For the circuit in Example 18.5, compare the values obtained for the gain of the circuit when using the expressions of Equations 18.7, 18.8 and 18.9, assuming that g_{m} = 72 mS and r_{d} = 50 kΩ.
\frac{v_{o}}{v_{i}} \approx – \frac{R_{D}}{R_{S}} (18.7)
\frac{v_{o}}{v_{i}} \approx – \frac{g_{m}R_{D}}{1 + g_{m}R_{S} + \frac{R_{D} + R_{S}}{r_{d}} } (18.8)
\frac{v_{o}}{v_{i}} \approx – \frac{g_{m}R_{D}}{1 + g_{m}R_{S}} (18.9)
From Equation 18.7 we have
\frac{v_{o}}{v_{i}} \approx – \frac{R_{D}}{R_{S}} = -\frac{3.3 kΩ}{1 kΩ} = -3.3From Equation 18.8 we have
\frac{v_{o}}{v_{i}} \approx – \frac{g_{m}R_{D}}{1 + g_{m}R_{S} + \frac{R_{D} + R_{S}}{r_{d}} } = – \frac{72 × 10^{-3} × 3.3 kΩ}{1 + 72 × 10^{-3} × 1 kΩ + \frac{3.3 kΩ + 1 kΩ}{50 kΩ} } = -3.251From Equation 18.9 we have
\frac{v_{o}}{v_{i}} \approx – \frac{g_{m}R_{D}}{1 + g_{m}R_{S}} = – \frac{72 × 10^{-3} × 3.3 kΩ}{1 + 72 × 10^{-3} × 1 kΩ }= -3.255It can be seen that, in this case, the simple expression in Equation 18.7 produces a value that agrees quite closely with the values obtained using the more complete expressions.