GATE EC Analog Communications questions

Which option(s) represents/ represent the dielectric loss tangent of a substrate?

Consider a real, narrowband signal $x(t)=A(t) \cos \left[2 \pi f_{c} t+\theta(t)\right]$ where the maximum frequency components of $A(t)$ and $\theta(t)$ are $f_{M}$ and $f_{c}\left(=1000 f_{M}\right)$, respectively. Which of the following statements is/are correct for $-\infty < t < \infty ?$

Consider a frequency-modulated (FM) signal $$f(t)=A_{c} \cos \left(2 \pi f_{c} t+3 \sin \left(2 \pi f_{1} t\right)+4 \sin \left(6 \pi f_{1} t\right)\right)$$ where $A_{c}$ and $f_{c}$ are, respectively, the amplitude and frequency (in $\mathrm{Hz}$ ) of the carrier waveform. The frequency $f_{1}$ is in $\mathrm{Hz}$ , and assume that …

Consider a message signal $m(t)$ which is bandlimited to $[-W, W]$, where $W$ is in $\mathrm{Hz}$ . Consider the following two modulation schemes for the message signal: Double sideband-suppressed carrier (DSB-SC): $$f_{D S B}(t)=A_{c} \: m(t) \cos \left(2 \pi f_{c} t\right)$$ Amplitude modulation (AM): …

An amplitude modulator has output (in Volts) $$s(t)=A \cos (400 \pi t)+B \cos (360 \pi t)+B \cos (440 \pi t) .$$ The carrier power normalized to $1 \Omega$ resistance is $50$ Watts. The ratio of the total sideband power to the total power is $1 / 9$. The value of $\text{B}$ (in Volts, rounded off to two decimal places) is $\_\_\_\_\_\_\_$.

Let a frequency modulated $\text{(FM)}$ signal $x(t)=A \cos \left(\omega_{c} t+k_{f} \int_{-\infty}^{t} m(\lambda) d \lambda\right)$, where $m(t)$ is a message signal of bandwidth $\text{W.}$ It is passed through a non-linear system with output $y(t)=2 x(t)+5(x(t))^{2}$. Let $B_{T}$ denote the $\text{FM}$ bandwidth. The minimum value of …

Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of $50\%$. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is ______________

A sinusoidal message signal having root mean square value of $4\:V$ and frequency of $\text{1 kHz}$ is fed to a phase modulator with phase deviation constant $2$ rad/ volt. If the carrier signal is $c\left ( t \right )=2\cos\left ( 2\pi 10^{6} t\right )$, the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal …

Consider a superheterodyne receiver tuned to $600 \text{ kHz}$. If the local oscillator feeds a $1000 \text{ kHz}$ signal to the mixer, the image frequency (in integer) is ____________________ $\text{kHz}$.

The components in the circuit shown below are ideal. If the op-amp is in positive feedback and the input voltage $V_{i}$ is a sine wave of amplitude $1$ $\text{V}$, the output voltage $V_{o}$ is

For the modulated signal $x\left ( t \right )=m\left ( t \right )\cos\left ( 2\pi f_{c}t \right )$, the message signal $m\left ( t \right )=4\cos\left ( 1000\pi t \right )$ and the carrier frequency $f_{c}$ is $1\: MHz$. The signal $x(t)$ is passed through a demodulator, as shown in the figure below. The output $y(t)$ of the demodulator is

$S_{PM}(t)$ and $S_{FM}(t)$ as defined below, are the phase modulated and the frequency modlated waveforms, respectively, corresponding to the message signal $m(t)$ shown in the figure. …

In the circuit shown, $V_{1}=0$ and $V_{2}=V_{dd}.$ The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of $I_{out}$ is _________ $mA$ (rounded off to $1$ decimal place).

Consider the following amplitude modulated signal: $$s\left ( t \right )=\cos\left ( 2000\:\pi t \right )+4\cos\left ( 2400\:\pi t \right )+ \cos\left ( 2800\:\pi t \right ).$$The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is _________.

Let $c\left ( t \right )=A_{c} \cos \left ( 2\pi f_{c}t\right )$ and $m\left ( t \right )=\cos \left ( 2\pi f_{m}t\right )$. It is given that $f_{c}>> 5f_{m}.$ The signal $c\left ( t \right )+m\left ( t \right )$ is applied to the input of a non-linear device, whose output $v_{o}\left ( t \right )$ is related to the input …

The unmodulated carrier power in an AM transmitter is $5$ kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is $50 \%$. If it is reduced to $40 \%$, then the maximum unmodulated carrier power (in kW) that can be used without overloading the transmitter is _________

A modulating signal given by $x(t)=5\sin (4\pi 10^3t -10\pi \cos 2\pi 10^3t)V$ is fed to a phase modulator with phase deviation constant $k_p=5$ rad/V. If the carrier frequency is $20$ kHz, the instantaneous frequency(in kHz) at $t=0.5$ ms is ____________

Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the modulation index ($\mu$) when the maximum and minimum values of the envelope, respectively, are $3$ V and $1$ V, is ___________.

In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms $W1$, $W2$, $W3$ and $W4$.

Consider an $FM$ signal $f(t)= \cos\left [ 2\pi f_{c} t+\beta _{1}\sin2\pi f_{1}t+\beta _{2}\sin2\pi f_{2}t\right ].$ The maximum deviation of the instantaneous frequency from the carrier frequency $f_{c}$ is