Question 7.SP.1: (a) For the JFET amplifier of Example 4.2, use the drain cha......
(a) For the JFET amplifier of Example 4.2, use the drain characteristics of Fig. 4-6 to determine the small-signal equivalent-circuit constants g_m and r_{ds}. (b) Alternatively, evaluate g_m from the transfer characteristic.
(a) Let v_{gs} change by ±1 V about the Q point of Fig. 4-6(b); then, by (7.3),
Transconductance g_{m} \equiv {\frac{\partial i_{D}}{\partial v_{G S}}}\bigg|_{Q} \approx {\frac{\Delta i_{D}}{\Delta v_{G S}}}\bigg|_{Q} (7.3)
g_{m} \approx {\frac{\Delta i_{D}}{\Delta v_{G S}}}\bigg|_{Q} = {\frac{(3.3 – 0.3) \times 10^{-3}}{2}} = 1.5 \mathrm{{mS}}
At the Q point of Fig. 4-6(b), while v_{DS} changes from 5 V to 20 V, i_D changes from 1.4 mA to 1.6 mA; thus, by (7.4),
Source-drain resistance r_{d s} \equiv {\frac{\partial v_{D S}}{\partial i_{D}}}\bigg|_{Q} \approx {\frac{\Delta v_{D S}}{\Delta i_{D}}}\bigg|_{Q} (7.4)
r_{ds} \approx {\frac{\Delta v_{B S}}{\Delta i_{D}}}\Bigg|_{Q} = {\frac{20 – 5}{(1.6 – 1.4) \times 10^{-3}}} = 75\,\mathrm{kΩ}
(b) At the Q point of Fig. 4-6(a), while i_D changes from 1 mA to 2 mA, v_{gs} changes from −2.4 V to −1.75 V; by (7.3),
g_{m} \approx {\frac{\Delta i_{D}}{\Delta v_{G S}}}\bigg|_{Q} = {\frac{(2 – 1) \times 10^{-3}}{-1.75 – (-2.4)}} = 1.54 \mathrm{{mS}}