$2\mathrm{.}2$ In the following circuit Cir $2\mathrm{.}2,$ calculate R$1,$ R$2,$ RC and RE to achieve gain of $10.$ Note the followings:

The supply voltage is $5$ V $.$ Choose collector current around $1$ mA $.$ Choose R$1$ and R$2$ such that the design is independent of Beta. Choose RE such that the design is not prone to VBE variations. $($Hint: Use low values for RE$)$ Choose RC to get gain of $10.$ Choose Q$1$ as $2$N$4401.$

$2\mathrm{.}3.$ Simulate the above circuit using SPICE to verify your calculations. Note the followings: The frequency of interest is $1$ kHz $.$ Choose C$1$ such that it does not affect the AC output but it is not too large, either. Start with $10$ micro$-$farad capacitor and reduce it until it starts affecting AC amplitude then decide on the value of C$1.$ Gain: Apply a $10$ mV peak sine$-$wave to the input, check the output waveform using transient analysis. By dividing the output amplitude to the input amplitude find the gain.

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