not be getting progressively louder, but it’s still tremendously annoying and a grossly incorrect rendition of the original sonic event.

Especially in the context of system stability, it’s important to understand that there is a difference between gain settings and “effective loop gain.” For instance, a microphone with greater sensitivity increases the effective loop gain of a system, because it increases the system output for a given, re-entrant signal from an input…if the downstream gain settings remain fixed.

“We plugged in that condenser, and we got crazy feedback!”

“Of course we did. That condenser is 10 dB more sensitive than the mic it replaced, and you didn’t roll the preamp gain back at all. You would have gotten feedback with the original mic if you had suddenly gunned it +10 dB, that’s for sure.”

In the same vein, any physical change that increases the intensity of re-entrant signal relative to the original input is also an increase in effective loop gain. If somebody insists on having a microphone close to a PA speaker, then the system’s electronic gain structure has to be dropped if you want to compensate. (Sometimes, you don’t want to fully compensate, or you can’t for some reason.)


Okay, then.

What do I mean by “stability?”

For our purposes, “stability” is a tendency for a system to return to a desired equilibrium after having been disturbed. In an audio system, the “disturbance” is the input signal. If our sound rig was perfectly stable, the removal of the input signal would correspond with an instantaneous stoppage of output signal. The system would immediately come to “rest” at zero output (plus any self noise).

Systems used only for playback tend to have very high stability. When an input stops, the system stops making noise almost immediately.

Yes, there are limitations. Loudspeaker drivers don’t actually come to a stop instantly, for example.


Playback-only systems have such great stability because they tend to be “open loop.” The system’s output is not reintroduced to the system input in any meaningful way. (Record players are an exception to this, as I alluded to in the introduction.)

But PA systems being used for actual bands in an actual room are at least a “semi-closed” loop. Some portion of the output signal makes it back to the input devices, and travels through the system again. This increases the time necessary for the system to settle back to “zero output plus noise” for any given input signal – and, if you REALLY want to split hairs, you have to deal with the reality that the system never actually settles to zero at all. The signal runs through the loop indefinitely, until the loop is broken by way of a mute button, a fader being set to -∞, or the system having its power removed. To be fair, the repeating signal is usually lost completely to the noise floor in a relatively short amount of time. Even so.

Cooking up a “laboratory” example of this is fairly easy. You just take a sample of audio, run it through a delay line, and apply feedback to the delay line. To get a quantitative perspective on things, you can figure out the time required for the total output to decay into an arbitrary noisefloor. You do this by taking the signal loss through each traversal of the loop, dividing the noisefloor dB (a negative number indicating how much signal decay you want) by the “loop traversal loss” dB, and then multiplying that number by the loop traversal time.

For example, let’s say that I have a desired noisefloor of -100 dB, referenced to the original input signal level. The loop time is 10 ms, which I encounter regularly in real-life applications. If the loop traversal loss is -50 dB (meaning that the signal drops 50 decibels each time it exits and re-enters the system), then:

-100 dB/ -50 dB = 2

2 * 10 ms = 20 ms

In 20 ms, the signal has dropped far enough that I can ignore it.

Fifty dB of rejection is REALLY high for a small-venue PA system. That kind of system “instability” is impossible for me to hear. Take a listen yourself:

A traversal loss of 20 dB means that it takes over twice as long to hit the desired noisefloor – 50 ms. I can sorta start to hear some issues if I know what to look for, but it’s nothing that’s really bothersome.

A signal that decays at the rate of only 10 dB per loop traversal is audibly “smeared.” A 100 ms decay time is actually pretty easy to catch, and I’ll bet that if the instability was band-limited (as it usually is), we’d be well inside the area where the mic is starting to get “ringy and weird” in the monitors.

…and then the singer wants nine more dB on deck, which bumps the decay time to a full second. The monitor rig is getting closer and closer to flying out of control.

You get the idea. This simulation is rather abstract, but the connection to real life is that adding gain to a system reduces loop traversal loss. That is, if a signal has a loop traversal loss of -20 dB, and we increase the applied gain by 10 dB, the loop traversal loss is now only -10 dB. It takes longer for the signal to settle into the noisefloor. The system stability has decreased.

And, of course, if we go far enough with our gain we’ll get the total loop gain to be one or greater. FEEEEEEEDBAAAAAACK!

The Upshot

What this all comes down to is pretty simple:

Anything that causes you to increase a system’s effective loop gain is undesirable…but sometimes you have to do undesirable things.

Live sound is not simply an academic exercise. There are all kinds of circumstances that end up pushing us into the increase of total loop gain, and while that’s not our most preferred circumstance, we often have no choice. Even though any increase in gain also increases the instability of our systems, there’s a certain amount of instability which can be tolerated. Also, because there’s always SOME amount of re-entrant signal, there’s no setup which is fully stable – unless we give everybody in the room a set of in-ears. ($$$)

Also, we can get a bit of help in that our systems aren’t linearly unstable. We tend to get instabilities in strongly band-limited areas, which means that surgical EQ can patch certain problems without ruining the whole day. We reduce our loop gain in a very specific area, which hopefully buys us the ability to get more gain across the rest of the audible bandwidth.

Of course, if something comes along which lets us reduce our effective gain, that makes us happy. Because it helps keep us stable.