NEGATIVE VOLTAGE FEEDBACK AND THE STABILIZED GAIN AMPLIFIER 



without feedback, the amphtude and frequency distortion may be known 

 and tolerable, but the gain is likely to vary a lot as valves and batteries wear' 

 out. If the proposed experiment is designed so that the amplifier is part of a 

 null detector, or if a cahbrating input is always available, gain instability 

 does not matter. If not, it does, and gain stability is achieved by negative 

 feedback. 



Suppose we have a direct coupled amplifier possessing three similar inter- 

 stage couplings whose upper turn-over frequencies are 10,000 cycles. Suppose 

 the voltage gain is 100,000 times and we try to reduce this to 1,000 by negative 

 feedback. Then 1/5 = 1,000, B = 0-001, and AB = 100, which is unques- 

 tionably much greater than 1, so we ought to be all right. When we try it 

 out, however, we find the whole device oscillates violently at about 17,500 c/s. 

 Why? 



In the expression gain = Al{l + AB), if AB is positive, the feedback is 

 negative and the gain is less than A. If AB is negative but not as negative 

 as —1, the feedback is positive and the gain is more than A. When AB = — 1, 

 the gain is infinite, which means that the output can be finite when there is 

 no input, i.e. the device oscillates. 



In practice A is complex, as there is both gain and phase shift. Let it be 

 ae^^, where a is the modulus of the gain and 6 the shift phase. Then the 

 gain expression is (oLe^^)l(\ + cuBe^^). In the pass-band of the amplifier d is 

 small, e^^ is nearly unity, so that a/(l + ^B) is substantially correct for the 

 gain expression. Outside the pass-band there is appreciable phase shift and 

 e^^ is important. The gain expression goes to infinity when a5e^^ := — 1. As 

 01.B is real and positive, e^^ must be real and negative and the solution for 

 must be 1 80 degrees and for a5, +1- a5 is called the 'loop gain' of the system, 

 and Q is of course the total amplifier phase shift. Oscillation will occur if the 

 loop gain exceeds 1 at the frequencies where the total phase shift is 180 degrees. 



In the case under consideration there is one such frequency. At the upper 

 end of the pass-band the intervalve couplings are acting as low-pass filters 

 and introducing phase lag. As there are three of them and they are similar, 

 oscillation occurs when the phase shift of each is 60 degrees, and reference to 

 Graphs 9 and 10 shows that this happens at co = 1-751 RC and that at this 

 frequency | Kout/ J^inl = 0-5. As the couplings turn over at 10,000 c/s, oscilla- 

 tion will occur at 1-75 X 10,000 = 17,500 c/s, because the loop gain = 100 X 

 0-5 X 0-5 X 0-5 = 12-5, which is more than 1. 





Figure 11.3 



To prevent the oscillations we have to reduce the gain at 17,500 c/s whilst 

 leaving it as unaffected as possible in the pass-band, and without introducing 

 any more phase shift. This may be done by modifying the anode load of one 

 of the stages as in Figure 11.3, giving us the low-pass circuit which is the 



165 



