GATE EC 2023 Question Paper (05-Feb-2023) (Shift 2)

In an extrinsic semiconductor, the hole concentration is given to be 1.5𝑛${}_{\text{i}}$ where 𝑛${}_{\text{i}}$ is the intrinsic carrier concentration of 1 × 10¹⁰ 𝑐𝑚⁻³ . The ratio of electron to hole mobility for equal hole and electron drift current is given as __________ (rounded off to two decimal places).

The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $(\mathrm{s})=\frac{\mathrm{k}(\mathrm{s}+\mathrm{z}{)}^{\mathrm{a}}}{{\mathrm{s}}^{\mathrm{b}}(\mathrm{s}+\mathrm{p}{)}^{\mathrm{c}}}$, where 𝑘, 𝑧, 𝑝, 𝑎, 𝑏 and 𝑐 are positive constants. The value of (𝑎 + 𝑏 + 𝑐) is __________(rounded off to the nearest integer).

Let x₁(t) = u(t + 1.5) − u(t − 1.5) and x₂(t) is shown in the figure below. For y(t) = x₁(t) ∗ x₂(t), the ${\int }_{-\infty }^{\infty }\mathrm{y}(\mathrm{t})\mathrm{dt}$ is ________ (rounded off to the nearest integer).

Let 𝑋(𝑡) be a white Gaussian noise with power spectral density $\frac{1}{2}$ W/Hz. If 𝑋(𝑡) is input to an LTI system with impulse response 𝑒${}^{-\text{t}}$ 𝑢(𝑡). The average power of the system output is ___________ W (rounded off to two decimal places).

A transparent dielectric coating is applied to glass (𝜀${}_{\text{r}}$ = 4, 𝜇${}_{\text{r}}$ = 1) to eliminate the reflection of red light (𝜆₀ = 0.75 μm). The minimum thickness of the dielectric coating, in μm, that can be used is _________ (rounded off to two decimal places).