Maximum Acoustic Gain & Feedback Control Fundamentals

Every feedback problem on a show comes down to the same physics: a mic and a loudspeaker sharing a room, and how much gain you can add before that loop turns into a howl. These are my working notes on maximum acoustic gain and feedback control from going through Section 5.3 of the Yamaha Sound Reinforcement Handbook — the operating margin to leave yourself, the formula behind it, and the three things you can actually do at a gig to buy more clean gain.

Reference: SRH-FEEDBACK-01. This page is background theory and rules of thumb, not a step-by-step procedure — read it as reference material, not a sequence to tick off.

Key facts: operate a system about 6 dB below the point where it just starts to ring — not right at the edge. Feedback happens the instant the mic-to-speaker-and-back loop hits unity gain (0 dB) at some frequency where the path is in phase. You gain more headroom by shrinking the source-to-mic distance and/or growing the mic-to-loudspeaker distance. Swapping omnidirectional mics and speakers for directional ones is worth roughly 6 dB of extra real-world headroom, once you account for how directivity falls apart at low frequency.

What's Actually Happening When a System Feeds Back

Picture the simplest possible rig: one mic, one amp, one loudspeaker. Some of the sound coming out of that speaker inevitably makes it back into the mic, gets re-amplified, and comes out of the speaker again — a closed loop. As you push the gain up, you eventually hit a point where, at some specific frequency, that loop's gain reaches unity (0 dB) and the path stays in phase all the way around. Once that happens the loop is self-sustaining and you get the classic ring or howl.

The important bit is that the system starts to sound bad well before you can actually hear it ring. As the loop gain creeps up toward unity, the whole system starts resonating at those in-phase frequencies, which colors the tone — usually described as a hollow or ringy character — even while it's still technically "under" feedback. That's the real reason for backing off a further 6 dB rather than just riding the edge of audible feedback.

The Maximum Gain Idea

"Maximum acoustic gain" is just the answer to: how much louder can I make this source through the system than it would be unaided, before I hit that feedback ceiling? The handbook builds this out with four distances laid out along the mic-to-audience path:

• Ds — source to mic (how close the performer is to the capsule)
• D0 — mic to loudspeaker
• D1 — loudspeaker to the listener you're checking
• D2 — straight-line distance from the source to that same listener

Those combine into a standard gain-before-feedback equation, with a 6 dB margin already folded in: ▣ Diagram

Max gain (dB) = 20 log(D0) − 20 log(Ds) + 20 log(D1) − 20 log(D2) − 6

Run the classic version of this with an outdoor lecture rig: a speaker's mouth sits 1 ft from an omni mic (Ds), that mic sits 20 ft from an omni loudspeaker (D0), the loudspeaker is 10 ft from the back row (D1), and the straight-line distance from the lecturer to that same back-row listener is 18 ft (D2). Work through the equation — 20·log(20) − 20·log(1) + 20·log(10) − 20·log(18) − 6 — and you land around 26 − 0 + 20 − 25 − 6 ≈ 15 dB. That's roughly how much gain that particular rig can add, using nothing but omnidirectional gear, before it starts to sing.

The source's actual level cancels out of the equation entirely — a loud voice and a quiet one hit the same ceiling. What's left is two levers you can actually pull: shrink Ds (get the mic closer to the source) and/or grow D0 (get more separation between mic and loudspeaker). Everything else in feedback control is really just different ways of exploiting those two facts.

Directional Mics and Speakers Buy You More Headroom

Swap the omnidirectional loudspeaker for a directional one and aim it so the mic sits off its main lobe — out on roughly the −6 dB angle of its polar response — and the sound arriving back at the mic drops by about 6 dB. Do the same trick with the mic: swap in a cardioid and orient it so the loudspeaker sits on the capsule's own −6 dB angle, and you pick up a similar advantage there too. On paper, stacking both gets you +12 dB of extra gain before feedback. ▣ Diagram

In practice it rarely works out that cleanly. Full-range loudspeaker boxes tend to go omnidirectional at low frequency no matter how tight their pattern is up top, and a cardioid mic's rejection isn't flat across the spectrum either — a cheap capsule with a lumpy polar response might not actually beat a smooth-sounding omni in the real world. A useful rule of thumb: expect directional gear to realistically buy you about 6 dB combined, not the theoretical 12 dB, and confirm it by ear — walk the mic in front of the speaker and it'll typically feed back at a higher frequency; walk it behind the box and the ring drops to a lower frequency.

The Three-Point Technique

Strip all of the above down to the field version and it's three things, in order of how much control you actually have over them on a given stage:

• Use directional mics and loudspeakers — and actually aim them. A cardioid pointed the wrong way, or a box splayed so the mic sits right in its main lobe, buys you nothing.
• Keep the loudspeaker as far from the mic as the room and rig allow. It's a big part of why PA gets flown high above the stage instead of sitting on the deck next to the vocal mic.
• Keep the mic close to the source. Tight to the mouth or the instrument — it's why performers often look like they're eating the capsule, and it's the cheapest gain-before-feedback you'll ever get.

Source: Davis, Gary D. & Jones, Ralph. The Sound Reinforcement Handbook, 2nd ed. (Hal Leonard/Yamaha). Section 5.3, pp.47-52. Rewritten in Ryan's own words from the source material.