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Catching ZZZs - Part 2
A series on understanding impedance...
By Mike Rivers

Last month we laid the groundwork for your understanding of impedance. This month we’ll address impedance matching of amplifiers and speakers, headphones, microphones, and pickups

How not to destroy your amplifier

One instance where it’s traditionally been important to match source and load impedances is the connecting of loudspeakers to power amplifiers. Since pushing air molecules around is hard work, we need significant power for the speaker to do its job of converting electrical to mechanical energy.

Remember that power is defined as voltage multiplied by current. A power amplifier, like any other electrical device, has limits for both the current and voltage it can produce, but those limits are much higher than our preamp output. Those ratings, as well as the amplifier’s impedance rating, are important.

A speaker with a lower impedance than the rated output impedance of the amplifier will tend to draw excessive current, possibly damaging the amplifier. Connecting one that’s higher than the rated output impedance won’t draw all the current the amplifier can produce when putting out its maximum voltage, so all the power you paid for won’t get to the speaker.

Back when all power amplifiers had vacuum tubes, the tube’s fairly high output impedance was converted to a more practical value with the use of a transformer (called, not surprisingly, the output transformer). Often a power amplifier’s output transformer will have multiple taps on the secondary with impedances of 4, 8, or 16 ohms, though a single output impedance (usually 8 ohms) was also common.

Connecting an 8-ohm speaker to the 8-ohm transformer output assures that maximum power is transferred from the amplifier to the speaker. Here’s why.

Let’s say the amplifier’s maximum output voltage is 40 volts when loaded with its rated impedance. If the amplifier has an 8 ohm output impedance and you connect an 8 ohm speaker, you’ll have 40 volts going into the series combination of the two impedances, 16 ohms. This gives a current of 2.5 amps. (Remember Ohm’s Law? I = V/R = 40/16 = 2.5.)

Since the two sections of the voltage divider (the output transformer and the speaker) are equal, the amplifier’s output voltage divides equally between the output transformer and the speaker. 20 volts times 2.5 amps is 50 watts delivered to the speaker.

Suppose we replace the speaker with a 16 ohm one. Crank up your abacus and you’ll find that at 40 volts, the current is now 1.6 amps. That gives you only 44.4 watts into the speaker. If you use a 4 ohm speaker, you’ll have a current of 3.33 amps (assuming the amplifier won’t poop out trying to deliver greater than its rated current, a real possibility)—yet when you do the math, that also yields 44.4 watts! The power drops off as you mismatch impedances in either direction.

Today’s solid state power amplifiers have source impedances of just a few tenths of an ohm, so they interface much in the same manner as line level equipment. However, there’s a caution: they can’t continue to provide more and more current as you lower the load impedance. You’ll typically find power ratings stated something like “100 Watts at 8 ohms, 150 Watts at 4 ohms,” which indicates that it’ll stay within its safe operating limits down to 4 ohms, but you won’t quite get twice the power with a 4 ohm load as you will with an 8 ohm load. This is because a well-designed amplifier limits the output current to a safe value so as not to exceed the power supply’s rating.

Is it loud enough in the phones?

Then there’s the headphone issue. Headphones used to be designed (and some very good ones are still made) with a fairly high impedance, 600 to 2000 ohms, making it possible to connect them directly across an amplifier’s loudspeaker output without affecting the amplifier load when a speaker was also connected.

Along came the portable cassette player, and with it the need to get fairly loud headphone volume out of an amplifier powered by 3 volts’ worth of batteries. Low-impedance (100 ohms or less) headphones became the norm since they can draw more current at a lower voltage, hence receive more power than high-impedance phones.

If you have several sets of new and older headphones in your studio, you’ve probably discovered that the older high-impedance ones aren’t as loud as the newer low-impedance ones. Of course there’s the matter of differences in efficiency, but the important fact is that a high-impedance headphone will draw less current from the amplifier than a low-impedance headphone.

Since a power amplifier (even a specially designed headphone amplifier) has a much lower output impedance than any headphone, any headphone connected to that amplifier, regardless of its impedance, will see essentially the same voltage. With 2 volts coming out of the amplifier, Ohm’s Law tells us that a 600 ohm headphone will receive a power of 6.67 milliwatts, while a 40 ohm headphone will receive 100 milliwatts. That’s quite a difference!

There’s another impedance associated with power amplifiers that’s generally not a matter of concern with line-level or non-mechanical loads. This is the impedance that a speaker sees when looking back into the amplifier’s output (it’s actually a load impedance for the speaker!). In a modern solid-state amplifier, it’s extremely low, generally on the order of a few tenths of an ohm. Why does this matter? Because of momentum and mechanical resonance—once a loudspeaker is set into motion, it tends to remain in motion, and it will generate some voltage on its own, just like a microphone.

If this seems strange, remember that mics and speakers are both transducers—one turns moving air into voltage, the other turns voltage into moving air. But a speaker can work in reverse, sending voltage down its audio connections if made to vibrate. (In fact, Scott Dorsey designed a very effective DIY kick drum mic using a speaker; we featured the project in our July 2000 issue.)

By applying that voltage to essentially a short circuit, the extraneous motion (that is, motion not caused by the amplifier’s output) can be quickly damped out. This “backwards” impedance is often called the amplifier’s damping factor, and in general, the lower it is, the more accurately the motion of the speaker cone will represent the signal that’s going into the amplifier, with minimum ringing and overshoot. In plain language, that translates to “tighter bass.”

Microphones

Virtually all dynamic mics and some condenser mics have a transformer inside the case. The transformer changes the output voltage of the mic, and in the process also changes the source impedance of the microphone. (A dynamic mic’s output is always boosted by the transformer, but with condenser mics, sometimes the transformer actually reduces the output level.)

The voltage ratio or turns ratio of a transformer is equal to the ratio of the number of turns of wire on the input (primary) side to the output (secondary) side. The impedance ratio is equal to the square of the turns ratio. If a transformer increases the output voltage of the microphone element by 10 times, it will increase the source impedance by 100 times (10 squared). So if the basic element has an impedance of 1.5 ohms, our transformer would step it up to 150 ohms, typical of most modern Low-Z dynamic mics.

The rise of home recording in the 1940s (going back to wire and disc recorders—yes, Virginia, there was home recording before hard drives) and the associated demand for low-cost microphones brought us the first common truly high-impedance mics. Piezoelectric crystal and (later) ceramic microphone elements are built from materials which generate electricity directly from mechanical stress, but which are very poor electrical conductors. Hence they have an extremely high source impedance.

On the other hand, they have fairly high output level for a given sound pressure. Electronics manufacturers liked this design because their amplifiers didn’t require input transformers which were otherwise necessary to match the low impedance of a dynamic mic to the high input impedance of a tube amplifier. They could also usually save a tube in the process since, with a higher voltage out of the microphone, less amplification was required.

The fidelity of these piezo mics was pretty poor, but good enough for the times. Today about their only applications are for speech (paging and communications) and for amplifying blues harmonica—typically by plugging the piezo mic directly into a guitar amplifier, which makes for a good voltage and impedance match.

Demand for higher-quality microphones in the home brought us the high-impedance dynamic mic. Instead of employing a transformer in the microphone with a 1:10 turns ratio, simply changing the ratio to around 1:300 brought the output level and impedance up to about that of a piezo mic while retaining most of the quality of the dynamic element.

Something happened in the ’70s that changed the way we build microphones and microphone input circuits. We discovered that most low-impedance microphones sound better when working into a load impedance of about 1200 ohms than they do when working into a matched load of the 150 ohms typical of professional mic preamps of the day.

Today, the input impedance of nearly all console and outboard mic preamps is in the range of 1,000 to 2,500 ohms, sort of halfway toward being a “voltage transfer” interface. Microphones, especially dynamics, tend to be somewhat load-sensitive, and the lack of a “standard” microphone input impedance leads to contradicting opinions of the sound of a particular mic or preamp. This was discussed extensively in the December 2002 through February 2003 issues of this magazine, so I won’t dwell on those impedance matching issues further, other than to note that if you have a preamp with an impedance switch, it’s worth experimenting to see how it affects your mics’ tone.

Pickups—another special case

Instrument amplifiers are one of the places where tubes are still king, and for good reason. In addition to the “tube sound” of compression and distortion, a vacuum tube circuit, by nature, has an extremely high input impedance, typically 1 to 10 megohms (MΩ). That’s because the electrons are hitting a vacuum rather than a chunk of silicon when they reach the input circuit.

A magnetic instrument pickup comprises a large coil of very fine wire wound around a magnetic core. Along with a vibrating string, it acts as a generator, producing a reasonable amount of voltage (as much as a volt or two when you’re really whammin’), but due to the large amount of wire in the coil, its source impedance is quite high. This sort of pickup gets unhappy when looking into a load impedance lower than about 50 kΩ. Connecting a pickup to a low-impedance input (for example, a microphone preamp) causes most of its signal to be dropped across its own high internal impedance (recall our example with the headphones connected to a line-level output). This will reduce the signal level available at the plug and cause the pickup to sound dull.

The common studio tool used to record the pure pickup sound is a direct box. This is nothing more than an impedance converter. A passive direct box consists of a transformer, occasionally with a few components added to control ringing or shape the frequency response to emulate a speaker cabinet. A transformer direct box typically has an input impedance between 50 kΩ and 100 kΩ, and an output impedance and voltage to match a low-impedance, high-gain microphone input. Active direct boxes have a solid-state or tube input stage typically providing an input impedance well above 1 MΩ for truly minimal loading of the pickup.

There’s no reason why guitar pickups have to be high-impedance, it’s just that they’ve always been designed that way. (Well, OK, it takes fewer components to build a guitar amplifier with a high-impedance, low-gain input than with a low-impedance, higher-gain input. The concept of building equipment to meet a low price point is hardly new.) The electric-guitar industry is much larger than the recording industry, so they call the shots.

Always technically hip, Chet Atkins wound his own low-impedance pickups for direct recording back in the ‘50s, and there was a Les Paul Professional Recording model guitar which had low-impedance pickups and was equipped with an XLR connector (along with a companion model amplifier). It wasn’t well accepted, however, because you couldn’t plug it into just any amp, and it wasn’t compatible with common stomp boxes.

Next time, in our third and last installment of this treatise on impedance, we’ll get to the juicy parts. Promise.

Mike Rivers (talkback@recordingmag.com) meets with resistance when he talks about this stuff, but rarely lets it impede him too much.

 




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