> <Nobody has matched impedances since the 1950s.> PRR, I've been thinking about this and I'm somewhat confused. You stated in another message that power changes at various impedances. I have heard this in my headphones. My Grado's are much louder than my AKG's. I've also discovered that I can not plug a microphone directly into my Tascam cassette recorders' mic inputs. I must use a XRL line transformer or it won't work. Could you go into a little more detail about not matching impedances?
"Matched" impedances means that outputs are 600 ohms and inputs are 600 ohms.
I should have said that this is still done at RF frequencies. Up there, any wire more than a few feet long will cause reflections unless the source, cable, and load are all the same impedance. Cables are mostly 50 or 75 ohms, so sources and loads are 50 or 75 ohms. The nearest example is your Cable TV system. If you could find a simple "Y" splitter and fed 2 or 3 TV sets from their 75 ohm source and cable, you would have ghosts on the screen. Each strong vertical object would show an echo a millimeter or so to the right. With a long cable and bad mismatch, you get a series of light and dark bands to the right of everything. (You would also have a reduction in level, see below, although TV sets will compensate this up to a point.)
In audio, you would need miles of cable to cause this effect, because audio frequencies as electric in space or in copper are miles long. Only long-line systems need to match to control cable effects. Classic telephone lines were 900 ohms (open-pair) or 150 ohms (multi-pair cables). Telephone transmitters and receivers were 100 to 900 ohms. They didn't go for true matching, they tried to minimize the difference between a short line and a long line. For dedicated lines that would be trimmed to precise levels, impedances of 150 and 600 ohms were common and they usually did load the far end of the line to about the same as the source impedance.
Another reason RF systems are "matched" is that gain is expensive. An amplifier always has an input impedance and an output impedance, and requires real power (if only microwatts) at its input. You get the most power transfer from output to next input if both impedances are matched.
Worked example:
If you have an output that makes 1 volt behind 1 ohm, and you hang a 1 ohm load on it, the voltage at the load is 0.5 volts. The power at the load is 0.25 watts.
If you feed the same output into a 10 ohm load, the voltage at the load is 0.909 volts. The power at the load is 0.083 watts.
If you feed the same output into a 0.1 ohm load, the voltage at the load is 0.0909 volts. The power at the load is 0.083 watts.
Power into various loads from 1V 1 ohm:
_ 10 ohms = 0.083W
__ 1 ohm = 0.250W
_ 0.1 ohm = 0.083W
When power is precious, matching matters.
In modern audio, the situation is different. Gain is relatively cheap. Feedback means the small-signal impedance is different from the native impedance of the device.
And matching is a problem when you want to split a signal to two loads. This may be the main speaker amp plus a tape recorder. Much bigger splits are often done.
With that 1 volt 1 ohm source, with one 1 ohm load you get 0.5 volts. With two 1 ohm loads in parallel, each load gets 0.33 volts, a significant 3.5dB drop in level. Cutting one of those loads in and out will audibly effect the music. Hang 10 of those loads, the drop is 14.8 dB, a major drop. Level management gets messy when you have a varying number of "matched" loads.
no loads = 1 volt
1 load === 0.50 volts
3 loads == 0.25 volts
10 loads = 0.09 volts
The classic broadcast solution was to build amps with 20K input impedances. This does not increase the cost much, if at all. (In fact, after 1927, "600 ohm input" amps were usually 50K input plus a 601 ohm resistor.) If the source were 600 ohms at 1 volt with one permanent 600 ohm resistor on it, this is what you get with various numbers of 20K amps Y-ed across it:
no loads = 0.5 volts
1 load === 0.493 volts
3 loads == 0.478 volts
10 loads = 0.435 volts
From 1 to 10 loads, the change is only 1.2 dB, inaudible. (Actually such systems would often use the 150 ohm connection, and 0 to 30 loads connected gives less than 1 dB drop.)
Alternatively, you can stop buying 600-ohm amps and get amps with "zero"-ohm output impedance. Amps with negative feedback usually have a super low output impedance, and have to be padded-up with a resistor to meet 600-ohm specs. Using a 1 volt zero ohm source, the level with any number of loads would be 1 volt. Using a more typical 50 ohm source, 0 to 10 20K loads gives 1V to 0.98V, only a 0.2 dB drop.
So an un-matched system, where load impedance is very much higher than source impedance, is much more versatile. The drawback, that lines are not loaded in the cable impedance, does not matter for audio in lines less than a mile long.
Also, an un-matched interface gives the full source voltage, rather than half-voltage as a matched interface gives. The amp input gets less current and power if it is high impedance, but current and power gain is cheap in modern amplifiers (tubes approach infinite current gain, and transistors are dirt cheap compared to the chassis you put them in). Working with constant voltage levels is much simpler than trying to compute a system that matches for best power transfer.
You had specific observations and I have drifted. And my boss wants me to do some work. Reply and I'll ramble some more, maybe say why you need a transformer (not truly a "matching" transformer) between a 150 ohm dynamic mike and a typical cassette input.
-PRR
