## Chapter 7

## Q. 7.9

For the CE amplifier specified in Example 7.8, what value of R_{e} is needed to raise R_{in} to a value four times that of R_{sig}? With R_{e} included, find A_{vo}, R_{o}, A_{v} , and G_{v}. 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 R_{in} = 4 R_{sig} = 4 × 5 = 20 kΩ, the required R_{e} is found from

20 = (β +1)(r_{e} +R_{e})

With β = 100,

r_{e} + R_{e} \simeq 200 Ω

Thus,

R_{e} = 200 − 25 = 175 Ω

A_{vo} = -α \frac{R_{C}}{r_{e} + R_{e}}

\simeq – \frac{5000}{25 + 125} = −25 V/V

R_{o} = R_{C} = 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} × |G_{v}|

= 50 × 10 = 500 mV = 0.5 V

Thus, while |G_{v}| 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.