GATE EC question library

The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following condition, (here $W$ is message bandwidth and $\omega_{c}$ is carrier frequency both in rad/sec)

In the following figure the minimum value of the constant ' $C$ ', which is to be added to $y_{1}(t)$ such that $y_{1}(t)$ and $y_{2}(t)$ are different, is

A message signal with bandwidth $10 \; \mathrm{kHz}$ is Lower-Side Band SSB modulated with carrier frequency $f_{c 1}=10^{6} \mathrm{~Hz}$. The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency $f_{c_{2}}=10^{9} \; \mathrm{Hz}$. The bandwidth of the output would be

A medium of relative permittivity $\varepsilon_{r 2}=2$ forms an interface with free-space. A point source of electronagnetic energy is located in the medium at a depth of $1$ meter from the interface. Due to the total internal reflection, the transmitted beam has a circular cross-section over the interface. The area of the beam cross-section at the …

A medium is divided into regions I and II about $x=0$ plane, as shown in the figure below. An electromagnetic wave with electric field $\mathrm{E}_{1}=4 \hat{a}_{x}+3 \hat{a}_{y}+5 \hat{a}_{z}$ is incident normally on the interface from region-I. The electric field $E_{2}$ in region-II at the interface is

When a plane wave travelling in free-space is incident normally on a medium having $\varepsilon_{t}=4.0$, then fraction of power transmitted into the medium is given by

A rectangular waveguide having $\mathrm{TE}_{10}$ mode as dominant mode is having a cutoff frequency of $18-\mathrm{GHz}$ for the $\mathrm{TE}_{w,}$ mode. The inner broad-wall dimension of the rectangular waveguide is

A mast antenna consisting of a $50$ meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of $600-\mathrm{kHz}$. The radiation resistance of the antenna in ohms is

Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $$\beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{f \times} \longrightarrow \infty$$ The capacitance $\mathrm{C}_{\text{c }}$ can be assumed to be infinite. …

Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $$\beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{f c} \longrightarrow \infty$$ The capacitance $\mathrm{C}_{\text{c }}$ can be assumed to be infinite. In …

Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $$\beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{f c} \longrightarrow \infty$$ The capacitance $\mathrm{C}_{\text{c }}$ can be assumed to be infinite. In …

Common Data for Questions 74, 75: Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function The impulse response of filter matched to the signal $s(t)=g(t)-\delta(t-2)^{*} g(t)$ is given as

Common Data for Questions 74, 75: Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function An Amplitude Modulated signal is given as $$x_{\mathrm{AM}}(t)=100(p(t)+0.5 g(t)) \cos \omega_{c} t$$ in the interval $0 \leq t \leq 1$. One set of possible values of the modulating signal and …

statement for Linked Answer Questions 76 and 77 A regulated power supply, shown in figure below, has an unregulated input (UR) of $15$ Volts and generates a regulated output $V_{\text{out }}$. Use the component values shown in the figure. In the figure above, the ground has been shown by the symbol $\nabla$ The power dissipation across the transistor …

statement for Linked Answer Questions 76 and 77 A regulated power supply, shown in figure below, has an unregulated input (UR) of $15$ Volts and generates a regulated output $V_{\text{out }}$. Use the component values shown in the figure. In the figure above, the ground has been shown by the symbol $\nabla$ If the unregulated voltage increases by …

Statement for Linked Answer Questions 78 and 79 The following two questions refer to wide sense stationary stochastic processes It is desired to generate a stochastic process (as voltage process) with power spectral density $$S(\omega)=\frac{16}{16+\omega^{2}}$$ by driving a Linear-Time-Invariant system by zero mean white noise (as voltage process) with …

Statement for Linked Answer Questions 78 and 79 The following two questions refer to wide sense stationary stochastic processes The parameters of the system obtained in $\text{Q.78}$ would be

Statement for Linked Answer Questions 80 and 81 Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$ $$x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \pi f_{m} t\right) \cos 2 \pi f_{c} t$$ The average side-band power for the $\text{AM}$ signal given above is

Statement for Linked Answer Questions 80 and 81 Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$ $$x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \pi f_{m} t\right) \cos 2 \pi f_{c} t$$ The $\text{AM}$ signal gets added to a noise with Power Spectral Density $S_{n}(f)$ given in the figure below. The ratio of average …

Statement for Linked Answer Questions 82 and 83 Consider a unity-gain feedback control system whose open-loop transfer function is $$G(s)=\frac{as+1}{s^{2}}$$ The value of '$a$' so that the system has a phase-margin equal to $\frac{\pi}{4}$ is approximately equal to