Issue 60
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April 15, 2014


What the? Is it a bird, is it a meal? No, it’s a tool for the fight against feedback in your PA system.

Text: Hugh Covill

My partner Rosie was peering over my shoulder at my preparatory notes for this article on PAG-NAG when she was heard to blurt out: “PAG what? Isn’t PAG-NAG a vegetarian dish or something? I thought AT was an audio magazine…”

So what did I do? I began a summary explanation of acoustic gain. I distinguished PAG-NAG from food and suggested that her confusion might be with Gado-Gado. It was at this point that she began to get that familiar glazed-over look, which I’ve come to know means she’s lost interest completely in what I’m saying and is regretting feigning interest in the first place. She retreated…

Returning to my thoughts I was left with a realisation that, yes, a lot of the subjects I write about in AT are quite dry and not immediately appetising. They’re like eating vegetables when you’re a kid – hard to digest, but good for you in the end. (Note to self – must hit up Andy for some tasty interviews with some superstar mix guys… backstage near the rider/catering with plenty of impressive/expensive flashing audio gear).

Understanding acoustic gain and the variables that drive it are vital to establishing a ‘healthy’ live sound practice. Let’s stir the pot again and see what bubbles up!


Let’s dive right in with some definitions, starting with our old friend, gain. Gain is not a measure of volume per se. It’s expressed in decibels and from this we can deduce that gain is a ratio of two relative quantities (be it pressure, Volts, distance or power). In the case of gain, it’s the ratio of the output level to the input level. Alternatively, gain can simply be described as the amount of amplification of an audio signal.

‘But what’s this PAG-NAG?’ I hear you ask. Well, PAG is an acronym for Potential Acoustic Gain. It’s a measure of how much you can increase the amplification of a sound system before it begins to feedback. NAG is an acronym for Needed Acoustic Gain, and is a measure of how much gain is required for a particular application. The PAG-NAG calculation therefore goes basically something like this: How much acoustic gain have I got to work with and how much acoustic gain do I need? If the gain required (NAG) is more than the gain available (PAG) then your show will be plagued with feedback. Mathematically, the goal is for PAG minus NAG to equal zero (or preferably a positive number).

You often hear folks talk about “gain before feedback” or that “swapping mics gave us better gain before feedback.” What they’re talking about of course is acoustic gain, but in a relative sense: i.e. mic brand X had better gain before feedback relative to mic brand Y. Acoustic gain is an absolute measure. Here’s how you work it out…


Grab your sound level meter and measure a stage source (a person talking into a microphone works well) from the back of the auditorium with the PA turned off. Record the reading. Now measure again, this time with the PA turned on. Bring up the sound system until the level of the talker is adequately loud and intelligible. The difference in measured SPL can be considered the amount of acoustic gain.

Now, if when you turned the sound system up, it began to feedback before you reached a satisfactory volume then the system does not have adequate acoustic gain and as an engineer it’s your job to examine why that is.

Acoustic Gain, empirically speaking, is derived using this equation:

20logD1 + 20logEAD – 20logD2 – 20logDs – 10logNOM – FSM = 0 (or a positive number)

The equation variables are illustrated in Fig 1 (below).



Let’s discuss the variables used to determine acoustic gain. I won’t dwell too much on the maths involved – though it’s not particularly onerous – it’s the underlying fundamentals that are more important to grasp.

How often you’re going to perform an acoustic gain calculation will pale by comparison to the number of times you’ll be challenged by feedback when operating a PA. An understanding of acoustic gain is therefore mainly an understanding of the factors that can cause feedback. Developing a knowledge of what these factors are will set you up with concrete tools you can then confidently employ to mitigate feedback as a factor. Whether you’re designing a PA system for a venue, or operating one, understanding acoustic gain is an essential building block of your knowledge base.


D0 The distance between the source and the sound system listening position.

D1 The distance between the loudspeaker and the microphone.

D2 The distance between the loudspeaker and the sound system listening position.

Ds The distance between the source and the microphone.

FSM The Feedback Stability Margin.

NOM The Number of Open Microphones.

EAD The Equivalent Acoustic Distance.

All the above terms are fairly self-explanatory with the exception of the last three. These relate to the NAG (Needed Acoustic Gain) part of the puzzle.

FSM is an acronym for ‘Feedback Stability Margin’ and is simply how much useable level above the nominal operating level (0dB) is required, i.e. if your system is stable running at nominal, how much are you likely to push your faders up to accommodate solos, quiet speakers etc. For me, a margin of 10dB is good; 6dB is considered a minimum.

Remember that running your system close to the point of feedback is also adversely affecting the tone of your mix. I touched on NOM in my last article concerning aux-fed subwoofer systems. NOM is an acronym for the ‘Number of Open Microphones’. Doubling the number of open microphones in a PA system reduces the available acoustic gain by 3dB and is consequently a significant factor in the acoustic gain equation. Twenty open mics equates to 13dB less gain before feedback using the 10log (NOM) equation. EAD is an acronym for ‘Equivalent Acoustic Distance’. I’m not going to dwell on this or give you the long definition, which comes with its very own formulae and takes into account source SPL, ambient noise and exact distance measures. Simply put, the EAD is the point in space beyond which reinforcement of the source becomes necessary to aid intelligibility and clarity of communication.

So let’s ascribe some actual figures to these variables and see what the equations yield. See Fig. 2.


Assuming that from the distances in Fig. 2 we obtain an acoustic gain number of 2.5dB, i.e. PAG-NAG= 2.5dB. Is that good? Well, it depends. I used a single mic for the equation so in this example we have sufficient gain for a single mic gig only. If I added a second mic (that would be doubling the number of open microphones and hence 3dB less of available gain) the system would become unstable

However, to my mind at least, the maths is not principally important. It’s what the maths is alluding to that’s important. Specifically to

• Minimise the distance between source and microphones.

• Maximise the distance between microphones and loudspeakers.

• Minimise the distance between loudspeakers and audience.
The reason for this apparently blasé attitude towards the formula is that the equation is predicated on omni-directional behaviours. That is to say, the microphone and loudspeaker polar patterns are assumed to be omni. So straight away we can expect to get better numbers because modern sound systems tend to utilise directional speakers and microphones, which reduce the chance of sounds feeding directly into one another, and thus feeding back. Although most loudspeakers become more omni-directional at lower frequencies there have been great advances in controlling sound energy dispersion over the last 10 years with the maturing of cardioid subwoofer techniques and line array technologies. Similarly, microphones with well-defined directional characteristics have been favoured for use in live sound because they offer better feedback rejection.

Feedback is simply the sound from a loudspeaker being picked up by a microphone and returned back into the same loudspeaker, to be re-amplified all over again. When this happens you’ve got a problem. At sufficient gain, a loop condition is reached and the sound system acts like an oscillator at the most resonant frequencies. Everyone knows the sound; it’s the scourge of the live show. PAG-NAG provides us, empirically speaking, with the tools to resolve this problem. So let’s look again at Fig 2 and see where we can make the most significant improvements that will reduce or eliminate our chance of feedback.

All of the distance variables are 20log equations, so straight away we know that halving or doubling these distances is going to yield a 6dB change. The distance between the source and the microphone is where you’ll get best improvement in useable acoustic gain because the distance is already the smallest. If we reduce this distance by half (30cm to 15cm) we’ve suddenly improved our number by 6dB. If we halve this distance measure again (15cm to 7.5cm) we get the same improvement: 6dB.

Let’s contrast this with the distance between microphone and loudspeaker. To get the same 6dB improvement we would have to move the loudspeaker eight metres! The same holds for the distance between the loudspeaker and the system listener. So as you can see, moving the source of our sounds closer to the mics offers us the best chance of combating feedback. By moving the source from 30cm to 7.5cm from the microphone we have acquired an extra 12dB of useable gain and our PA can now accommodate a small band, i.e. 10 open microphones and still remain stable.


So there we have it, a cursory look at acoustic gain. For the most part, rote knowledge of the equations cited isn’t particularly important. What is important is to understand the underlying factors that affect your useable acoustic gain and have a good grasp of decibel relationships. Getting up close and personal to your open mics is the simplest way to improve your chances of defeating feedback, so let everyone you work with know that if they’re not close to the mic, the chances of the PA feeding back are greatly increased. Acoustic gain and feedback is everyone’s responsibility in the end. Wherever a mic’s position is fixed – in front of a guitar amp, for example – closer is better. Meanwhile if a mic’s in the hands of a singer, it’s up to you to tell them that closer to the mic makes your job easy, further away makes it hard.

I can’t remember how many times I’ve listened to lectern microphones at the edge of feedback with the speaker a good two feet from the microphone. In this scenario, you’ll often see the mix guy with his head in a parametric equaliser frantically pulling stuff out, when just politely talking with the presenter about his distance from the microphone can yield a real improvement. However, when that’s not an option – or the presenter won’t move – perhaps you can replace the lectern mic with something that possesses a longer gooseneck. Or better still, fit the presenter with a radio lapel. Of course, most of these changes really need to happen beforehand, so the trick is to word-up the speakers and presenters about their need to stay in close to the mic wherever possible. The point is, solving these problems electronically (with parametrics or graphic EQs etc.) should be your last port of call, not your first, as these destroy the frequency response of your system. There is often much you can do physically, intellectually and in the management of the mix (use your mute groups etc. to turn off unused microphones, for example) to improve the situation.

As always this article comes with the familiar caveat: ‘there’s much I’ve skimmed over’. This topic is a large one and while this article is simply a cursory glance at the concept of acoustic gain, hopefully you’ll be left with a clear understanding of what’s basically involved to reduce feedback. Remember, make sure the sources are close to those mics and wherever possible, minimise the number of open mics on stage. That way your PA will stand a fighting chance of providing you enough acoustic gain for the job at hand. Happy listening!


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