When the distortion is small, the second and third harmonic-distortion terms of an amplifier can be calculated from the small-signal gains at the quiescent and extreme operating points. Starting with the power series given in (5.41),

(a) Calculate an expression for the small-signal gain A_v = dv_o/dv_i.

(b) Let v_i =vÌ‚_i sin ωt as in (5.52), and derive expressions forA⁺_v ,A_vQ, and A^ˆ’_v as defined in Problem 5.7.

(c) Define two normalized differential gain error terms as

(i) E⁺ = (A⁺_v ˆ’  A_vQ)/A_vQ

(ii) E^ˆ’ = (A^ˆ’_v ˆ’ A_vQ)/A_vQ

and calculate expressions for (E⁺ + E^ˆ’) and(E⁺ ˆ’ E^ˆ’).

(d) Compare the results of part (c) with (5.54) and (5.57) to calculate HD₂ and HD₃ in terms of E⁺ and E^ˆ’.

(e) Use the results of part (d) and Problem 5.7 to calculate HD₂ and HD₃ for the circuit of Fig. 5.8 under the conditions given in Problem 5.7. Compare the results to the results of the Example in Section 5.3.2.

Figure 5.8

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VDD M1 IR RL M2 Мз -V DD