Preamplifier (2)

We went on to try cascading three gates as shown below to give a closed loop gain of 1000

Aol = 22 for a single stage, so ignoring loading effects Aol = 22 * 22 * 22 = 10,000 approx.

Acl = (Rf/Ri+Rf) * (Aol/(1+BAol)   

where B = Ri/(Rf+Ri) = 0.01/10.01 = 0.001 to three significant figures

whence Acl = (10/10.01)*(10,000/(1+10,000*0.001)) = 0.9990 * 909 = 908

By experiment we find Acl = 920 at input frequency Fin of 1kHz and Acl = 640 at Fin = 100kHz.
The three stage amplifier is suitable both in terms of available gain and bandwidth (140kHz) as an input preamp for our detector.  Apart from the IC it uses only four components.  (Not shown: supply decoupling C 0.01uF)
Note that as the input is AC coupled via C1 the circuit is self-biasing into its optimum DC condition.
 
An alternative design used three separate stages each designed for a gain of ten and then cascaded.  The circuit used lots more components and no benefit was noted, so we use the simpler circuit.