P.A. 101

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Illustration: Phillip Brooker

Sound reinforcement may not be the most glamorous area of the music industry, but it's certainly an important one. If you want your performance to reach your audience whether you're playing in a church or a coliseum you depend on the P.A. system to get it there. Having a good understanding of sound-reinforcement concepts will not only assist you in dealing more effectively with your own system, it will also help you make informed gear purchases and better communicate your sound needs to other musicians and engineers at your gigs.

In this article, we'll cover some basic ground about the most important sound-reinforcement components and key concepts. So whether you're new to gigging or are a longtime musician, we'll help you raise your P.A. IQ.

First, let's review the obvious stuff. Every sound-reinforcement system consists of three main elements: mixer, amplifier, and speakers. These elements can be used to create a wide variety of systems, from the all-in-one units designed for solo performers to the full-blown, multikilowatt road rigs that touring companies carry. In all cases, the basic mission remains the same: to blend and process signals so they're loud enough to hear, clear enough to understand, and pleasing enough to keep the audience interested.

The kind of system you need depends on the makeup of your band and the size of the venues you're playing. To a lesser degree, the type of music you perform and the audience's composition are also factors. As you evaluate your choices, you should ask yourself the following questions:

How many inputs do I need? Remember to count each vocal microphone, as well as all instrument mics and line-level signals that will go through the sound system.

How loud do I need the P.A. to be? Are you hammering out rock 'n' roll in a noisy, crowded bar? Will the singer be competing against a wall of Marshall amps? Or are you just adding some depth to an acoustic instrument so the people in the back of the room can hear it?

I know what I want the audience to hear-how can I control what the band hears? Onstage monitoring is almost as important as projecting the sound to the audience. Before buying a system, figure out how many separate monitor mixes you'll want and how many monitor speakers you'll need based on the physical dimensions of your stage setup. For example, a four-piece band playing small clubs usually needs at least two monitor cabinets-one for the front line and one for the drummer. Adding a second front-line monitor would be a big improvement.

What else will I be doing? If you plan to take breaks, you'll probably need a way to pump prerecorded music into the house. You may also want to record your performances, in which case you might want a mixer flexible enough to route different mixes to the house and to your recorder. (For more on what you need for live recording, see "Caught in the Act" in the May 2000 issue of Electronic Musician.)

Once you've answered these questions, draw a chart that maps all the inputs you'll need. Be realistic. If your band specializes in small clubs, you probably won't need to reinforce the guitar and bass amps with the P.A. If you'll be playing larger stages (such as outdoor venues), you'll probably need to pump those instruments through the system, and the band members will most likely require more monitoring than in a small club because they're going to be spread farther apart.

If you're a gigging musician looking for a system, you have a choice of three main types of rig.

All-in-one systems. These units combine a small mixer (sometimes as few as three channels), a power amp, a speaker system, and often some effects in one easy-to-carry package. Some keyboard amps and acoustic guitar amps qualify because they can handle mic and line inputs, and they offer a wide enough frequency response to reproduce a variety of instruments. Solo performers will find these units useful because they're easy to transport, can be set up quickly, and are simple to operate. Generally, these types of systems have only a few inputs: a microphone jack, an instrument jack, and an auxiliary input for a CD or cassette deck. Many of the newer models also provide onboard effects. In large venues or in band situations, you can employ an all-in-one unit as a personal self-powered monitor.

Powered mixers. Offering a nice balance of integration (mixer and power amp in one unit) and flexibility (expandability options and the ability to choose your own speakers), powered mixers are the choice of many club-level acts. There are two common types: heads that look like large power amps with integrated mixing controls, and consoles with built-in power sections. Both versions generally offer a full array of line and mic inputs, multiband EQ, aux sends and returns, fold-back inputs (for the CD player), and a master-section graphic EQ. Many newer models have stereo power amps, built-in digital effects, and recording outputs.

Mixing consoles with separate power amps. The bottom line is that most powered mixers are designed for small acts with relatively simple needs. Unpowered mixers, on the other hand, come in all shapes and sizes-including huge behemoths-and offer a wider variety of outputs than you get with most powered mixers. Therefore, using an unpowered mixer and separate power amps is by far the most flexible way to go; you can mix, match, and upgrade the individual parts of the system as necessary. On the downside, you need to do more wiring with discrete components, and larger consoles often are complicated to use, hefty, and a pain to haul around.

Both types of mixers offer main, monitor, aux, and effects buses. In addition, many unpowered mixing consoles offer direct-channel outputs (useful for multitrack recording), multiple aux sends on each channel, semiparametric or fully parametric EQ on each channel, individual channel inserts (useful for plugging in outboard gear such as compressors and gates), and submix buses that can route an alternate mix to a monitoring system or 2-track recorder (see the sidebar "A Typical Mixer Channel").

Digital mixers offer many features that are beneficial for live performance. Configurations vary, of course, but you often get flexible EQ, onboard dynamics processing, and snapshot automation, which allows you to set up and store a mix for each song. Some digital mixers offer individual channel delay, which is useful for correcting phasing problems between speakers that are installed far apart on the stage. As with analog consoles, you can rack-mount some models, such as the Yamaha 01V.

Before choosing a digital mixer, however, make sure it has enough analog inputs to meet your needs. The typical low-cost digital unit offers a mix of analog and digital I/O. The 01V, for example, is a 24-channel board, but only 16 of those channels have analog inputs.

Feel the Power

If you use an unpowered mixer, it's important to mate it with a power amp that has enough juice to process your music cleanly. A powered mixer or all-in-one system makes these decisions for you, of course, but some of them let you bypass the internal power amp and use an external power amp instead.

Ideally, you should shop for your power amps and your speakers at the same time. Make sure the amp and speakers match in impedance (see the sidebar "Impedance and Speaker Load") and power rating. Matching the power rating is very important: if you overpower your speakers, the result can be thermal or mechanical failure. But if you underpower your speakers, distortion-and ultimately, speaker damage-may result. When the signal clips (distorts), the amp could be called on to suddenly deliver double the usual amount of power, which can be bad news. We'll return to this point in a moment.

Sound-reinforcement speaker systems usually have three power-handling specifications: continuous power, program power, and peak power. Loosely defined, continuous power is the average long-term level of power that the speaker can handle. However, it is usually measured using a sine wave, which does not reflect the demands a music signal will place on the system. Program power is the maximum average level of power, measured over the medium term, that the speaker can handle-but it is measured using a test signal that approximates an actual music signal. Peak power tells you how much power the speaker can handle for an instant, which is less than a second.

For a professional P.A. system, which usually has to handle large amounts of power over several hours, you want a power amp that can deliver approximately the program power rating of the speaker system but-and this is important-does not exceed half of the peak power. The reason: if clipping causes the system to demand twice the normal power from the amp, you need to make sure that doesn't exceed the speaker's peak power rating, even for an instant. If your speaker has only continuous and peak ratings, you'll have to use some common sense in approximating the probable program power, remembering to keep the power at no more than half of the peak power.

Keep in mind that the considerations here are different than with a home stereo system, where sound-pressure levels are lower and power demands are much less.

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Figure 2: If you have access to more than one power amp, you can use one to power the mains and two sides of the second amp to feed two separate monitor mixes.

Are Two Heads Better?

In live situations, you can use a typical 2-channel power amp in a number of ways. Note that the house mix and the monitor mix may call for different approaches.

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Figure 3: Running a stereo power amp in bridged mode turns it into a more powerful mono amp.

For example, you could run a stereo house mix, which allows you to create a more realistic soundstage and utilize stereo effects. However, operating a stereo sound system can add considerably to the challenge of mixing-among other things, it invites complex phase problems resulting from sound reflecting off of walls and other surfaces-and it can create a lot more problems than it solves. Running a stereo monitor mix can really open up a can of worms, and most club bands probably shouldn't do it.

In many club situations, therefore, you probably will run the house and monitor systems in mono. One way to do this is to run in dual mono, feeding the same mono mix to both sides of a 2-channel power amp, so that each side of the house and each side of the stage has its own power amp channel (see Fig. 2). That setup gives you the ability to adjust the sound-pressure level on each side of the house or the stage without affecting the mix. If you don't need that sort of flexibility, however, you could use one amp channel to drive the house mix and the other to drive a monitor mix.

However, if your gig requires only a mono stage mix, running your power amp in bridged mode may be the most efficient method (see Fig. 3). In bridged mode, the two sides of the amp operate in tandem to form a single, monaural power amp. One channel's hot output remains positive, while the other channel's positive output actually becomes negative, so you connect the positive output of each channel of the power amp to the speaker. Because the two sides are combined, the amp delivers significantly more power when bridged to mono. Although logic would indicate that the power should double when the left and right channels are bridged (assuming the same output impedance), the exact amount of power you actually get in bridged mode depends on the amplifier's design.

You could use a bridged power amp for the house mix, too, but since you probably are driving two speaker stacks that require significant juice, you probably are best off either running a powerful amp in dual mono or using two or more amps for the mains. If you have more than one power amp, naturally, you get more flexibility.

Divide and Conquer

In many club P.A. systems, each speaker cabinet includes both a low-frequency driver (the woofer) and a mid/high-frequency driver (a horn or tweeter), and you simply connect the output from your power amp to one jack on the speaker cabinet. Inside the speaker cabinet is a circuit called a crossover, which uses filters to divide the signal according to frequency, sending the portion of the signal that is above the split point (called the crossover point) to the high-frequency driver and routing the portion below the crossover point to the low-frequency driver. In most cases, the crossover is a passive circuit, and the crossover point is preset at the factory to match the speakers and the cabinet's acoustics. Such a system is easy to use, but it does not offer much flexibility, and it usually is not intended for use in larger, more sophisticated sound systems.

If you want to be able to adjust the crossover to suit your tastes-tweak the crossover point or slope, for instance-and especially if you want to use separate bass and high-frequency cabinets, you need an external crossover. In many cases, these crossovers are active (powered) units, and their sound quality is generally superior to that of most passive crossovers. If you go this route, you need to separately power the low- and high-frequency drivers, which is called biamping.

With biamping, you use an outboard crossover to split the signal before it reaches the power amp, and you feed the high- and low-frequency information to separate channels or amplifiers. If you are using separate bass and mid/high cabinets, you have to biamp, but biamping also is a way to get more efficiency from two-way speaker cabinets that allow you to power their bass and high-frequency drivers separately, bypassing the internal crossover.

If you want the ultimate in sound-system efficiency and accuracy-and are willing to haul a lot more gear-you can use a triamped system. With triamping, you assemble a three-way system comprising (for each side) a bass bin, midrange cabinet, high-frequency cabinet, and three-way external crossover. The principle is the same as with biamping: each cabinet is driven by a separate power amp channel. There are a number of ways to amplify a triamped system; for instance, you could run three stereo power amps in dual mono-one each for the left/right bass bins, midrange cabinets, and high-frequency cabinets. Alternatively, you could dedicate a power amp to each bass bin, running in bridged mode, which is a more efficient way to power those big cabinets but requires a fourth power amp. You could even dedicate an amp to each of the six cabinets (the left and right lows, mids, and highs) if necessary.

Speak to Me

Speakers deliver the sound to your audience, so they're among the most vital components in your system. In the bad old days, speaker horns were big, and bass cabinets were bulky and weighed a ton. Can anyone say hernia? Fortunately, speaker design has come a long way, and today's cabinets are lighter, easier to position, and have wider frequency responses than ever before.

Typical stage speakers are two-way enclosures, with separate low- and high-frequency drivers (in contrast to the typical guitar speaker, which has a single full-range driver with limited frequency response). A speaker enclosure is like a self-contained universe: the size and type of the drivers influence its sound, but so do environmental factors such as the size and makeup of the cabinet. As noted in the discussion of biamping, you could use separate low- and high-frequency cabinets, but this would mean more hauling and wiring, and it is not as popular an approach for club sound as it once was.

When choosing speakers for your amps, remember to factor in power handling, as discussed earlier. It is also important to make sure the impedance of the speaker matches the output impedance of the amplifier. If you're planning to run more than one speaker on each amplifier channel, make sure the total impedance of all the speakers matches the amp's impedance. Otherwise, you're asking for trouble in the form of distorted sound and/or damage to the amp and speakers.

Thanks to the miracle of modern design, loudspeakers have become much easier to position on stage. You can mount most small to midsize enclosures on a stand, which allows you to raise them above the stage, giving the sound waves a clearer path to the back of the room. Although speaker stands aren't absolutely necessary, they're a great investment. Conventional wisdom says to position the house speakers on either side of the stage, slightly in front of the performers and their microphones. If you position your speaker behind a microphone, you'll be in for a long night of feedback.

With the speakers positioned in front of the musicians, though, how can the members of the band hear themselves and each other? Stage monitors-also known as wedges-are designed to project sound back to the performers without interfering with the mix heard in the house. (Be forewarned that if you turn the monitors up too loud in a small venue, they will interfere with the sound out front.) The typical stage monitor sits on the floor and points up at the performer. Other monitoring options, such as in-ear wireless monitors, are becoming more affordable for working musicians. (For a review of in-ear monitors, see "Stick It in Your Ear" in the April 2000 issue of Onstage.)

In most cases, you'll want to feed the stage monitors a different mix than the one heard in the house. The number of separate monitor mixes you can create depends on two factors: the number of sends in your board (each send can create a separate mix), and the number of available channels of power-you'll need a separate power source to deliver each mix to its respective monitor speakers.

No matter what kind of speakers you use, connect them to your power amps with the best speaker cable you can afford, and never use instrument cables. Good cables make an audible difference in the sound and can also save headaches at the gig; there's nothing more frustrating than being sunk by a bad cable. Cable that's too light a gauge for the task at hand restricts the signal flow, causing significant power loss and potentially damaging your system. The longer the cable run, the more power you lose, so in choosing the right cable, you have to consider the amount of power being handled, the impedance of the load (that is, the speakers), and the length of the cable run.

In general, you should use at least 16 AWG (American wire gauge) speaker cable, but that is pretty light. In most cases, 14 AWG cable is a good choice for carrying moderate power levels over relatively short cable runs (say, 25 feet or so). But you will see a significant performance increase if you go to 12 gauge cable or heavier, especially if you have 100-foot runs or need to push a couple of hundred watts down the line. Large, high-power rigs often use 10 gauge or even heavier cable, and if you want to go that way, fine, but you probably won't need that for the average club P.A. In contrast, instrument cables are usually between 26 and 22 gauge, which is clearly inadequate for handling speaker-level signals. Unlike instrument cables, speaker cables do not need to be shielded.

Powered speakers are another option. Although generally used as monitors, they sometimes-especially in very small systems-can be used as mains.

All Aboard for Outboard

In the recording studio, you use outboard gear such as compressors, gates, effects, and other signal processors to put the finishing touches on mixes. In sound-reinforcement situations, the primary purpose of outboard signal processors is to maintain sound quality in a transparent fashion rather than to add sonic interest. (Of course, a sound engineer who knows the band's material well can still put creative effects to good use.)

Compression. A compressor is often essential for controlling the dynamic range of individual voices and instruments. Use it carefully, however, because it can increase the risk of feedback on some acoustic instruments and can significantly affect the sound's timbre.

Limiting. For practical purposes, a limiter is a compressor with a compression ratio that is high enough to prevent a signal from getting noticeably hotter. A limiter with a very high compression ratio is referred to as a brickwall limiter because it stops the signal's level from increasing as surely as if the signal had hit a brick wall. Most live engineers strap a limiter across the main mix outputs as a means of protecting the speakers (and the audience) from sudden unexpected peaks. Again, you have to be extremely careful about how you set the limiter, because if you limit the signal too severely, your system will be working hard, yet not generating enough power. The result will be inadequate signal coming from the speakers and an increased potential for feedback.

Gating. Noise gates are useful tools for sound reinforcement; when a signal level drops below the user-selected threshold, the gate closes, silencing the channel. Applying a gate to a vocal mic effectively mutes the mic when no one is singing into it, which can reduce the amount of unwanted bleed into the mic from other stage sources (such as guitar amps and drums), as well as reduce the chance of feedback.

Equalization and feedback control. Used properly, an equalizer can shape your sound to near perfection. It can also solve some thorny sonic problems. But overuse of EQ can do more to undermine your mix than that screaming drunk in the first row. There are two main uses for EQ on stage: tone control and feedback control.

To a degree, tone shaping is a matter of personal taste. But if you're a performer doing double-duty as a sound engineer, maintain some perspective on the sound. Have a friend sit in the audience and listen to the clarity of the mix. Many inexperienced sound engineers tend to overboost high- and low-midrange frequencies to get more boom and sizzle in the mix. This can lead to muddiness, distortion, ear fatigue, and an annoyed audience.

EQ can also be extremely useful for clarifying a monitor mix, allowing the musicians to hear the monitors better without the engineer having to jack up the power. That helps keep down the sound-pressure level on stage, which is a key element in obtaining a good mix.

Feedback control is one of the essentials of live sound. Whenever you set up your P.A., you'll need to "ring out" the system. Now, what I am about to say is oversimplified, because you would need another article to properly discuss ringing out a sound system. In general, you need to set up your microphones and then use a signal generator or test-tone CD and CD player to inject a pink-noise signal through the system. Boost specific frequencies with an equalizer (usually a graphic EQ) to see which ones induce feedback. The ones that ring are the ones you'll need to attenuate. Use the narrowest bandwidth possible to do this; the ideal type of EQ configuration has a notch filter, which focuses on very specific frequencies. The narrower the frequency, the less the cuts will affect the overall tonal balance of the mix.

While many live engineers still use the manual method, automatic feedback eliminators can ring out the system for you. They work by sensing which frequencies are feeding back and then quickly applying a very narrow, precise notch filter to attenuate those frequencies. The advantage of an automatic system is that it can detect problems continuously as the performance evolves-and that can save the day if a new feedback source crops up.

Note that mic feedback (ringing) is only one kind of feedback you may encounter on stage. (No, I am not referring to remarks from the audience.) Acoustic instruments also generate resonant feedback, which is best tackled at the source (the instrument itself) rather than at the mixing board. Resonant feedback happens when a certain frequency causes the body of an acoustic instrument to vibrate on its own. Flat-top acoustic guitars are particularly prone to this problem, especially if they're sitting on stage in the path of a speaker. Grand pianos are vulnerable, too.

Ambient effects. Delay and reverb are important tools in sound reinforcement. Use caution: a venue has its own natural ambience, and too much reverb coming from the stage muddies things up considerably. If your singers insist on a wash of reverb, feed more into their monitor mix than you feed into the house. This will keep the singers comfortable without bathing the house mix in mud.

Hit the Road, Jack

If you're serious about your sound, invest in a complete and integrated sound-reinforcement system that can deliver your music with no excuses. Even if most of your venues provide a house system, the more you know about how that system works, the better you can work with the sound engineer to get your music across.

A Typical Mixer Channel

Before choosing a mixer, take a look at this breakdown of a typical mixer channel. Not all mixers offer every feature listed here, but you might not need all of these features.

Direct output. A direct feed from the channel, these outputs are commonly used to feed a recording mixer.Insert point. Inserts are send-and-return jacks used to feed outboard effects such as compressors, gates, and EQs. Some mixers use separate 11/44-inch jacks for the send and the return. Other boards employ one 11/44-inch TRS (tip-ring-sleeve) jack for both send and return circuits.

Line input. Balanced or unbalanced 11/44-inch line inputs are commonly used for line-level gear such as keyboards, preamps, effects, and some outboard submixers.

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Mic input. Typically, you use an XLR input for connecting microphones and balanced signals from a direct box. (A direct-injection box, or DI, is useful for plugging in instrument-level signals such as those from guitar and bass.) However, some low-end mixers may offer 11/44-inch TRS mic jacks for use with high-impedance dynamic mics.

Gain (or trim) pot. This potentiometer (basically a variable resistor) attenuates the input level. For the best sound, you usually should set the gain to the highest setting that doesn't produce distortion. Adjusting the gain pot is a part of setting all of the signal levels throughout the system, so that the system as a whole delivers the maximum amount of undistorted sound while allowing headroom for the engineer to make adjustments during the show. Creating this balance is called gain structuring.

Line/mic switch. This useful feature allows you to match the operating level of your input to the output of your gear. In some mixers, the switch routes the input signal to the channel mic preamp for use with mic-level signals or circumvents the mic preamp for use with line-level signals.

Equalizer. The typical 3-band EQ offers high and low shelving bands (each with fixed cutoff frequencies). The midrange band usually is semiparametric, which means it lets you set the level and "sweep" the center frequency, altering which frequencies are affected. Some boards offer fully parametric EQ, which also offers control of the bandwidth or Q. However, some mixers have more elaborate channel EQ. The most common variety is a 4-band EQ that has high and low shelving bands and two semiparametric or parametric midrange bands.

Low-cut switch. This low-frequency rolloff is especially useful for eliminating the stage rumble that transmits up a mic stand and through the system.

Auxiliary sends/monitor sends. Aux sends typically feed effects processors, whereas monitor sends, as you would guess, carry monitor mixes.

Many consoles allow you to set the sends as either prefader or postfader, using a front-panel switch or an internal jumper. Typically, an effects processor should be connected to a postfader send so that the position of the channel fader affects the send. (As the name implies, a postfader send splits off of the signal path after the channel fader.) This send can be used to add reverb, delay, and other sweetening to the mix. Some boards have buses labeled "effects send"; in most cases, these are simply postfader aux sends, but with mixers that have built-in effects, the effects send is usually hardwired to the internal effects processor.

Since a prefader send splits off before the channel fader, its level is not affected by the fader. That is desirable for monitors because the engineer can adjust the house mix during the show without changing the monitor mix.

Bus assign. If your mixer offers submix buses (often called subgroups), you use the bus assign buttons to route channels to subgroups. You can use the submix bus to group multiple channels (such as a drum, background vocal, or keyboard mix) so that the entire submix can be controlled with a single fader. Subgroups also are handy for creating a separate mix that feeds a 2-track recorder.

Pan. As with home stereo gear, the pan pot sets the stereo position of the channel. Some mixers offer stereo pairs of channels (for example, channels 17/18) with line inputs; in this case, the pan control sets the balance between the odd- and even-numbered channels.

Fader. This sets the output level feeding the master and submix buses.

Impedance and Speaker Load

Impedance-the total opposition by an electrical circuit to the flow of a signal or current at a given frequency-is one of the most important specs you need to know when matching a speaker or a group of speakers to a power amp. Why should you care? Because impedance-expressed in ohms, the symbol for which is the Greek letter omega (z)-determines the amount of load placed on your system. In audio terms, mismatched impedance wastes power and can result in poor sound or, worse, damaged gear. The impedance of the speaker system should exactly match the output impedance of the amplifier.

The number of watts (W) an amp puts out depends in part on the amp's output impedance. Change the impedance, and the power rating changes, too. As a rule, the amount of power is inversely proportional to the impedance, so if you halve the impedance, the power rating will double. For instance, a 200W output at 8z would become 400W at 4z. When evaluating an amp's power rating, it's important to know the impedance of the circuit used to measure that power. An amp that puts out 400W at 8z is twice as powerful as an amp that puts out 400W at 4z.

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Figure A: Of the three ways to wire speakers (series, parallel, and series/parallel), parallel connections are the most common in sound reinforcement applications.

The speaker connection also impacts the load (see Fig. A). Speakers are part of an electrical circuit, and the laws of physics govern that circuit. Let's say a power amp delivers 100W into an 8z load. If you connect one 8z loudspeaker, you'll be averaging 100W through that circuit. (This isn't literally true, because other factors come into play, but it's close enough for our purposes.) But what if you want to connect a second 8z speaker? There are three ways to connect multiple speakers to an amplifier: series, parallel, and series/parallel. The impedance-and consequently the power output-changes depending on which wiring scheme you use.

Wiring in series. In a series connection, the speakers connect in a linear fashion, from one to the next. The total impedance (Z) is the sum of the impedance of each speaker in the circuit-that is:

So if you have two 8z speakers wired in series, your total impedance will be 16z; two 4z speakers would give you a total impedance of 8z; and so on. One note about series connections: if one speaker fails, the whole circuit stops working.

Wiring in parallel. Parallel connections are much more common in sound reinforcement. In this method, the positive terminals of each speaker connect to each other (from the positive terminal on the power amp) and the negative terminals connect to each other (from the negative terminal on the power amp). Wiring in parallel reduces the impedance, allowing the amp to put out more power. How do you figure out the change in impedance that results from parallel wiring? One way is to use the following formula:

Z1, Z2, and Z3 represent the impedance of each speaker in the circuit. Fortunately, the equation is a lot easier to grasp when you're only dealing with a pair of matching speaker cabinets. In that instance, you can simply divide the nominal impedance by 2. So if you have two 8z cabinets, you divide the rated impedance (8z) by the number of cabinets (2) to get 4z.

Wiring in series/parallel. The third wiring option is series/parallel. Commonly used in multispeaker guitar cabinets, this scheme turns up less often in sound-reinforcement installations. However, it works well as a method to maintain a specific impedance load while adding additional speakers to a system.

The math needed here is a bit more involved. First, you calculate the impedance of each serial circuit. We'll use lowercase letters (a, b, c, and so on) to indicate the individual drivers that are wired in each serial circuit.

Then you divide those totals as you would in a standard parallel connection:

Let's say you have four 8z speakers wired in series/parallel. Each series would offer an impedance of 16z:

We have two 16z loads wired in parallel. The equation is:

With two circuits wired in parallel, we could simply divide 16 by 2 and get with a net impedance of 8z.

Emile Menasche is a guitaris, writer, and songwriter in New York City.