Frequency Response

All the components in the bandpass filter given below are ideal. The lower -3 dB frequency of the filter is 1 MHz. The upper -3 dB frequency (in MHz, rounded off to the nearest int...

In the context of Bode magnitude plots, 40 dB/decade is the same as ______.

A continuous time signal $x(t) = 2 \cos(8 \pi t + \frac{\pi}{3})$ is sampled at a rate of 15 Hz. The sampled signal $x_s(t)$ when passed through an LTI system with impulse response...

The open loop transfer function of a unity negative feedback system is G(s) = k / (s(1+sT₁)(1+sT₂)), where k, T₁ and T₂ are positive constants. The phase cross-over frequency, in r...

The open loop transfer function of a unity negative feedback system is $$G(s) = {k \over {s(1 + s{T_1})(1 + s{T_2})}}$$, where $$k,T_1$$ and $$T_2$$ are positive constants. The pha...

Let an input $$x[n]$$ having discrete time Fourier transform $$x({e^{j\Omega }}) = 1 - {e^{ - j\Omega }} + 2{e^{ - 3j\Omega }}$$ be passed through an LTI system. The frequency resp...

For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles Np and the number of system zeros Nz in the frequency range 1 Hz ≤ f...

For a unity feedback control system with the forward path transfer function $$G(s) = {K \over {s\left( {s + 2} \right)}}$$ The peak resonant magnitude M r of the closed-loop freque...

Consider an LTI system with magnitude response $$$\left| {H(f)} \right| = \left\{ {\matrix{ {1 - \,{{\left| f \right|} \over {20}},} & {\left| f \right| \le 20} \cr {0,} & {\left|...

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of th...

The number and direction of encirclements around the point −1 + j0 in the complex plane by the Nyquist plot of G(s) =$${{1 - s} \over {4 + 2s}}$$ is

Consider a four-point moving average filter defined by the equation $$y[n] = \sum\limits_{i = 0}^3 {{\alpha _i}x[n - i]} $$. The condition on the filter coefficients that results i...

The phase margin (in degrees) of the system G(s)=$${{10} \over {\left( {s + 10} \right)}}$$ is ___________.

A real - values signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linear time invariant system whose frequency response is $$H(f) =...

For the transfer function G$$\left( {j\omega } \right) = 5 + j\omega ,$$ the corresponding Nyquist plot for positive frequency has the form

A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}}\,\,$$ has an output $$y(t) = \cos \left( {2t - {\pi \over 3}} \right)\,$$ for the input signal $$x(t...

A system with transfer function H(z) has impulse response h(.) defined as h(2) = 1, h(3) = - 1 and h (k) = 0 otherwise. Consider the following statements. S1: H(z) is a low-pass fi...

The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function. The frequency response H(ω) of the sy...

The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function. The output of this system to the sinu...

The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}$$ .The step response of the system is:

The frequency response of a linear, time-invariant system is given by H(f) = $${5 \over {1 + j10\pi f}}$$. The step response of the system is

The open-loop transfer function of a unity-gain feedback control system is given by $$G(s) = {K \over {(s + 1)(s + 2)}},$$ the gain margin of the system in dB is given by

Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s \over {{s^2} + as + b}}.$$ The 3-dB bandwidths of their freq...

The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through (-1,j0) point in the GH plane. The gain margin of the system in dB is equal to

A signal x(n)$$ = \sin ({\omega _0}\,n + \phi )$$ is the input to a linear time-invariant system having a frequency response $$H({e^{j\omega }})$$.If the output of the system is $$...

The open loop transfer function of a unity feedback system is given by g(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$ Based on the above results, the gain and phase mar...

The open loop transfer function of a unity feedback system is given by G(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$ The gain and phase crossover frequencies in rad/se...

The impulse response $$h\left[ n \right]$$ of a linear time invariant system is given as $$h\left[ n \right] = \left\{ {\matrix{ { - 2\sqrt 2 ,} & {n = 1, - 1} \cr {4\sqrt 2 ,} & {...

The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0 $$k\Omega $$ and C = 1.0 $$\mu F$$. Let H(t) denote the frequency response of the RC-LPF. Let $${f_1}...

The gain margin and the phase margin of a feedback system with G(s)H(s)=$${s \over {{{\left( {s + 100} \right)}^3}}}$$ are

The gain margin for the system with open-loop transfer function G(s)H(s)=$${{2(1 + s)} \over {{s^2}}}$$ is

The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0 $$k\Omega $$ and C = 1.0 $$\mu F$$. Let $${t_g}$$ (f) be the group delay function of the given RC-LPF...

The phase margin of a system with the open-loop transfer function G(s)H(s)=$${{(1 - s)} \over {(1 + s)(2 + s)}}$$ is?

A system has a phase response given by $$\phi \,(\omega )$$ where $$\omega $$ is the angular frequency. The phase delay and group delay at $$\omega $$ = $${\omega _0}$$ are respect...

The first dominant pole encountered in the frequency response of a compensated op-amp is approximately at

The phase margin (in degrees) of a system having the loop transfer function is $$G(s)H(s) = {{2\sqrt 3 } \over {s(s + 1)}}$$

The loop transfer function of a single loop control system is given by $$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \right)}}{e^{ - ST}}$$ Using Nyquist criterion, find the condi...

In the Bode-plot of a unity feedback control system, the value of phase of G($$j\omega $$) at the gain cross over frequency is $$ - 125^\circ $$. The phase margin of the system is

Match the following with List-1 with List-2 List-1 (a) Very low response at very high frequencies. (b) Overshoot (c) Synchro-control transformer output List-2 (1) Low pass systems...

The transit time of the current carriers through the channel of an FET decides its ____________characteristics.

The 3-dB bandwidth of a typical second- order system with the transfer function $${{C\left( s \right)} \over {R(s)}} = {{\omega _n^2} \over {{s^2} + 2\xi {\omega _n}s + \omega _n^2...

The bandwidth of an n-stage tuned amplifier, with each stage having a band width of B, is given by

In a multi-stage RC-Coupled Amplifier the coupling capacitor.

A unity feedback system has open-loop transfer function $$G(s) = {1 \over {s\left( {2s + 1} \right)\left( {s + 1} \right)}}$$ Sketch Nyquist plot for the system and there from obta...

From the Nicholas chart, one can determine the following quantities pertaining to a closed loop system:

Specify the filter type if its voltage transfer function H(s) is given by H(s) = $${{K({s^2} + {\omega _0}^2)} \over {{s^2} + ({\omega _0}/Q)s + {\omega _0}^2}}$$

The popular plot of G(s)=$${{10} \over {s{{\left( {s + 1} \right)}^2}}},$$ intercepts real axix at $$\omega = {\omega _0}$$ Then, the real part and $${\omega _0}$$ are respectively...