GATE EC 2016 Question Paper (30-Jan-2016) (Shift 1)

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth (in kHz) required for a roll-off factor of 0.25 is ________∙

A super heterodyne receiver operates in the frequency range of 58 MHz − 68 MHz. The

intermediate frequency 𝑓${}_{\text{IF}}$ and local oscillator frequency 𝑓${}_{\text{LO}}$ are chosen such that 𝑓${}_{\text{IF}}$ ≤ 𝑓${}_{\text{LO}}$. It is required that the image frequencies fall outside the 58 M Hz − 68 MHz band. The minimum required 𝑓${}_{\text{IF}}$ (in MHz) is ________.

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal (𝑡) = 5 cos 1600𝜋𝑡 + 20 cos 1800𝜋𝑡 + 5 cos 2000𝜋𝑡. The value of the modulation index is __________

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m², −4 nC/m² and ρs, respectively. The value of ρₛ (nC/m²) required to ensure that the electric flux density $\vec{\mathrm{D}}=0$ at radius 10 m is _________

The propagation constant of a lossy transmission line is (2 + 𝑗5) m⁻¹ and its characteristic impedance is (50 + 𝑗0) Ω at 𝜔 = 10⁶ rad s−1. The values of the line constants L, C,R, G are, respectively,