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Catching ZZZs - Part 1
A series on understanding impedance...
By Mike Rivers

Nearly everyone in this business has heard the term “impedance” at one time or another, but the concepts of source and load impedances and how they relate are often misunderstood. We speak of low-impedance (“Lo-Z”) microphones and high-impedance (“Hi-Z”) direct instrument inputs, loudspeaker impedance, and 75 ohm coaxial cable for digital and video signals...but what are we really saying

In this session, the first of three, we’ll take a first look at what impedance means, primarily in terms of connecting various gozoutas and gozintas—when it’s important to match input and output impedances, when it’s important not to, when you need to be concerned about it, and when you don’t.

It’s difficult to discuss impedance without giving some examples, so in Parts 2 and 3 we’ll be looking at microphones, speakers, and power amps, as well as pickups and digital devices. We’ll also have to revisit some mathematical formulas that might take you back to your high school days, but that’ll be in Part 3 and we’ll try to keep it painless. That’s also where we’ll explain why electrical engineers use the letter Z to represent impedance.

Parts 1 and 2 will be very basic and will give you most of the practical results you’ll need, but I would strongly advise that you first read my article ‘The Nuts And Bolts Of Amps And Volts’, which will give you the groundwork you’ll need for this article series to make sense.

Sources and loads

Ever notice how the lights in the house dim briefly when the refrigerator or air conditioner switches on? If the wiring is old and thin enough, the lights stay a little dimmer all the time the refrigerator is running. On a much smaller scale, the same thing happens when you interconnect any two pieces of studio equipment.

No, your house lights won’t dim when you connect a mic preamp to your sound card input, but if you were to measure the output voltage of the preamp before and after making the connection, you’d see that making the connection caused a drop in the output level of the preamp. The sound card input draws a small amount of current from the preamp, and there is therefore some voltage dropped across the preamp’s output impedance.

With modern equipment, the voltage drop is very small, essentially insignificant. The reason why, with only a couple of exceptions, is that today’s studio gear is designed with relatively low source (output) impedance and relatively high load (input) impedance. To understand why this is a good idea, let’s apply Ohm’s Law, as discussed in last month’s article.

To review, the common expression of Ohm’s Law is the formula in picture #1.

This means that the current I flowing through a resistance R is directly proportional to the applied voltage V and inversely proportional to the resistance.

For now, we’ll talk about circuits and situations where “resistance” and “impedance” are interchangeable. It won’t be until Part 3 that we look at situations where we must break apart impedance into resistance, which doesn’t depend on the frequency of the signals in the circuitry, and reactance, which does.

Mismatching impedances

A simple but effective model of an unbalanced output (we’ll use unbalanced sources for simplicity, but the same thing works for balanced sources) is a voltage source with a resistor in series with it. This could represent the output of a preamp, a mixer, a signal processor, or a recorder. The input to any device can be simply modeled by a resistor connected between its input terminals. Undignified as it may be to represent your expensive recorder with a single resistor, it allows us to complete our simple circuit:

Most modern equipment makes liberal use of operational amplifiers (opamps) which, in most common output configurations, have an output impedance of 50 ohms (Ω) or less. A typical opamp input circuit presents a load of 5–20 kΩ (5,000 to 20,000 ohms).

Let’s say that our output signal is a vocal coming from a mic preamp, and our singer holds a note long enough for us to make some measurements. The preamp, when not connected to anything but a meter that we assume draws no current, puts out 1 volt. I’ve used a middle-of-the-road 10 kΩ value in the diagram above to represent the input impedance of the recorder. Connecting the preamp to the recorder completes the electrical circuit and current flows through both the 50 Ω source and the 10 kΩ load impedances.

Applying Ohm’s Law, we see that this current is about 0.0000995 amperes (0.0995 milliamperes)—not very much current, but here we’re just pushing electrons around so it doesn’t have to do much work.

Ohm’s equation I=V/R can also be written as V=I x R. In this form, we can look at each of the two resistances above, one at a time, plug in the current I we just calculated, and get V across each resistor. We see that this amount of current causes a voltage of 0.995 volts to appear across the load, with the remaining 0.005 volts dropped across the internal output impedance of the source. The source and load impedances form a voltage divider (see last month’s article if you need to remind yourself of what that is), but due to the ratio of the two impedances that form a voltage divider, nearly all of the voltage out of the preamp is available to the recorder where we want it, with a negligible amount lost to the internal resistance of the preamp’s output circuit. (By the way, in the real world, every source has some impedance, so it’s impossible to get a perfect (100%) voltage transfer. But we can come darn close.)

For illustrative purposes, let’s now do something not so smart and replace the recorder with a set of headphones. Typically, headphones have an impedance of 50 to 100 ohms, so let’s substitute 100 for 10,000 and run the numbers again. Now, for the same 1 volt out of the preamp, we have a current of 6.67 mA (don’t forget that we still have the preamp’s source impedance of 50 ohms added to the 100 ohms of the headphones), quite a bit more than in our previous example. Looking at the values of the two resistors that now form the voltage divider, we see that we have quite a different ratio than before.

In the first example, the 50 ohm source impedance, and hence the voltage dropped across it, was insignificant compared to the load impedance. Now that our load is much closer in value to the source impedance, look at what happens when we crank the numbers: We drop a relatively substantial 0.33 volts across our source, leaving only 0.66 volts available to drive our headphones. Chances are this won’t be very loud even when turned up to 11!

A typical “+4 output level” device can put out around 10 V before it runs out of headroom, so there’s probably a little room to crank it up. Multiplying our numbers by 10, it looks like we should be able to drive our headphones except for one thing—most opamps typically used in modern audio circuitry are unable to provide 66.7 mA of output current, so we’ll run out of horsepower and get distortion before reaching our desired output level.

So here’s the lesson: With modern equipment that’s designed for voltage transfer, you don’t want to match source and load impedances. You want a low source (output) impedance and a high load (input) impedance. A good rule of thumb is about a 50:1 ratio as a minimum. Since most equipment today is designed with a much higher ratio than that, you can easily “mult” an output to several inputs without overloading your source. You might want to split a tape track output to more than one mixer input channel so you can set different equalization and effects in different parts of the song, and this exercise illustrates that it’s not an electrical problem to do so.

One exception is some “vintage” and broadcast gear that was designed in the days when everything—input and output—was either 600 or 150 ohms. Output circuits in this sort of equipment were designed to work into a 600 ohm load and in fact depended on it to give the proper operating levels. Connecting an Ampex broadcast recorder to a modern console without terminating the recorder with a 600 ohm resistor may cause the console’s input headroom to be exceeded on peaks. Ampex was good enough to anticipate this situation and provided a “Bridge/Terminate” switch right on the front panel. When we get to digital interconnections in Part 3, we’ll see another application of this concept.

Hold that thought, though, because it’s time to take a break until next month when the second of our three installments will take you through impedance matching with power amps and speakers, headphones, microphones, and pickups.

Mike Rivers (talkback@recordingmag.com) delves deep into matters of audio enlightenment from his home base in eastern Virginia.




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