> Perhaps you object...Don't have a cow. I'm not picking on you. Or that 741. I kinda like 741s, in their place.
The question is: when you have a big cap on the output of an amplifier, who is in charge? The cap or the amplifier?
For the medium power devices we are likely to use, with anything like the suggested 440µFd hanging on its output, over most of the audio band, the cap is in charge and the amplifier isn't important to the sound.
But also, as shown, the amplifier is not going to be happy. The 440µFd load is nearly a dead-short over most of the audio band. In this case, and for most reasonably similar cases, the op-amp's gain essentially vanishes above about 40Hz due to the heavy capacitive loading.
In this specific case, it would be mildly happier if the feedback were taken from the other end of the 10Ω resistor. That increases the DC impedance. And the op-amp is still very heavily loaded. It would start to work like an op-amp if the resistor were changed to say 100Ω, but that would reduce the DC balance.
And here's where the nub of the problem lays. Why are elegant designs like Cmoy's so prone to showing large DC error? Why are we talking about ultra-beefy rail-splitters that pit caps against chips in a fight that I am not sure we can win?
Look at the Cmoy from the DC point of view:
I've used new part-numbers, so refer to this drawing instead of Cmoy's. Ignore the 1G resistor, that was just to keep SPICE from puking. The 1mV "battery" is a realistic offset-voltage for a chip-amp. In Cmoy's defense, he did not have a 32Ω load in mind, and the problem is far less with higher loads. But people who use 32Ω loads do have big DC offset. Why?
I'm sure Tangent and FA will follow this explanation. The typical 1mV offset, when fed-back, forces 1mV across R7. The ratio R7/R6 forces 10mV across R7. We have 11mV across R6+R7.
That also means 11mV across Rload. If Rload is 32Ω, then 0.011V/32Ω= 0.34mA DC flows through Rload. The only place this can come from is Rsplitter, which is in effect two 10K resistors in parallel (via the power battery) or 5K. 0.34mA times 5KΩ is 1.7V DC.
The point that should be "half-way" between battery terminals is 1.7V away from half-way!
Somehow a 1mV error has been multiplied 1,732:1 !
The audio (and DC) gain of the op-amp and R6-R7 is 11:1.
But Rload and Rsplitter create a second gain-set loop. If Rload is 32Ω and Rsplitter is 5KΩ, then this ratio is 32/5000= 156:1. This multiplies the basic 11:1 gain. 156*11= 1,719.
Any DC error in the op-amp becomes 1,700 time larger at the "halfway" point.
Note that if Rload is 300Ω, as Cmoy intended, the multiplication is only 194:1. A 1mV op-amp error becomes a fairly mild 200mV error at the halfway point.
In either case, the DC across the headphones (for a single channel) is 11*Vo where Vo is offset voltage. Typically 11mV. (However it does get messy when we have two channels on one jack and one splitter.) The headphones won't fry. Actually it works well, except headroom is reduced as "halfway" error rises. 1.7V error here is 1.7V less peak output level on one side of the wave. Since music is statistically symmetrical, this is like 3.4V less peak-to-peak level.
The answer is a lower splitter impedance. Using a passive splitter, we could go to a pair of 1K resistors. Rsplitter is then 500Ω, halfway error tends to be more like 0.17V, which is no big deal on 9V supply. However two 1K resistors is a 4.5mA drain, which is more than some chips, and liable to impact battery life.
I think in many cases, a pair of 2.2K resistors bypassed with BIG caps is a very happy solution.
But how big? What does it matter what the output impedance is?
If the splitter impedance is "dirty", such as an amplifier with crossover distortion, that will get into the audio. And for impedances like ours, we need much-much more than 1mA transistor current to eliminate crossover (feedback masks it but IMHO not very well). Also any amplifier doubles your power consumption because it lacks energy-averaging/storage over the audio cycle. A biased electrolytic cap is actually a pretty clean low-Z device and very efficient.
If the impedance is clean, how low does it have to be? For less than 1dB power loss it should be under 1/10th of load impedance, say 3 ohms. But with common-ground stereo any impedance causes crosstalk. A high-spec 40dB at 20Hz suggests 25,000µFd! However perception and recording practice tends to eliminate stereo in the bass. 26dB separation at 100Hz gives 1,000µFd, a very reasonable value.
With two 2.2K resistors and two 470µFd caps, there is no doubt "who is in charge". There is no active device straining to fight a big storage capacitor. It is conceptually elegant.
[Edited by PRR on 04-15-2004 at 02:31 PM.]
posted 04-15-2004 02:27 PM CST (US) 
