Potential acoustic gain

Before we dive into the geometry, let's take a brief moment to review the concept of gain before feedback, or potential acoustic gain (PAG).

Now let's take a look at the way positioning and distances contribute to gain before feedback, and how we can improve and maximize our PAG. →

Basic sound reinforcement system

Below is a diagram of a basic sound reinforcement scenario. There are four main components: a sound source (in this case a person speaking), a microphone input, a loudspeaker output, and a listener (a member of the audience).

Basic sound reinforcement system

The mixing console and its operator are equally important to a sound reinforcement system. But the operator and the physical location of the equipment are not key to determining the potential acoustic gain. The operator is just waiting for us to tell them how loud they can go before feedback occurs.

A function of distance

Let's look at some key physical relationships between these objects in the space. There are four key distances we are interested in that will allow us to calculate the PAG. They are labeled D₀, D₁, D₂, and D_S (the "S" is for source).

A function of distance

We know that feedback occurs when, at the location of the microphone, the amplified sound from the loudspeaker equals the sound from the original source. Using these four distance relationships along with the inverse square law, we have the equation for the PAG. Drag any figure to see how each distance changes the result.

Maximizing gain before feedback

You may have noticed several key relationships that result in an improved PAG. Click the eye to step through them, or drag any figure to experiment on your own.

Using a directional microphone

In addition to manipulating distance relationships, a more directional microphone can provide a significant boost in gain before feedback. The amount of off-axis rejection depends on the angular relationship between the microphone and the loudspeaker. Toggle the polar pattern above and drag the loudspeaker to find the mic's null.

Using a directional loudspeaker

Loudspeakers have directivity too. A more directional loudspeaker focuses sound toward the listener and away from the microphone, improving gain before feedback. Real-world loudspeaker directivity depends heavily on frequency, so the correction value here is estimated for demonstrative purposes. Toggle the coverage angle above and reposition the speaker to see how the off-axis attenuation toward the microphone changes the PAG.

How much gain?

Setting aside microphone and loudspeaker directivity, certain geometries result in no gain before feedback — the system feeds back the instant you turn it on. Beyond physical or aesthetic constraints on where you can place loudspeakers and microphones, the goal is always to maximize the PAG. Watch the speaker move from a useful position to a useless one.

Faders in action

Let's bring the operator back into the mix. With the geometry above we've calculated 1 dB of PAG: the listener can hear the reinforced sound at most 1 dB louder than the unaided sound from the source. A 1 dB increase in loudness is essentially imperceptible — installing a sound system in this case is wasted effort. Click the operator to try the fader.

Closer to the source

Now move the source closer to the mic. Cutting D_S from seven feet down to a few feet adds about 6 dB of potential gain — going from 1 dB to roughly 7 dB. That does not mean the system is safe from feedback. If the operator pushes the reinforced sound 7 dB above the direct sound at the listener, it will still feed back. But 7 dB of usable gain is a meaningful improvement over 1 dB — the operator finally has some room to work. Click the operator to try the fader.

Move the equipment before you touch the EQ

The PAG formula is a product of two ratios. The first, D₁ / D_S, is the system side of the bargain: the loudspeaker should be far from the microphone, and the microphone should be close to whatever is making sound. The second, D₀ / D₂, is the audience side: the listener has to be far enough from the source that they need a sound system at all, and the loudspeaker should be close enough to them that it does not have to work hard.

1. Get the microphone close to the source. This is almost always the biggest move you have.
2. Get the loudspeaker far from the microphone, and aim its dead zone (or the microphone's) at the other one.
3. Get the loudspeaker as close to the listeners as the production will allow.
4. If you still need gain after all of that, then reach for the EQ. You will need a lot less of it.