OK, I'll tell you how to make a non electrolytic Simple for very little money, but you will need to do some serious experimenting.
You already have the power supply figured out. Motor run caps. So build your board, wire in some motor run caps, leave the cathode bypass caps out, and test the board. The gain will be low without the caps, but you should still get sound. You can tack some caps on the back of the board to test if you want. It is always a good idea to start with a working board otherwize you won't know if your experiment was successful.
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The area I am not too sure on is 6.3v 1500uf Cathode bypass cap. How low of a value can I go here.
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I use oversize capacitor values in my amplifier designs. There is a real reason for this despite what some "experts" say in other forums. I took a bunch of capacitors into work and tested them on a fancy HP component analyzer. Real capacitors are not perfect, they have a resistance and an inductance associated with them. I simply tested a bunch of caps and picked the ones that had the lowest ESR and ESL. I guess that is the engineer in me. I doubt that you han hear the difference with any good cap over 200uF.
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Remember, there is no cap like no cap.
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OK, lets run with that. If we want NO CAP, how do we get NO CAP? Ask yourself, what would SY do? You guessed it LED's. Using an LED for the cathode of the 12AT7 works good. I have done it. No cap and no resistor, just an LED. The catch......you need the right LED. LED's are quite variable as to their forward voltage drop for different part numbers of the same color. 12AT7's are quite variable as to the cathode voltage required to get a reasonable plate voltage. The current is fixed by the CCS chip. It is possible that the two sections of a given tube are different enough to require two different colored LED's.
Finding the right LED requires some experimenting and a bunch of LED's. I soldered a pair of alligator clips on short wires into my board and started trying a bunch of LED's. You want an LED that puts the plate voltage in the 175 to 250 volt range. A more technical approach is to put your chosen 12AT7 in your working Simple SE and measure the cathode voltage. Then look for an LED that has that much forward voltage at 10 mA.
OK now what do you use for the cathode bypass in the output stage? I would be tempted to wire a few motor run caps together and hide them under the deck, but there may be other alternatives. LED's? Well yes this is possible, but it will take a BUNCH of LED's. Yes, I have tried it. Yes it works, and yes the amp lights up the whole room! I have a friend who builds all sorts of Gizmos using PIC chips and LED's and he buys LED's by the hundreds from a vendor in Hong Kong. There are some big LEDs available now that operate at 100+ mA and drop 3 or 4 volts. They are blue or white and are often sold as "1 watt" LED's even though they run at about 1/2 watt. He brought over a bunch and we wired some into a Simple SE. I think we had 12 in series in each channel to get the current right.
Another possibility is to use a big zener diode. It would take a 10 watt zener diode. The voltage would need to be the same as the cathode voltage measured on the same tubes in the board with cathode resistors. I have not tried this yet though.
It has been suggested to use fixed bias. I have done this, but a negative voltage source is required. This implies another power supply.
