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 $$10.$$

An op-amp has an open-loop gain of $${10^5}$$ and an open-loop upper cutoff frequency of $$10$$ $$Hz.$$ If this op-amp is connected as an amplifier with a closed-loop gain of $$100,$$ then the new upper cutoff frequency is

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

A sample-and-hold $$(S/H)$$ circuit, having a holding capacitor of $$0.1$$ $$nF,$$ is used at the input of an $$ADC$$ (analog-to-digital converter). The conversion time of the $$ADC$$ is $$1\,\,\mu \sec ,$$ and during this time, the capacitor should not lose more than $$0.5\% $$ of the charge put across it during the sampling time. The maximum value of the input signal to the $$S/H$$ circuit is $$5V.$$ The leakage current of the $$S/H$$ circuit should be less than