GATE EE 2023 Question Paper (05-Feb-2023) (Shift 1)

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is

Consider the OP AMP based circuit shown in the figure. Ignore the conduction drops of diodes D₁ and D₂. All the components are ideal and the breakdown voltage of the Zener is 5 V. Which of the following statements is true?

Consider a lead compensator of the form

$\mathrm{K}(\mathrm{s})=\frac{1+\frac{\mathrm{s}}{\mathrm{a}}}{1+\frac{\mathrm{s}}{\beta \mathrm{a}}}$, β > 1, α > 0

The frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of 𝐾(𝑠), is 6 dB. The values of 𝑎, 𝛽, respectively, are

A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is −400 W and the line current is 𝐼${}_{\text{R}}$ = 2 A (rms), then the power factor of the load per phase is

An 8 bit ADC converts analog voltage in the range of 0 to +5 V to the corresponding digital code as per the conversion characteristics shown in figure. For 𝑉${}_{\text{in}}$ = 1.9922 𝑉, which of the following digital output, given in hex, is true ?