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

VDD M1 IR RL M2 -V DD