An amplifier with an input capacitance of Cin is to be ac-coupled to a preceding stage having an output resistance Rout . Considering both of the topologies depicted in Fig. 18.22 and allowing a maximum signal attenuation of 20%, determine the minimum value of the coupling capacitor and the

Question

An amplifier with an input capacitance of [latex]C_{i n}[/latex] is to be ac-coupled to a preceding stage having an output resistance [latex]R_{ ext {out }}[/latex]. Considering both of the topologies depicted in Fig. 18.22 and allowing a maximum signal attenuation of [latex]20 \%[/latex], determine the minimum value of the coupling capacitor and the resulting time constant if [latex]C_P=0.5 C_C or C_P=0.2 C_C[/latex].

Accepted Answer

In Fig. 18.22(a), the attenuation is given by [latex]A_v=C_C /\left(C_C+C_{i n} ight)[/latex], yielding [latex]C_C \geq 4 C_{i n}[/latex] for a 20% signal loss. The total capacitance seen from node X to ground is therefore equal to [latex]C_P+C_C C_{i n} /\left(C_C+C_{i n} ight)=C_P+0.8 C_{i n}[/latex]. It follows that the time constant is [latex]2.8 R_{ ext {out }} C_{ ext {in }} for C_P=0.5 C_C[/latex] and [latex]1.6 R_{ ext {out }} C_{ ext {in }}[/latex] for [latex]C_P=0.2 C_C[/latex].

In Fig. 18.22(b), [latex]C_P[/latex] itself attenuates the signal: [latex]A_v=C_C /\left(C_C+C_{i n}+C_P ight)[/latex], indicating that no value of [latex]C_C[/latex] can yield a signal loss of 20% if [latex]C_P \geq 0.25 C_C[/latex].

These calculations yield two important results. First, the topology of Fig. 18.22(a) is generally preferable. Second, the addition of a coupling capacitor, e.g., to isolate the bias levels, substantially degrades the speed.

Question 18.2: An amplifier with an input capacitance of Cin is to be ac-co...

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