GATE EC 2018 Question Paper (10-Feb-2018) (Shift 1)

For a unity feedback control system with the forward path transfer function

$\mathrm{G}\left(\mathrm{s}\right)=\frac{\mathrm{K}}{\mathrm{s}\left(\mathrm{s}+2\right)}$

The peak resonant magnitude Mr of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _______.

The figure below shows the Bode magnitude and phase plots of a stable transfer function

$\mathrm{G}\left(\mathrm{s}\right)=\frac{{\mathrm{n}}_0}{{\mathrm{s}}^3+{\mathrm{d}}_2{\mathrm{s}}^2+{\mathrm{d}}_1\mathrm{s}+{\mathrm{d}}_0}$



Consider the negative unity feedback configuration with gain in the feedforward path. The closed loop is stable for 𝑘 < 𝑘₀. The maximum value of 𝑘₀ is ______.

In the circuit shown below, the (𝑊/𝐿) value for M₂ is twice that for M₁. The two nMOS transistors are otherwise identical. The threshold voltage 𝑉${}_{\text{T}}$ for both transistors is 1.0V. Find Vₓ.

Note that 𝑉${}_{\text{GS}}$ for M₂ must be > 1.0 V.



Current through the NMOS transistors can be modelled as

${\mathrm{I}}_{\mathrm{DS}}=\mu {\mathrm{C}}_{\mathrm{ox}}\left(\frac{\mathrm{W}}{\mathrm{L}}\right)\left(\left({\mathrm{V}}_{\mathrm{GS}}-{\mathrm{V}}_{\mathrm{T}}\right){\mathrm{V}}_{\mathrm{DS}}-\frac{1}{2}{\mathrm{V}}_{\mathrm{DS}}^2\right)\mathrm{for}{\mathrm{V}}_{\mathrm{DS}}\le {\mathrm{V}}_{\mathrm{GS}}-{\mathrm{V}}_{\mathrm{T}}$

${\mathrm{I}}_{\mathrm{DS}}=\mu {\mathrm{C}}_{\mathrm{ox}}\left(\frac{\mathrm{W}}{\mathrm{L}}\right)\frac{{\left({\mathrm{V}}_{\mathrm{GS}}-{\mathrm{V}}_{\mathrm{T}}\right)}^2}{2}\mathrm{for}{\mathrm{V}}_{\mathrm{DS}}\ge {\mathrm{V}}_{\mathrm{Gs}}-{\mathrm{V}}_{\mathrm{T}}$

A solar cell of area 1.0 cm², operating at 1.0 sun intensity, has a short circuit current of 20 mA, and an open circuit voltage of 0.65 V. Assuming room temperature operation and thermal equivalent voltage of 26 mV, the open circuit voltage (in volts, correct to two decimal places) at 0.2 sun intensity is ________.

A junction is made between p⁻ Si with doping density N${}_{A1}$ = 10¹⁵ cm⁻³ and p Si with doping density N${}_{A2}$ = 10¹⁷ cm⁻³.

Given: Boltzmann constant k = 1.38 × 10⁻²³ J.K⁻¹, electronic charge q = 1.6 × 10⁻¹⁹ C. Assume 100% acceptor ionization.

At room temperature (T = 300K), the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be ________.