GATE EC 2011 Question Paper (13-Feb-2011) (Shift 2)

A numerical solution of the equation $f(x)=x+\sqrt{x}-3=0$ can be obtained using Newton-Raphson method. If the starting value is x = 2 for the iteration, the value of x that is to be used for the next step is

The electric and magnetic fields for a TEM wave of frequency 14 GHz in a homogenous medium of relative permittivity εᵣ and relative permeability μᵣ = 1 are given by

$\vec{E}=E_P{e}^{j\left(\omega t-280\pi y\right)}{\hat{u}}_z\frac{V}{m}$ and $H=3e^{j\left(\omega t-280\pi y\right)}{\hat{u}}_x\frac{A}{m}$

Assuming the speed of light in free space to be 3 × 10⁸ m/s, the intrinsic impedance of free space to be 120π, the relative permittivity εᵣ of the medium and the electric field amplitude $E_p$ are

A message signal $m\left(t\right)=cos2000\pi t+4cos4000\pi t$ modulates the carrier $c\left(t\right)=cos2\pi f_{c}t$ where fc = 1 MH${}_z$ to produce AM. For demodulating the generated AM signal using an envelope defector, the time constant RC of the defector should satisfy

The block diagram of a system with one input u and two outputs y₁ and y₂ is given below.



A state space model of the above system in terms of the state vector $\underline{x}$ and the output vector

y = {≤ft[ {*20c y_1&y_2 } ]^T} is

Two systems H₁(z) and H₂(z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one-unit delay. The transfer function of the second system H₂(z) is