Do audio impedance mismatches cause reflection (ie, 8-Ohm output to 20kOhm input) ? Does it matter?

I understand that audio source⇒input impedance mismatches are normal, and this answer provides a good reason as to why. However, having worked with RF more than audio, mismatches cause reflection that can damage the transmitting source.

Question: Are there situations in audio systems where impedance mismatch reflection is of concern?

I am asking more in the high-power sense, not so much for signals from microphones where an impedance match might be important to minimize losses before the preamp.

• For relatively low frequencies, when the load impedance is fixed, you want the source impedance to be as low as possible. See the third paragraph of the MPTT article. en.wikipedia.org/wiki/Maximum_power_transfer_theorem Commented Jul 13 at 17:05

Are there reflections? Thanks to Oliver Heavyside - Yes.

Do they matter in power amplifier / speaker connections- No.

Calculate the wave length of a 20 kHz signal, and compare it to the typical length of speaker wires. In terms of signal distortion, the phase difference between the incident and reflection waves is way too small to matter.

In terms of the MPTT, the output impedance of a typical audio power amp is over 10x less than that of the (8 ohm) load, and way way less than whatever the characteristic impedance of the speaker cable is. It is not an ideal MPTT case, but the situation doesn't need it.

OTOH, the phone company sends 3 kHz signals down miles of wire. At those distances, reflections can make a noticeable difference.

• Just to be clear (and for others), by MPTT do you mean "maximum power transfer theorem"? Commented Jul 13 at 16:43
• Yes. Never given its due credit, not only in engineering but also in life. AND - it applies perfectly to playing poker for money. Commented Jul 14 at 0:32
• Typo: his name's "Heaviside" rather than "Heavyside". Commented Jul 14 at 14:45

Yes in fact there can be reflections due to impedance mismatched in the audio system, just like in any other system, but due to low bandwidth as the frequencies are so low, you generally run into them in long cabling like telephone lines.

But in your specific example of a high power systems, for example an amplifier driving an 8 ohm speaker, there needs to be some consideration.

Ideally, a speaker voice coil (with zero resistance and inductance) and cone are massless and the current (not voltage) you drive through the coil will cause it to move immediateately to the new position set by current.

We all know this isn't true, in real life, the coil has resistance and inductance, and the moving parts have a mass that needs to be moved. Plus, we generally drive speakers with a voltage signal, not current, so the inductive coil reacts slowly.

So for an ideal step in the voltage signal, it takes time for the current to change in the inductance and the cone to start moving due to due to inertia of the mass, and same happens at the new setpoint, cone will overshoot and slow down, and move back, etc, with decaying oscillations until settles on the new setpoint.

Which means, the moving coil will also generates voltage when the cone is moving it, so even if the voltage is fixed, the current is not, until cone oscillations stop.

So in order to dampen those oscillations and preventing the voltage from changing and affecting e.g. another speaker connected on the same voltage (e.g. woofer and tweeter in same cabinet), it means the output impedance of the amplifier must be as low as possible to keep the voltage fixed even if currents fluctuate.

That is why your speaker amplifier does not have an 8 ohm output impedance to match it to a speaker. For maximizing the power transferred to speaker and minimizing losses in the amp, the amplifier output must have very low output impedance.

Which basically means that impedance matching is about selecting impedances suitably based on context, instead of making source and load impedances equal which however is true for most of your cases with RF signal.

As audio is generally bandwidth limited to 20 kHz, the wavelength of 20 kHz sine wave in a cable (where speed of signal is two thirds of speed of light) is about 10km, and if you use some rules of thumb, quarter length transmission line of 2.5km can become a problem, and some rules of thumb say less than 1km does not need to be considered as transmission line.

Telephone lines are (were) impedance matched as it was a 600 ohm system.

So if your wiring is less than 1km, 8 ohm output driving almost any cable and terminated into 20 kohm input will generally not have reflections that need to be considered. The signal will travel that 1km in 5 microseconds, and a 20 kHz sine has a period of 50 microseconds.

Yes, impedance matching does matter in audio systems, if the wires are long enough. That usually means long microphone cords.

The effect with 100 ohm impedance wiring, driving a 6 ohm speaker, is that the wiring has net inductance, which lowers the high frequency current to the speaker(and high frequency phase is seen to be leading). The effect with 100 ohm impedance wiring, driven by a 1000 ohm preamplifier output is that the wiring has net capacitance that lowers the high frequency voltage excursion at the driven end of the wire (and high frequency phase is seen to be lagging).

If the speaker impedance were the same as the transmission line impedance of the wiring, the inductive lead and capacitive lag would cancel (just like a resistive attenuator) and frequency response would be flat.

These effects are usually well within the range of tone control adjustments.

It is not 'reflections' that models these transmission line mismatch effects, but stray inductive or capacitive impedance of the wiring: the signals all arrive nearly on time, but the wiring acts as frequency-dependent load. Any time-delay in the electrical signal is negligible compared to speaker-to-ear distance mismatches in the listening room.

Suppose a voltage source is connected to a load via a transmission line:

We have a source impedance, load impedance, and transmission line length and impedance.

What matters is the length of the transmission line versus the wavelength at the frequency of interest.

• If transmission line length is significant relative to wavelength:

Reflections due to impedance mismatch at both ends of the transmission line will turn the pulse and frequency response of the system into a mess, and enough power can be reflected back into the source to destroy components.

In this case, impedance matching is required if we want the system to simply work. There's no other choice, and this matching means the load sees a source impedance equal to the transmission line impedance. Thus maximum power transfer into the load will occur when its impedance is matched to the transmission line.

However, if the source uses resistive impedance matching, this means we're wasting 50% of the source power in this resistor to transfer the other 50% into the load.

• If transmission line is very short relative to wavelength:

Reflections due to impedance mismatch at both ends of the transmission line always occur, even in this case. But with a very short transmission line, the difference compared to the previous case is reflections don't have undesirable effects. The signal reflects at both ends of the transmission line so fast relative to the rate of change of voltage at the source, that the losses in each round trip cause it to be well damped in the end.

Thus, when the transmission line is very short, the system will work (perform as intended, with flat frequency response, etc) even if impedances are not matched.

This allows dropping the impedance matching requirement and its drawback of having to waste 50% power. It is much more efficient.

When the length of the transmission line is negligible, maximum power transfer into the load occurs with minimal source and wire impedance.

So the answer to "why don't we match impedance of amps, wires, and speakers" is: because at the usual audio frequencies and "living room sized" transmission line lengths, matching would cause large power losses without providing performance gains.

As a side note:

Most loudspeakers are designed to be driven by a low impedance voltage source. Since they have wide impedance variations across frequency due to mechanical resonances, inductance, crossover filters, etc... any impedance in series with the source will create a voltage divider between the source and load impedances, which results in a change in frequency response corresponding to the frequency-dependent impedance of the load.

In addition, current drawn by loudspeakers often contains a lot of harmonic distortion, especially woofers undergoing large displacement. This is due to changes in inductance as the coil moves through the gap, plus other factors like springs not being entirely linear. I got something like 20% THD or more on the current on a bunch of loudspeakers, so the effect is pretty large. It's easy to measure, all you need is a soundcard, an amp, and a low value power resistor to measure current.

This distorted current creates a voltage drop across the source impedance, which then adds to the signal being reproduced by the loudspeaker. Thus, if source impedance is high enough, for example due to thin wires, on top of the previously described frequency response change, the tweeters or midrange drivers will receive this voltage drop from to distorted current drawn by the woofer, and they will treat it as signal and reproduce it as sound.

Thus, increasing source impedance will sound different, and bi-wiring is not entirely audiophile woo-woo.

No they don't matter in audio systems. The wavelengths of transmission lines didn't cause reflections on PCBs until about 50MHz at which point you need to start worrying about transmission line effects.

You do need to worry about matching loads to sources if you want maximum power transfer.

These are two different things

• A few clarifications could be in order. Even 1 Hz signals will cause reflections if they have fast digital edges that require large bandwidth. And you will not want to match an 8 ohm speaker with amplifier that has 8 ohms output impedance. You want something like 8 milliohms of output impedance. I guess that is what you meant by "matching", zero ohms on the amp, 8 ohm speaker. Commented Jul 13 at 20:54
• Even 1 Hz sinusoidal signal will be reflected, but the reflections aren't noticeable because they bounce back and forth and damp out faster than the signal oscillates. Commented Jul 14 at 1:34