Electronic – How voltage and power transfer in cascaded amplifiers work

I have just recently come to understand that for maximum power transfer the amplifier and speaker impedances should match.

Not this is not the case with audio - an audio amp can have an output impedance that is substantially lower than 1 ohm yet nobody makes (as far as I know) 1 ohm speakers. If the amp had an 8 ohm output it could only deliver half the voltage to an 8 ohm speaker and the rest of the power would be wasted in its output impedance.

It's only RF circuits that you need to be concerned about matching impedances but this is more to stop reflections down PCB tracks and cables.

The rest of your question is based on a false premise about audio impedances so it's not worth attempting to answer. However I will try and give some insight about the transformers used.

Like any power transformer without a secondary load, ideally you want to be able to apply a voltage to the primary and have zero current entering the transformer - that would be perfect and, when you connected a secondary load that consumes power, the power needed to be input to the primary would be identical to that consumed by the load. Reality isn't that bad actually.

Primary magnetization inductance is basically what the primary impedance is when the secondary load is disconnected - it can't be infinite but it can be relatively small but, not as small as a speaker impedance because then a lot of the power amp's energy is wasted driving a reactive current that serves no purpose.

If it were a 50 Hz power transformer connected to 230V ac, a 10 henry mag inductance would take a "standby" current of 73 mA. If such a transformer were designed for audio and, you weren't too bothered about below 100 Hz (deep bass) then a 10 henry inductance would take 35 mA at 100 Hz BUT, it's possibly a 20V RMS drive and not 230VRMS so a 100 mH mag inductance would do and it has an impedance of 63 ohms at 100 Hz. This, of course will only get higher (better) as the audio frequency rises into the mids and the treble.

63 ohms is fine for an amplifier that can drive an 8 ohm speaker so that hopefully takes care of that side of things. Next - there are turns (windings) on the primary that do not couple power to turns on the secondary and these can be a right royal pain for audio transformers because they are in-series with the power transfer and at high frequencies these "leakage" inductors are going to somewhat attenuate high frequencies. The bottom line is that audio transformer designers try to make sure that approximately 99.5% of the magnetic flux in the primary is coupled to the secondary so, if the primary is nominally 100 mH open circuit then less than 500 uH is seen as useless to the transformer and a detriment to high audio frequencies.

Even so, 100uH as a blocking impedance is nearly 13 ohms at 20 kHz.

Bottom line is that audio transformers are really good at providing low loss power transfer across a wide range of frequencies. No impedance matching is necessary.

Reflections occur or are noticeable when there is a transmission line involved and that transmission line is long enough for significant reflections to occur. This is generally accepted to be a length of about one-tenth of a wavelength. So, at 1 MHz, the wavelength is 300 metres and so unmatched transmission line problems start at about 30 metres. Higher frequencies naturally have unmatched problems on shorter line lengths.

However, the impedance of a transmission line for radio frequencies of about 1 MHz and above can be taken to be purely resistive. In other words it doesn't present a complex impedance hence it should be matched with an equivalent resistance to avoid reflection problems and this also ties in with the maximum power transfer. So no real problems here.

For an antenna, it can have a highly capacitive impedance if it is regarded as "short". An example being a monopole that is less than one-quarter of a wavelength. The radiation resistance it would naturally present when a quarter wave long would fall from 37 ohms to a much smaller figure when the antenna is shortened. The effective series capacitive reactance rises from near-zero at a quarter wave to tens, hundreds or thousands of ohms as the antenna shortens.

So this is an example of where using an inductor (a conjugate component) can cancel the short antenna's capacitive impedance and allow a better transfer of power.

An antenna is used to match a circuit impedance (50 Ohm) to the free space impedance (120 pi). Ideally we get no reflection, thus I would expect that all the power has been transferred to the environment

Of course there is a reflection - that is the mechanism by which we get an impedance transformation to that of free space at a particular frequency. And, adding a conjugate component to cancel out the inherent capacitive reactance of a "short" antenna doesn't alter how the antenna works but it does allow a better transfer of power.