Chapter 7
Q. 7.9
For the CE amplifier specified in Example 7.8, what value of Re is needed to raise Rin to a value four times that of Rsig? With Re included, find Avo, Ro, Av , and Gv. Also, if \hat{v}_{π} is limited to 5 mV, what are the corresponding values of \hat{v}_{sig} and \hat{v}_{o}?
Step-by-Step
Verified Solution
To obtain Rin = 4 Rsig = 4 × 5 = 20 kΩ, the required Re is found from
20 = (β +1)(re +Re)
With β = 100,
re + Re \simeq 200 Ω
Thus,
Re = 200 − 25 = 175 Ω
A_{vo} = -α \frac{R_{C}}{r_{e} + R_{e}}
\simeq – \frac{5000}{25 + 125} = −25 V/V
Ro = RC = 5 kΩ (unchanged)
A_{v} = A_{vo} \frac{R_{L}}{R_{L} + R_{o}} = -25 × \frac{5}{5 + 5} = -12.5 V/V
G_{v} = \frac{R_{in}}{R_{in} + R_{sig}} A_{v} = -\frac{20}{20 + 5} × 12.5 = −10 V/V
For \hat{v}_{π} = 5 mV,
\hat{v}_{i} = \hat{v}_{π} \left(\frac{r_{e} + R_{e}}{r_{e}}\right)
= 5 \left(1 + \frac{175}{25}\right) = 40 mV
\hat{v}_{sig} = \hat{v}_{i} \frac{R_{in} + R_{sig}}{R_{in} }
= 40 \left(1 + \frac{5}{20}\right) = 50 mV
\hat{v}_{o} = \hat{v}_{sig} × |Gv|
= 50 × 10 = 500 mV = 0.5 V
Thus, while |Gv| has decreased to about a third of its original value, the amplifier is able to produce as large an output signal as before for the same nonlinear distortion.