GATE EC 2015 Question Paper (31-Jan-2015) (Shift 1)

The open-loop transfer function of a plant in a unity feedback configuration is given as

$\mathrm{G}\left(\mathrm{s}\right)=\frac{\mathrm{K}\left(\mathrm{s}+4\right)}{\left(\mathrm{s}+8\right)\left({\mathrm{s}}^2-9\right)}$

The value of the gain K (> 0) for which(- 1 + j 2) lies on the root locus _____________

A lead compensator network introduces a parallel combination of R and C in the feedforward path. If the transfer function of the compensator is ${\mathrm{G}}_{\mathrm{e}}\left(\mathrm{s}\right)=\frac{\mathrm{s}+2}{\mathrm{s}+4}$.The value of RC is___________.

A plant transfer function is given as,

$\mathrm{G}\left(\mathrm{s}\right)=\left({\mathrm{K}}_{\mathrm{p}}+\frac{{\mathrm{K}}_{\mathrm{I}}}{\mathrm{s}}\right)\frac{1}{\mathrm{s}\left(\mathrm{s}+2\right)}$

When the plant operates in a unity feedback configuration the condition for the stability of the closed-loop system is

The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with probability 0.8. The cross-over probability is $\frac{1}{7}$. If the received bit Y = 0, the conditional probability that ‘1’ was transmitted is _________.

The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a common bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total bandwidth of the signal received by the base station of the cell will be at least (in kHz)__________.