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There are actually a few ways to convert a single rail to split rail power supply, and this is probably one of the simplest ways. Instead of literally splitting the voltage of the power source and pulling half of it below 0V, we can actually create an artificial (virtual) ground at around 1/2Vcc. So instead of pulling the voltage down, we sort of pull the ground up. The topology is quite simplified, so don't expect good quality factors from the amp, but the most important thing this whole exercise does is that it removes the need for an output capacitor. This means more bandwidth, less distortion, better slew rate, and good square wave reproduction. You can clearly see that it looks quite like a split rail amplifier, the signal swings above and below a given point, which is normally accepted to be 0V, but in this case the ground point is pulled up to around 1/2Vcc. This gives a headroom of 20V above the ground reference point and 20V below it, much like a typical split rail PSU. There is one disadvantage to this method though. The lifted ground point is more noisy than a typical zero volt ground. This effect can be partially cancelled by filtering the noise, with bypass capacitors, but it still doesn't give a noise free ground. The problem is the high current that must pass through the speaker and into the virtual ground, and the residual noise iss hard to completely filter out. This is similar to a bridged amplifier, but one arm is not dynamic, as normal, but is kept static around a single point. It does however have a very nice advantage though. The two 22k resistors act as a DC current limiter and also as an automatic offset regulators. Basically they ensure that no DC current can pass through the speaker at any fault condition, and also they adjust the virtual ground voltage, to the same level the amp is set, so that the potential difference through the load is minimal (it ensures a constant output DC offset). So even if the output transistors drift in HfE the DC current through the speaker will never exceed a few mA .
It's all about the position of the ground! Place it to the positive of the supply and you pull everything below zero volts, place it on the negative side and you pull everything above 0V. Place it on the virtual ground we made and you split the power supply in the classic way between positive and negative, with 0V as the ground reference
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