bv_cvxbook_extra_exercises

We limit the total power to one for simplicity we

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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 Mi...
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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.

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