> a single transistor
Clearly Ian didn't give the whole spec: that 400-5KHz spec popped up later.
It isn't clear that we are limited to ONE transistor. However, not to be snide, but if Ian and chum could overlook the bypass that doesn't bypass, then maybe one transistor is a good thing to work on before he gets reckless with multi-transistor work.
The specs, as I know them, can be met, several ways, with a single ordinary transistor and no "exotic parts" like transformers. That's part of why they are so goofy (0.75V p-p from a 5V supply???).
> I'd second dayvel's suggestion.
History agrees with you. However today that driver transformer is hard to source (the 1KCT:8 tranny is a fluke and I don't know why RS still lists it). Mouser has them. You could haunt yard-sales and score a 1963 transistor radio, strip the iron, but to avoid academic cheating Ian should have a "clean room" B-team dismantle the radio and hand over the parts without revealing the actual circuit to steal.
Since Ian probably won't score the iron and may not be allowed 2 transistors, I'll do this one.
With a 10K:2KCT driver, two transistors, and the 1KCT:8 output, we get:
4V peak on one side of the output primary, 8V peak across 1K, 0.715 peak or 1.43V p-p across the 8 ohms, well in excess of spec even with several dB loss in the core.
Max power is about 0.5VRMS in 8Ω or 32 milliWatts, well in excess of the implied 9mW.
In good class B, 32mW out means around 8mW of dissipation in each transistor. I've assumed 4V peaks on a 5V supply so there is another 25% waste, 10mW per transistor.
Peak current is around 4V/250Ω= 16mA. Peak transistor voltage under load is about 9V.
10mW, 16mA, 9V: we can use the CHEAPEST transistor we can find. (Indeed that is what you find in millions of 1960s tranny radios, rated upward of 100mW on 9V batt.)
Power input is around 52mW on a 5V rail so DC current is around 11mA, less than the specified 200mA (by a long shot). I know for fact that a used 6V lantern battery, too weak to run a lantern, will run a 9V pocket radio for months.
Ignoring crossover, the transistors average 5mA-10mA current so the Hie is around 6Ω-3Ω. Say 5Ω. Dynamic gain from 5Ω to 250Ω is around 50, so for 4V peak at the collector, we need 0.08V peak at the base. Total voltage gain from one base to the load is nearly 10!
In pure class B, gain at zero audio signal is zero (transistor cut-off, no gain). We need to pick a bias current to get nice sound, and also to estimate gain at less than max power. Note that at peak current, 16mA, the Hie will be like 2Ω in one transistor, very high in the other. With decent AB biasing, both transistors contribute for small signals. For the same gain at small signal, each Hie should be 4Ω, or 8mA. That's essentially Class A operation. In practice the Hie won't sink as low as 2Ω because our cheap transistors have an ohm or so of dead resistance (maybe 10Ω for 100mA transistors) and we can get away with much lower bias current and will have less gain.
IIRC (cheating), you typically found about 22Ω common emitter resistor, a few-mA bias, so the emitter impedance runs 30Ω small-signal 25Ω large signal. So gain from base to collector is around 250/30= 8, and peak base swing about 4/8= 0.5V. Overall gain from one base to load is about 0.8/0.5= 1.6, less than specified. In the orginal app we would be stepping-down from a volt-amp collector. Here we are given a fat 50Ω output and a lenient 150Ω input spec, so we could custom-wind a step-up input to reach the gain spec. Or we could fudge the emitter resistance down to maybe 10Ω and get gain of 2 with a unity-gain input iron.
With Re=10Ω and β=50 the input impedance is around 750Ω per base. We could ask CJ to send over a plain 150:600CT transformer and have input impedance to spare. However the standard pocket radio 10K:2KCT input iron gives a step-down and we'd be way short of voltage gain.
This plan gives zero damping. We could fudge-up the input transformer ratio to get more voltage gain and then work negative feedback around it.
A wackier scheme: as long as we are talking fancy driver transformers, defy Prof and try push-pull emitter followers into the handy 1KCT:8 tranny. Great damping (almost DF=10). Voltage gain from one base to load is 5.5:1 or 0.18, so to meet the spec of 2 we need input ratio from source to one base of 11, base-base about 22. Impedance ratio is 22^2=484. If input can not be less than 150Ω, then we need over 150*484= 73K base-base, or 36K each base. The base impedance is about 250Ω*β or 12K5, too low. We need to spec β over 150 to meet specs, but that is easy today for transistors of this size. Notice that to get very-low THD and good damping we needed β much higher than the minimal β needed to just-barely fulfil the sloppy assignment.
Screw transformers. They are wonderful but cost a LOT more than transistors, or even transistors plus capacitors. If you take the 5v supply and feed a (2 transistor) totem-pole output stage, you can get over 4V p-p which is way over the spec. Working into 8Ω it will draw about 100mA at full output, well under the spec. Working CC (emitter follower) it has voltage gain of unity, it flunks. Working CE it can have a large-signal voltage gain of 60 at 4V p-p, though only 11 at the required 0.75V p-p spec. To work CE kinda requires that the signal generator (or power supply!) "floats". That was not specified though I can imagine the undergraduate lab has all grounds bonded. A 150:150 transformer would fix that, if we get back to the problem of sourcing iron between classes, meals, and parties. The voltage gain can be degraded from 60-11 to 2 with some clever feedback, which could also damp the loudspeaker load and its impedance swings. However, given input iron, a 150:600 with emitter followers gives the specified gain and good damping, though you need β over 100.
Yet another answer is to saw open a TO-3, put in an LM380 with a 3.6Ω resistor from OUT to V+, seal it up as a "3 terminal device" with a 2N3055 part number. With DC through the speaker, it would give ample gain and great THD and damping, though the "base" current and voltage and biasing would be obviously odd. At first glance, "it can't work", yet it could.
Probably past my bedtime......