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Sorry PRR, we have hijacked your thread!
Ahem...
I started with a single-sided amp, shown on left. On right is two of these amps in push-pull, with a single feedback network:
Note how elegantly the feedback comes together. One objection to the single-ended form is that DC flows through the resistor we would use to set gain, so gain changes upset DC conditions. In push-pull, it doesn't. (You ask "Where's the DC?"... wait.) By changing the "20 ohm" resistor, the gain can be varied over a wide range, even down to Unity Gain which is sometimes handy. The "20 ohm" resistor (which you may remember adds to the noise of the 200 ohm mike) can go to 100 ohms (very little increase of noise) at gain of 26dB, whereas other mike-amps with higher impedance gain networks tend to have higher noise at gain of 40dB or 30dB. And as shown, it amplifies differential signals but not common mode signals.
Let's rough-out some operating parameters.
The first stage emitter current, for good low noise in microphone impedance, will be in the range of 1mA to 10mA. 3mA seems to be effective with available devices. The exact value will change when we double-up to make it differential. Also we may find a need to run some other current level. But pencil-in "3mA?".
The output stage has to carry enough current to feed the load and the feedback. In this case the feedback load is small compared to some loads we may face. To be faultless in a "Pro" studio, we are expected to be able to deliver voltages like +18dBm or +24dBm into 600 ohms, around 10V RMS and around 24mA peak if you actually have a 600 ohm load. The output stage bias current has to be at least this high. In fact in a resistance-coupled stage it has to be much higher. But for the moment pencil-in "24mA?".
But what currents? Here we have no DC path at all! Ooops!
A resistor or two to ground is logical, but interacts with the gain-set network and limits minimum gain and sets a significant common-mode gain. So let's try a couple of current sources. I've drawn them as transistors, and penciled-in the rough-guess operating currents:
What is the maximum gain possible? What is the open-loop gain (the "20 ohm" resistor set to zero)?
Remember that the emitter impedance of a silicon BJT is about 30/I, where I is current in milliAmps. And the base impedance is about Beta times higher. So the first stage, with 3mA current, has about 10 ohms emitter impedance. The second stage's emitter at 24mA will be around 1.3 ohms. Assume this transistor's Beta is 100 (just for rough-guess). The collector resistor on the first stage will probably be 0.6V/3mA or about 200 ohms. The base impedance of the second stage is about 1.3*100 or 130 ohms. 200||130 is about 70 ohms. First-stage voltage gain is about 70/6= 5. Second stage gain (unloaded) is the 1K load resistor over the 1.3 ohm emitter impedance or 1000/1.3= 770. Total gain is then 5*770= 3,800. This is just over 71 dB, and there is nothing to really stabilize the gain against variation except the feedback. And I have ignored collector impedance, which will reduce the 2nd stage gain from 770 to more like 500. We probably should not ask for 60dB of closed-loop gain. So it is close to a "good" design, but needs a little more.
Go back to the question about output current and load. What is the best output configuration for a resistance-coupled amplifier? There are several answers. It really depends how wasteful you can afford to be, and which way. Remember that a BJT can pull-down to nearly zero volts, but in a resistance-coupled amp the load only pulls-up as much as that DC load resistance can pull. In general you bias a transistor so its collector-emitter voltage is a little more than the peak AC voltage you need, and then wrestle with the resistor. If you have a power supply voltage much-much larger than the peak output voltage, you use a resistor much larger than the load resistance and set the transistor idle current to a little more than the peak AC signal. If you have a low supply voltage, you may have to idle at much more than peak AC output current so the resistor has enough "slack" to yank the load around when the transistor current falls. Here we seem to be in the intermediate case: we don't have a lot of excess supply voltage, and we don't want a lot of supply current. A rule of thumb to get you in the ballpark is: use a DC load resistor equal to the AC load, bias the transistor to sit at 1/3rd the supply voltage and twice the peak AC load current.
In this case each side of the amp sees half of the 600 ohm load, so those "1K" resistors "should be" 300 ohms. For other reasons, we will lose 10 or 12 volts off the bottom, so we have 36V supply. If the transistors get 1/3rd, the resistors get 2/3rd. 2/3rd of 36V is 24V. 24V/300ohms is 80mA per side, 160mA per complete amplifier, which times 48V is over 7 Watts total dissipation! I told you it was power-hungry!
The maximum efficiency of a resistance-coupled power amplifier is about 8%. This amp more like 5%. A transformer-coupled amp makes 50% on paper and 40%-20% in practice. Class B is 78%, and a typical audio op-amp chip runs around 50% when maxed-out. If you must meet a specific dBm output level spec, a resistance-coupled output needs about 10 times the power supply of a chip. Worse, since the resistance coupled amp eats full power all the time, while a class AB chip idles stone-cold, and a console is almost never asked to deliver full-power full-load sines on all outputs at once. The resistance coupled amp is such a pig for power that you almost never see it done above a couple milliwatts output in commercial products. But scroungers like us may turn-up power parts at surplus prices. And there is an element of "Mine is bigger (and hotter) than yours!". So what the heck, eat power.
Still, with those values, it can make nearly 24V peak in 600 ohms, which is nearly +27dBm. We don't need that much.
Also: the closed-loop voltage gain is a function of these load resistors. If we can get a little more voltage gain, we would like to set the feedback for 60dB or more closed-loop gain. With two 300 ohm resistors, the middle resistor (gain-set) has to be 0.6 ohms. This is a suspiciously low value... can we really get an accurate 0.6 ohms?
Another problem: on paper, all the DC can balance. In fact, the two input devices are never going to be exactly matched. Using the monolithic matched-pairs, there will be several milliVolts of offset across the gain-set resistor, partly Vbe mismatch but mostly base bias resistor and Beta mismatch. That might be tolerable in a fixed-gain amp, but one sweet feature is the simple way we can change gain from around 1,000 to about 1. But this really needs a switch (there is no pot with over 60dB range and under 1 ohm minimum usable setting), which will want to interrupt that milliVolt offset and make milliVolt pops, which when amplified by gain=1,000 will be awful loud.
So we need a DC blocking cap in series with the gain-set resistance, which needs to be very low. And since it has an unknown DC polarity (+ or -) across it, it needs to be bipolar. What is the biggest nonpolar cap I can conveniently buy? DigiKey lists a Panasonic 6,800uFd nonpolar, at a tolerable price. When faced with a 1 ohm resistor, this gives -3dB at 26Hz, -1dB at 52Hz. That's at maximum gain; bass response improves as gain is reduced. And since high gain tend to bring up room rumble, I'm not sure we really want 2Hz bass response at maximum gain, though it is useful at lower gains.
So all things considered, I went for two 500 ohm DC load resistors and a 1 ohm gain-set resistor for 60dB gain. And then fudged again to the standard value of 470 ohms, which is only 0.54dB "off". We can't fret about half-dBs, because with open-loop gain of only 71dB the "60dB" gain-set resistor will have to be well under 1 ohm.
Oh, why bias the input bases at 10 or 12 volts? They can't sit at ground: the emitters will be 0.6V negative of the bases, plus we need a few volts across the current sources. But the bases and emitters also must follow the input voltage, both differential and common mode. Since the gain can go near unity, the input differential voltage may be several volts. And in some situations the common mode voltage is several volts. Though we hope it is much less, this type of clipping on "signal" that is rejected further up the system will give mysterious splats and buzzts. We really need to bias the inputs up enough to cover any likely signal and common-mode voltage, plus our Vbe and current-source biases.
And we will need input and output coupling capacitors and DC bias/leak resistors.
Conceptually we arrive at this:
In my next chapter I will try to show that the gain and distortion of this design is not that great, and can be improved fairly simply. I've also omitted details of stabilization against RF oscillation and DC bias.
