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## 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 $\hat{v}_{o}$?

## 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.