Complicated capacitor LED driver model test

I decided to do the "LED experiment:" how fast can I charge a capacitor with a silicon 2N4123 transistor current follower — something like 10 µF — and how long will it for its charge to dissipate through the LED? In other words, how many LED's can I continuously refresh using this technique? My 20 mA LED that drops 2.2 volts will need about a 340 ohm resistor. It takes about 240 µs to charge a 5 µF capacitor to nearly full voltage — about 500 µs to squeeze in the last few millivolts. Dissipation takes only 650 µs to fall a full volt.

After a few iterations, I settled on a Darlington follower which drops the charge-time to 20 µs. Given a 1 µF capacitor, the rise time is below 10 µs and the decay runs for about 215 µs. If I move up to a 5 µF capacitor, the rise time stays below 10 µs but the decay jumps to 650 µs. If I then move up to a 10µs capacitor, the decay of 1 volt loss jumps to 1.4 ms.

Comparing to the prior pulse-width modulated test, I found the duty cycle needs to be about the same for the same brightness: 28 µs of the 2.1 ms cycle time or 1.3%, so I can theoretically drive 75 LED's in a perfect world.

Pulse-width modulated LED test

I played with a pulse-width modulated LED. The circuit wasn't pretty, but it worked … essentially a transistor amplifier that drives one differential input on an operational amplifier and the other is through a variable resistor set somewhere between the rails. The op-amp output drove an NPN transistor's base and the emitter was tied to ground. The collector went through a 1-ohm resistor through the LED to a 5-volt source — essentially, when the transistor was on, current followed a path through the LED, resistor, and the collector-emitter junction.

The peak-to-peak voltage on the 1 ohm resistor was 190mV, so in theory, I could have driven the LED to 200 mA average. The pulse-width modulator had a period of about 2.05 ms. The LED was barely on with a duty cycle of 14 µs which correlates to an average of 0.14 mA. It was "dim" around 50 µs or 4.9 mA. I considered it "fully on" at 134 µs which correlates to 13mA and "overdriven" by about 335 µs or 33mA. It appears the circuit works perfectly (and it doesn't appear to blow out the LED's.)

I also picked up some gray ribbon cable which I'll use inside the tubing to wire all the LED's.

Test polyethylene tubing

I tried out my idea of illuminating the polyethylene tubing and want to make sure a 12-inch spacing will look good enough. I quickly threw a test rig together and found the red clear LED's drop 2.2 volts, so the red LED needs a 340 ohm resistor for 20 mA with a 9-volt source. The red was adequate at a 12-inch spacing, throwing light about 3 inches down the tube — testing with brighter LED's should yield more perceived distance.

Standard red, focused LED's in polyethylene tubing