For the op-amp circuit shown in figure. Determine the output voltage $${v_0}.$$ Assume that the op-amps are ideal

A simple active filter is shown in figure. Assume ideal op-amp. Derive the transfer function $${v_0}/{v_i}$$ of the circuit, and state the type of the filter (i.e., high-pass, low-pass, band-pass, or band-reject). Determine the required values of $${R_1},{R_2}$$ and $$C$$ in order for the filter to have a $$3$$-$$dB$$ frequency of $$1$$ $$kHz,$$ a high frequency input resistance of $$100\,\,k\Omega $$ and a high frequency gain magnitude of $$10.$$

The transistor in the amplifier circuit shown in the figure is biased at $${{\rm I}_C} = mA.$$ Use $${V_T}\left( { = {{kT} \over q}} \right) = 26\,mV,$$ $${\beta _0} = 2000,\,{r_b} = 0$$ and $${r_0} \Rightarrow \infty $$
$$(a)$$ Determine the AC small signal midband voltage gain $$\left( {{\raise0.5ex\hbox{$\scriptstyle {{V_o}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {{V_i}}$}}} \right)$$ of the circuit
$$(b)$$ Determine the required value of $${C_E}$$ for the circuit to have a lower cutoff frequency of $$10Hz$$

In the single stage transistor amplifier circuit shown in figure, the capacitor $${C_E}$$ is removed. Then the ac small signal midband voltage gain of the amplifier