sahib said:
There is a good tutorial here.
http://www.n9xh.org/license/pcara_general_upgrade_lesson_08.pdf
Not so good, really.
Firstly, although the impedance and voltage ratio stuff is correct, they are missing a point, which is very important in audio. Many transformers have a 1:1 ratio, so obviously, their
raison d'être is not impedance matching. The reason is galvanic isolation, thus providing a "balanced" connection.
Secondly, the mention of loudspeakers operating more efficiently when the loudspeaker impedance is equal to the amplifier's output impedance is not only mathematically wrong, but also practically.
Efficiency is not power; it is the ratio of the power dissipated by the load to the power produced by the source.
When both impedances are equal, the efficiency is only 50%. Theoretically, it also corresponds to the highest power dissipated in the load. Although that may be partially true, considered with no other constraints, in practice, there are some factors that don't allow the situation to happen.
Typically a SS amplifier rated at 100W into 8 ohms has an output impedance of a fraction of an ohm, let's say very conservatively 0.1 ohm. Would this amplifier really be capable of driving a 0.1 ohm load, producing a tremendous 4kW (and drawing 8kW)? No, because the PSU would sag, the output devices would melt unless a wise designer had incorporated active protections in the circuit.
Impedance-matching is an obsolete notion in audio design; it was valid when active circuits (valves) were expensive, which is not the case anymore.
Most connections today are bridging, which is defined by having the source impedance much smaller than the load. Typically, the output impedance of most modern audio gear is about 100r and the input impedance is about 10k+, which allows the parallel connection of multiple inputs to a single output. With that kind of ratio (100:1), the number of loads does not significantly affect the response. That's typically what happens in large PA systems where the last piece in the control unit (typically a bunch of processors cascaded) is connected to several cross-overs. Indeed, the efficiency is very good (90+%), but the power distributed to the load is not maximised, which does not matter.
Today, there are four reasons for having transformers in audio gear.
a) Tubes need transformers for providing the low output impedance expected (<600r for line level, <0.5r for loudspeakers)
b) Adding weight to a piece of equipment that may be perfectly viable with them, but needs some sanctified "character", or mojo, or snake-oil...
c) Galvanic isolation. Although electronically balanced input and output stages are perfectly viable in most situations, there are users who want (need?) the extra confidence transformers give when operating in rough conditions.
d) Noise factor optimization. All input stages, whatever the technology, have an optimal source impedance in regard with their noise performance. Typically, FET's and tubes want to see the highest possible level and don't suffer from high or very high source impedance. They will be used with 1:10+ transformers, giving an increase in signal of about 20+dB and a reflected impedance of about 20k (for a 200r microphone). Indeed the noise performance could be improved by using a higher ratio, but practical limitations in the construction of transformers (wire size, leakage impedance, parasitic capacitance) do not allow to go much futher.
OTOH, BJT's have an optimum source Z that is defined by their operating current. Originally, the first low-noise transistors were optimized for about 50-100uA collector current, which made their optimum source Z about 10k. So the first SS mic preamps ud=sed the same 1:10 transformers that were used in tube gear. Then semiconductor manufacturers made transistors optimized for much lower Z, which made possible the design of transformerless mic preamps, but that's another story...
