GATE EC 2013 Question Paper (10-Feb-2013) (Shift 2)

The following arrangement consists of an ideal transformer and an attenuator which is attenuated by a factor of 0.8. An a.c.voltage ${\mathrm{V}}_{\mathrm{w}{\mathrm{x}}_1}=100V$ is applied across $\mathrm{WX}$ to get on the open-circuit voltage ${\mathrm{V}}_{\mathrm{Y}{\mathrm{Z}}_1}$ across YZ. Next, an ac voltage ${\mathrm{V}}_{\mathrm{Y}{\mathrm{Z}}_2}=100V$ is applied across YZ to get an open circuit voltage ${\mathrm{V}}_{\mathrm{W}{\mathrm{X}}_2}$ across $\mathrm{WX}$ , then

${\mathrm{V}}_{\mathrm{Y}{\mathrm{Z}}_1}/{\mathrm{V}}_{\mathrm{W}{\mathrm{X}}_1},{\mathrm{V}}_{\mathrm{W}{\mathrm{X}}_2}/{\mathrm{V}}_{\mathrm{Y}{\mathrm{Z}}_2}$ are

Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂. When connected in series, their effective Q factor at the same operating frequency is

The impulse response of a continuous time system is given by h(t) = δ (t – 1) + δ (t – 3) . The value of the step response at t = 2 is

The small-signal resistance (i.e.,$\mathrm{d}{\mathrm{V}}_{\mathrm{B}}/d{\mathrm{I}}_{\mathrm{D}}$ ) in $\mathrm{k\Omega }$ offered by the n-channel MOSFET M shown in the figure below, at a bias point of ${\mathrm{V}}_{\mathrm{B}}=2V$ is (device data for M: device transconductance parameter, ${\mathrm{k}}_{\mathrm{N}}={\mu }_{\mathrm{n}}{\mathrm{C}}_{\mathrm{ox}}\left(W/L\right)=40\mu A/{\mathrm{V}}^2$ threshold voltage ${\mathrm{V}}_{\mathrm{TN}}=1V$, and neglect body effect and channel length modulation effects)

The ac schematic of an NMOS common-source stage is shown in the figure below, where part of the biasing circuits has been omitted for simplicity. For the n – channel MOSFET M, the transsconductance g${}_m$ = 1mA/V, and body effect and channel length modulation effect are to be neglected. The lower cutoff frequency in Hz of the circuit is approximately at