Output impedance

January 16, 2013
 by Paul McGowan

I was set to move onward in our explanation of the output analog stage of a DAC or preamp but one of my readers asked me to explain output impedance which I mentioned a few days ago. This is a subject that folks should understand at least at some level because so many things in high end audio are affected by it.

Output impedance refers to a device’s ability to deliver unrestricted current or power when passing a musical signal – it measures the amount of restriction or hold back of that signal. It is important to understand output impedance only as it is relative to the input impedance of whatever the amp is driving. In other words, the output impedance of a DAC is only meaningful when you are considering what that output is going to feed into (the preamp or amp it’s connected to).

The easiest way to imagine what output impedance means is to picture a resistor in series with the output of the amp. This resistor is always present regardless of how low the output impedance is because there’s no such thing as a perfect source or output. A perfect output would have zero output impedance – meaning the value of this mythical resistor is zero and therefore would have no affect on the musical signal passing through it.

As there are no perfect amplifiers with zero output impedance we have to assign a number to this resistor in the signal output of the amp. The easiest way to calculate this value is to drive music through the amp into another resistor connected to ground and measure how much of the musical signal is lost at the junction of the two resistors (remembering that when we pass music through a resistor we convert some of that musical energy to heat and it is lost). As the resistor to ground gets lower and lower in resistance (less resistance) the level at the junction will continue to decrease and, at one point, that level will be 1/2 of what you started with. It is at this point we can then say what the output impedance of the amp is – which would be exactly the same as the value of the load resistor going to ground.

Here’s what’s important: whatever you are trying to ask the output amplifier to drive must be at least 10 times higher in impedance and preferably 100 times or more. Why? Because you don’t want to lose any of the musical energy being sent to the receiving device and you don’t want to stress out the amplifier that’s sending the music in the first place.

So here are some practical examples. If the input impedance of your power amplifier is 10k then the output impedance of your DAC or preamp feeding it must be at least 1k and better if it’s 100 Ohms or less. If it’s 100 Ohms you’ll only lose a tiny amount of signal at the junction between the preamp and the amp – 100th of what you are sending, just for understanding sake (not entirely accurate but you get the idea).

Here’s another example: a loudspeaker. Let’s say your loudspeaker is an 8 Ohm speaker whose impedance dips as low as 3 Ohms at its lowest point (speakers don’t have flat impedance). That means the output impedance of your power amplifier should be at least 0.3 Ohms and probably better at 0.03 Ohms to really have very little affect.

Tubes generally have higher output impedance than solid state products. One piece of evidence you see in most tube power amplifiers is the output transformer of the tube amp. This is there to more closely match the high output impedance of the amplifier with the low input impedance of a loudspeaker.

Bottom line: output impedance is always better lower.

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6 comments on “Output impedance”

  1. “The easiest way to imagine what output impedance means is to picture a resistor in series with the output of the amp.”

    This is Thevenin’s Theorem.

    “As the resistor to ground gets lower and lower in resistance (less resistance) the level at the junction will continue to decrease and, at one point, that level will be 1/2 of what you started with. It is at this point we can then say what the output impedance of the amp is”

    That’s not how I remember learning it. As I recall, the output impedance is the open circuit voltage divided by the short circuit current. The maximum power transfer theorum states that maximum power is delivered to the load when the load impedance is equal to the source impedance, the condition you stated. You can calculate the load required for maximum power transfer using the method I learned. Can you calculate it the other way? Perhaps you can, I never considered it.

    From the point of view of the source, the load impedance includes the wire impedance. This is modeled by the Telegrapher’s equation. If the wire impedance is not purely resistive and the parameters are within an order of magnitude or two of the load, the wire will act as a filter. This is VERY undesirable. A wire makes an awful filter, you could hardly do worse. From the point of view of the load, the source impedance includes the wire. Here we also want the wire’s series impedance to be as low as possible and its shunt impedance to be as high as possible compared to the impedance of the stage driving the load. For example, a wire with a signifigant series resistance can alter the electrical damping factor of an amplifier as it affects the low frequency performance of a woofer. By being greater than zero, to the degree it is greater it increases the time it takes for the woofer’s mechancial energy to be dissipated as heat by driving the source with back emf as it acts as an electrical generator. This increases the speaker system’s amplitude at its resonance frequency.

    Loading an amplifier with the wrong impedance, say one that has a highly capacitive shunt impedance can destroy an amplfier by inadvertently turning it into an RC oscillator including at ultrasonic frequencies making the event inaudible.

    The ideal wire is the electrical equivalent of a shunt, that is a conductor having no series impedance and infinite parallel impedance. This too is not possible in the real world but appropriate low cost solutions have been developed and marketed by the mainstream wire industry for every conceivable application an electrical engineer could need. These standards and products were developed many decades ago. Practical results correlate excellently with those predicted by the mathematical models.

  2. Soundminded,
    Enjoying your comments, thanks. A question for you. In the wacky world of wire, based on your
    discussion above, from a technical standpoint, what first do you look for in your interconnects and speaker wires? Conductor material, insulation, geometry, wire gauge, terminations, length, secret boxes, all must affect the impedance the load sees?
    Thanks.

    1. coppy, before I answer that, there are a few things you should know about me to put my response in context. I’m not an audiophile. I am however an electrical engineer. While my college education was focused on electronics many many years ago my career took me in a different direction. I have never worked in either the consumer or professional audio industry (although I’ve built many video-teleconference rooms, probably over 100 of them.) I reckon that during my working carreer I’ve spent well over a million dollars, perhaps well over two million dollars of other people’s money on wire. My single largest purchase was for about $320,000 about 30 years ago for a data highway. I’ve bought communications cable of many types. I’ve probably had every major wire manufacturer’s sales rep in my office at one time or another. On occasion I’ve spoken with them about audiophile cables and their views were entirely consistent with mine.

      The purpose of a cable is or ought to be to get an electrical signal from one point to another with as little loss and distortion as possible. The ideal cable is a shunt. It has zero impedance in series and infinite impedance in parallel between conductors. No real world cables meet that test (at room temperature) however the mainstream wire and cable industry has developed products over the past many decades that are reliable, cost effective, and are relied on by professionals to perform their function satisfactorily. When shopping for cables I look for performance according to industry norms and standards, quality of manufacture, suitability for its purpose, and price. The reference standard that is most often cited in this industry is Belden. Many specifications for signal and communications wiring will say “Belden or approved equal.” Some manufacturers of certain types of equipment will not honor their warrantee if anything other than Belden cable is used to connect it. If I were assembling an expensive audio system, that’s the wire I’d use.

      Using wire as a control element to alter the sound of an audio system is a very iffy task. If you do not have all of the data for the source, load, and wire and know how to solve the equations with them, the results are entirely unpredictable. The same cable deliberately designed to alter the signal can have very different effect from one combination of components to another. If they don’t work in the manner and to the degree you want them to, you have no way to adjust them. It’s literally hit or miss, usually a miss. People who use cables this way often experiment endlessly trying to find exactly the right one for themselves often at great expense.

      In my own personal sound systems I have so many connections, so many wires that I use the least expensive cable I need. For speakers I use 16 gage speaker wire bought from Home Depot. For interconnects if I need more than I’ve accumulated over the years already I’ll buy the least expensive product possible. I do add shielding to my phonograph cables and I do it exactly the way wire manufacturers do. I run a length of bare wire along the cable (this wire is called the drain wire) and I wrap aluminum foil around the audio cable and the drain wire. I ground the drain wire to the preamp input. This makes an effective RF shield.

      Shielding speaker wires is not necessary, they are not subject to interference. Shielding power wires is also not only unnecessary, it can be very dangerous. The power wires are rated to be installed in free air so that they don’t overheat. Trying to shield them invalidates their current rating. I also do not recommend trying to defeat the ground wire in a power cord if the equipment came with it. The ground wire might one day save your life.

    1. Low capacitance is very important. Not only does it prevent high frequency filtering but it also prevents equipment such as amplifiers from becoming RC oscillators. Capacitance is controlled by the distance between conductors and the dielectric constant of the insulating material. As conductors move further apart to reduce shunt capacitance, series inductance increases.

      The geometry of most wire is round and stranded. Skin resistance does not appear to be much of a factor in speaker wire at audible frequencies. For a given gage, more strands will not reduce skin resistance effect because they are shorted together. Only Litz wire has strands individually insulated but you can obtain the same result simply by increasing the wire gage for ordinary wire. Copper in ordinary wire is already almost entirely free of oxygen. I think residual oxygen is only a small fraction of a percent. Silver is a better conductor than copper but much more expensive. You can obtain comparable results from copper at lower cost simply by increasing the gage.

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