Ever notice a constant clicking from your TiVo? It is somewhat faint but can be heard easily in a quiet room such as a bedroom at night. Surprisingly, what you hear is probably NOT the hard drive, but rather the fan.
The TiVo uses Pulse Width Modulation (PWM) to drive the fan. So rather than adjusting the voltage from, say, 7V for low speed up to 12V for high speed, the TiVo sends pulses of 12V at around 32hz to the fan. The longer the pulse (and shorter the pause between pulses), the faster the fan spins. This has many a couple advantages for these types of fans, which I won't go into, but one disadvantage: At low speeds it causes the fan to "click" at that same 32hz.
This is a well-documented phenomenon:
This URL actually includes a circuit for fixing it too:
However, that requires a capacitor, resistor and a transistor. My solution is much simpler.
Just add an appropriately-sized electrolytic capacitor in parallel with the fan. I've found that "appropriately-sized" is best found through trial and error. My S3 required only 7uF (4.7+2.2 in parallel) but my TiVo HD (with an after-market fan) required 47uF. If you select a value too small it won't do anything. If you use one too large, the capacitor will end up driving the fan while the PWM is off, resulting in a fan that runs at full speed no matter what the PWM is doing. Select just the right value and it "rounds" out the square-ish wave of the PWM signal which seems to prevent the motor of the fan from clicking while still allowing the TiVo to control the fan's speed.
Now, I'm not an EE but I did poke around with a scope to see the effects on the PWM signal, which I've attached for anyone interested.
Standard warnings apply: you will void your warranty taking apart your TiVo, and this is clearly a hack and may have detrimental side effects.
I can tell you that this has been running fine in my S3 for 4 months and my TiVo HD for... about 12 hours.