Unformatted text preview: speciﬁcation is that the overall gain of the system, i.e., the product a1 · · · an ,
is equal to Atot , which is given. a1 a2 an We are concerned about two eﬀects: noise generated by the ampliﬁers, and ampliﬁer overload.
These eﬀects are modeled as follows.
We ﬁrst describe how the noise depends on the ampliﬁer gains. Let Ni denote the noise level (RMS,
or root-mean-square) at the output of the ith ampliﬁer. These are given recursively as
N0 = 0, 2
Ni = ai Ni2 1 + αi
− 1/2 , i = 1, . . . , n where αi > 0 (which is given) is the (‘input-referred’) RMS noise level of the ith ampliﬁer. The
output noise level Nout of the system is given by Nout = Nn , i.e., the noise level of the last ampliﬁer.
Evidently Nout depends on the gains a1 , . . . , an . 90 Now we describe the ampliﬁer overload limits. Si will denote the signal level at the output of the
ith ampliﬁer. These signal levels are related by
S0 = Sin , Si = ai Si−1 , i = 1, . . . , n, where Sin > 0 is the input signal level. Each ampliﬁer has a maximum allowable output level
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.
- Fall '13
- The Aeneid