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Step of 8 2.020E Draw the differentiator circuit. i R i C 0A + V + - vo(t) - Figure 1 Step of 8 Consider the op-amp is ideal one. Consider in frequency domain, the resistor and capacitor are represented as R and 1 sC Apply Kirchhoff's current law at the inverting terminal of the op-amp. R sC R Therefore, gain of the differentiator is. sRC (1) Step of 8 Write the expression for time constant of the differentiator. Substitute 0.01 for and 10⁻² for in the equation. R 10⁻² Therefore, designed resistor and capacitor values of the differentiator are MO and respectively. Step of 8 Substitute for in equation (1). Magnitude of the differentiator is, wRC Phase of the differentiator is, Step of 8 Consider the value of frequency is, 10rad/s Determine the magnitude of the differentiator. wRC Substitute for R F for and 10 for in the equation. = =0.1V/V Therefore, magnitude at 10rad/sec is 0.1V/V The phase is independent of frequency and is equal to Step of 8 Consider the value of frequency is, Determine the magnitude of the differentiator. wRC Step of 8 Substitute for R F for and 10 for in the equation. =10V/V Therefore, magnitude at 10V/V The phase is independent of frequency and is equal to Step of 8 At high frequencies, input capacitor acts like short circuit and to limit the gain at high frequencies one resistor is added in series with capacitor. At high frequencies, the gain of the amplifier is, R R, Substitute 100 for G and 1MQ for R in the equation. 100 (neglect polarity of the gain) R, 100 Therefore, resistor connected in series with the capacitor is