Transistors

[Craig]

You did! And if beta changed, it would make very little difference as your potential divider for base bias is passing current which swamps it anyway.

However, I'd say that you haven't calculated input resistance, which is partly directly proportional to beta. The inherent transistor emitter resistance is 26 ohms, beta is 200 so we get 5.2k. This is much lower than the base bias divider, so input resistance is heavily dependent on beta, which could be critical if you are operating from a high-impedance source.

I'd also like to question the emitter bypass capacitor - for a low-frequency 3db cutoff of 10Hz, you want the capacitor'reactance to equal the emitter internal resistance (26ohms)  in parallel with the external 1k, and this gives 628uF, not 16uF!

Well, given the original poster I was trying to keep it simple - but you're right the input R is relatively small . However I thought a treatise on bootstrapping would be a bit OTT in the context of this thread.

You're right about the bypass capacitor though - I must admit I was surprised that it was so small, and just plain forgot it is determined by re and not Re. Of course you can reduce the value considerably by reducing the collector current. At 200uA Ic, re is 130 ohms, and you can get away with 120uF.

The other way around it is to go for a lower gain - say 50 instead of the re calculation that leads to 180 and a monster capacitor. Keep Ic at 1mA. So you split the emitter resistor into a resistor of 4700/50 = 94, subtract 26 ohms re to get a 68 ohm physical resistor, and a bypassed 1k. Then the capacitor is determined by 94 ohms and not 26, which gives 150uF, which is still quite large.

Then go for 200uA (a more common operating point, usually determined by noise), which leads to Rc ~ 22k and Re ~ 4.7k. Go for a gain of 50, giving an unbypassed Re of 440 - re (130 ohms) = 310 ohms, and a bypassed resistor of 4.3k. So the bypass capacitor is now 36uF. Do some rounding and go for 330 ohms and 3.9k with a 47uF capacitor. Gain is then 22k/460 = 48 with a 3dB frequency of ~ 7.5Hz.