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

A current sheet $\vec{J}=10{\hat{u}}_{y}A/m$ lies on the dielectric interface x = 0 between two dielectric media with ${\epsilon }_{r1}=5,{\mu }_{r1}=1$ in Region–1 (x < 0) and ${\epsilon }_{r2}=2,{\mu }_{r2}=2$ Region–2 (x > 0). If the magnetic field in Region-1 at x = 0 is ${\vec{H}}_1=3{\hat{u}}_x+30{\hat{u}}_{y}A/m$ the magnetic field in Region-2 at x = 0⁺ is

A transmission line of characteristic impedance 50 Ω is terminated in a load impedance Z${}_L$. The VSWR of the line is measured as 5 and first of the voltage maxima in the line is observed at a distance of λ/4 from the load. The value of Z${}_L$ is

X(t) is a stationary random process with autocorrelation function Rₓ(τ) = exp(-πτ²). This process is passed through the system shown below. The power spectral density of the output process Y(t) is

The output of a 3-stage Johnson (twisted-ring) counter is fed to a digital-to-analog (D/A) converter as shown in the figure below. Assume all states of the counter to be unset initially. The waveform which represents the D/A converter output Vₒ is

Two D flip-flops are connected as a synchronous counter that goes through the following QBQA sequence 00 “ 11 “ 01 “ 10 “ 00 “ … The combination of the inputs DA and DB are