$8.$ You are to design a common$-$emitter bipolar transistor amplifier using the techniques developed in class for the four$-$resistor bias design. The design shall provide a nominal collector bias current of $125$ uA and gain target of $\backslash (-80\backslash$mathrm$\{$~V$\}/\backslash$mathrm$\{$V$\}\backslash )$ assuming an AC coupled load of very large resistance and an AC coupled small$-$signal input source with very low output resistance. For the transistor spec, use $\backslash (\backslash$beta$=200,\backslash$mathrm$\{$~V$\}\_\{\backslash$text $\{$BEon $\}\}=0\mathrm{.}7\backslash )$ Volts, $\backslash (\backslash$mathrm$\{$n$\}=1\backslash ),$ and $\backslash (\backslash$mathrm$\{$v$\}\_\{\backslash$mathrm$\{$t$\}\}=25\backslash$mathrm$\{$mV$\}\backslash ).$ The circuit is provided a single supply voltage of $5$ Volts. Design for a nominal base voltage bias of $2$ Volts. $($Requested schematics are required!$)$

Provide both the small$-$signal midband circuit schematic and the full circuit schematic for your design and calculate the values of the four biasing resistors. Coupling capacitors should be shown in the full circuit schematic, but the values need not be calculated.