1 Watt Audio Amplifier Using BJT
I'll try and consider your thoughts about a \$1W\$ design. But quite frankly, the \$9V\$ source just isn't going to cut it. The reason is that assuming perfect efficiency and no headroom required for the circuit itself, the speaker requires \$V_{peak} = \sqrt{2\cdot P\cdot R}\$. In your case, this works out to \$V_{peak} = 4V\$. This is above and below the ground reference your speaker requires. So you need \$\pm 4V\$. Of course, you say you want to use \$9V\$. But this leaves only \$500mV\$ from each rail and I just don't believe you can readily consider that. So a traditional design would require you to give up on the \$9V\$ battery. (And in any case, you will want some kind of ground reference -- there are nice ICs for this, but you'll need something.)

You do have an alternative if you are absolutely stuck on the idea of using a \$9V\$ source. You can go to a bridge-tied load configuration. In effect, this is two amplifiers sourcing from the same battery but with one of them \$180^{\circ}\$ out of phase with the other one. The speaker is then tied between the two amplifier outputs. This would get you there. But it greatly complicates your design. If you want to see one of these, take a look at the TDA8551 that I mentioned in an earlier comment to you. That is a BTL amplifier. But I don't think you want to go there. Looks like you are trying to get through a design of some kind (with only a tiny subset of the necessary specifications to do it.)

So this means you have to give up on the \$9V\$ power supply and accept something different. For now, let's assume you can accept \$\pm 6V\$ rails, with ground, and go from there. (Otherwise, I can't offer you much. No time to go around trying to explain a full BTL here.)

Let's assume you don't want horrible cross-over complications, but that you want a simple output stage, too. That means two BJTs with a pair of diodes to help spread apart the base voltages. That block looks like:







simulate this circuit &ndash; Schematic created using CircuitLab

Through those diodes, you will need a waterfall of current (shown as the drive current), which the output transistors can tap into. This current magnitude needs to be enough to drive the transistor bases. Since the peak \$I_c = \frac{4V}{8\Omega} = 500mA\$, and if we assume we can keep the BJTs out of saturation, then we can reasonably plan a gain of \$\beta=50\$ and estimate a maximum \$I_b = \frac{500mA}{50} = 10mA\$. We'll need a little extra available, though. Just in case. So let's set this up for \$15mA\$. A current mirror is handy. So let's add one:







simulate this circuit

(I'm ignoring temperature issues everywhere. And other effects. Just keeping this very, very simple.)

This current mirror allows me to set up a current flow from the \$+6V\$ rail down to the \$-6V\$ rail. Roughly speaking, I set up a current of about \$I_{drive} = \frac{+6V - 800mV - \left(-6V\right)}{680\Omega} \approx 16.5mA\$. Which is fine.

Now, we have to drive the thing. And now I have a serious issue. You didn't say what your source looked like, at all. I have no idea what you need for gain, no idea what loading is allowed on the input, and frankly nothing else about it. I'm clueless.

So I'm going to borrow a page from the other answer you got and just cheat. I'm going to use an opamp. Normally, though, that is not what you do. You will have a pre-amplifier that is designed for your input source, then you will have some perhaps variable gain, then you will drive the CTRL line I have above with a specialized circuit for that. (Possible Miller compensation for BJTs, too.) Then the above output stage. Then negative feedback of some kind is necessary.

(None of this takes into account that your speaker is a complex impedance and not a resistor, that some operator might short out the wires leading to the speaker, and ... well... oh, who cares? You didn't care about any of that, so neither do I.)

So let's just paste on an opamp to give you a fixed gain of 10 and to drive that CTRL line. I won't even bother with a separate current sink BJT. Instead, the opamp will need to be able to sink up to the full \$16.5mA\$ supplied by the current source as well as any PNP BJT base current that may also be required. So let's say at least able to sink \$30mA\$. If you don't like that, you can add a BJT to further lighten the load. I won't specify the opamp. But it will need to be able to get within about \$1V\$ of the bottom rail and perhaps within \$2.4V\$ of the top rail (because of those two diodes adding another \$1.4V\$.)

So here is the new circuit:







simulate this circuit

That should be able to reach about \$\pm 4V\$ on the output. There is still a lot to improve. But it gets the basic idea across. The opamp adjusts its output, sinking current while doing that. The current source sources current for \$Q_1\$ for the positive half of the cycle, leaving the opamp to sink the rest. Then \$Q_1\$ shuts off and \$Q_2\$ takes over for the negative half of the cycle and the opamp now has to sink not only the current source current but also any base current required for \$Q_2\$. That's why I said you need one that can sink up to the over-estimated \$10mA\$ base current of \$Q_2\$ plus the \$16.5mA\$ of the current source, or \$30mA\$ or better. (The opamp won't need to source, as that is what the current mirror is doing.) Also, keep in mind the output requirements for the opamp (within \$1V\$ of the negative rail and within \$2.4V\$ of the positive rail.)

Lots more needs to be discussed if you intend to actually make one of these and have it work reasonably well. I didn't care in the least about the wasted current during cross-over, where in this design it's very likely that both BJTs will be conducting a fair amount of current when the speaker drive voltage is near ground. And, I suspect, using the opamp is cheating. If so, there is lots more design work ahead for a discrete amplifier capable of \$1W\$ output and doing that safely into a speaker or some oaf shorting the speaker output leads, while allowing a nice volume control, plus supporting some one or two different specified kinds of input sources.