Figure 8.53 shows a two-stage amplifier, where νS =VScos(2πf0t), with f0=80Hz and VS=5mV. Assume the op amps are ideal. The source resistance and the output resistances of the individual amplifiers are negligible. (a) Assume the coupling capacitors are conductors and specify the resistances R1

Question

Figure 8.53 shows a two-stage amplifier, where [latex] u_S=V_S \cos \left(2 \pi f_0 t ight) [/latex], with [latex] f_0=80 Hz [/latex] and [latex] V_S=5 mV [/latex]. Assume the op amps are ideal. The source resistance and the output resistances of the individual amplifiers are negligible.

(a) Assume the coupling capacitors are conductors and specify the resistances [latex] R_1, R_2 [/latex] such that the overall voltage gain is [latex] A_ u=2,500 [/latex].

(b) Specify the coupling capacitors such that the overall voltage gain for [latex] f \geq f_0 [/latex] equals or exceeds [latex] 0.8 A_ u=2,000 [/latex] .

Accepted Answer

(a) The overall voltage gain is given by

[latex] A_ u=\frac{V_{L r m s}}{V_{S r m s}}=k_1 k_2\left(\frac{R_2}{R_1} ight)^2, [/latex]

where

[latex] k_1=\frac{V_{2 r m s}}{V_{1 r m s}}, k_2=\frac{V_{L r m s}}{V_{3 r m s}} . [/latex]

If the capacitors are conductors, then [latex] k_1 \cong 1, k_2 \cong 1 [/latex] , and

[latex] A_ u=2,500 \cong\left(\frac{R_2}{R_1} ight)^2=(50)^2 \Rightarrow R_2=50 R_1. [/latex]

We choose

[latex] R_2=1 M \Omega \Rightarrow R_1=20 k \Omega . [/latex]

(b) Let [latex] k_1=k_2=\sqrt{0.8} [/latex] for [latex] f=f_0 [/latex] . From (8.71)

[latex] C_1 \geq \frac{k_1}{2 \pi f_0 R_2 \sqrt{1-k_1^2}}, C_2 \geq \frac{k_2}{2 \pi f_0 R_3 \sqrt{1-k_2^2}} [/latex] (8.71)

[latex] C_1=C_2=\frac{\sqrt{0.8}}{2 \pi f_0 R_1 \sqrt{1-0.8}}=199 nF \cong 200 nF. [/latex]

Question 8.25: Figure 8.53 shows a two-stage amplifier, where νS =VScos(2...

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