The input impedance (Z_i) and the output impedance (Z_o) of an ideal transconductance (voltage controlled current source) amplifier are

In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $${\beta _{DC}}$$ = 60, $${V_{BE}}$$ = 0.7V, $${h_{ie}} \to \,\,\infty $$, $${h_{fe}} \to \,\,\infty $$. The capacitance C_C can be assumed to be infinite.

Under the DC conditions, the collector-to emitter voltage drop is

For the circuit shown in the following figure, the capacitor C is initially uncharged. At t = 0, the switch S is closed. The voltage V_C across the capacitor at t = 1 millisecond is

In the figure shown above, the OP-AMP is supplied with $$ \pm $$ 15V.

A regulated power supply, shown in figure below, has an unregulated input (UR) of 15 volts and generates a regulated output V o u t . out. .Use the component values shown in the figure. If the unregulated voltage increases by 20% the power dissipation across the transistor Q$$_1$$

A regulated power supply, shown in figure below, has an unregulated input (UR) of 15 volts and generates a regulated output V $$_{out.}$$ .Use the component values shown in the figure. The power dissipation across the transistor Q1 shown in the figure is

In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $${\beta _{DC}}$$ = 60, $${V_{BE}}$$ = 0.7V, $${h_{ie}} \to \,\,\infty $$, $${h_{fe}} \to \,\,\infty $$. The capacitance C_C can be assumed to be infinite.

If $${\beta _{DC}}$$ is increased by 10%, the collector-to emitter voltage drop

An n-channel depletion MOSFET has following two points on its I_D - V_GS curve:

(i)V_GS = 0 at I_d = 12 mA and
(ii)V_GS = -6 Volts at Z_o =$$\infty $$

Which of the following Q-points will give the highest transconductance gain for small signals?

In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $${\beta _{DC}}$$ = 60, $${V_{BE}}$$ = 0.7V, $${h_{ie}} \to \,\,\infty $$, $${h_{fe}} \to \,\,\infty $$. The capacitance C_C can be assumed to be infinite.

The small-signal gain of the amplifier $${{{V_c}} \over {{V_s}}}$$ is

The following question refer to wide sense stationary stochastic process:

It is desired to generate a stochastic process (as voltage process) with power spectral density

$$$S\left( \omega \right) = {{16} \over {16 + {\omega ^2}}}$$$

By driving a Linear-Time-Invariant system by zero mean white noise (as voltage process) with power spectral density being constant equal to 1. The system which can perform the desired task could be

The following question refer to wide sense stationary stochastic process:

The parameters of the system obtained in Q. 12 would be

Let $$g\left( t \right){\mkern 1mu} {\mkern 1mu} \,\,\,\,\,{\mkern 1mu} = {\mkern 1mu} {\mkern 1mu} p\left( t \right){}^ * p\left( t \right)$$ 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 $$s(t) = g(t)$$ $$ - \delta {\left( {t - 2} \right)^ * }\,\,g\left( t \right)$$ is given as:

A zero-mean white Gaussian noise is passed through an ideal low-pass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period t_s = 0.03 msec. The samples so obtained would be

A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate as

The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the unit-step function)

x(t) = 125t(u(t) - u (t - 1) + (250 - 125t) (u (t - 1) - u (t - 2 )) so that slope - overload is avoided, would be

In the following figure the minimum value of the constant “C”, which is to be added to y₁(t) such that y₁(t) and y₂(t) are different, is

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 ω_c is carrier frequency both in rad/sec)

In the system shown below, x(t)=(sin t). In steady-state, the response y(t) will be

The transfer function of a phase-lead compensator is given by $${G_c}(s) = {{1 + 3Ts} \over {1 + Ts}}$$

where T > 0. The maximum phase-shift provided by such a compesator is

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$.

With the value of "a" set for phase-margin of $$\pi $$/4, the value of unit-impulse response of the open-loop system at t = 1 second is equal to

The unit-step response of a system starting from rest is given by $$$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mathrm t}\;\mathrm{for}\;\mathrm t\geq0$$$The transfer function 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

The unit impulse response of a system is: $$$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$ For this system, the steady-state value of the output for unit step input is equal to

The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

A linear system is described by the following state equation $$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right) + BU\left( t \right),A = \left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right].$$$
The state-transition matrix of the system is

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$ The value of 'a', so that the system has a phase-margin equal to $$\pi $$/4 is approximately equal to

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 frequency responses are, respectively

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 new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-5 number is represented by its corresponding 3-bit binary code. For example, the base-5 number 24 will be represented by its BCP code 010100. In this numbering system, the BCP code 100010011001 corresponds to the following number in base-5 system

Two D-flip-flops, as shown below, are to be connected as a synchronous counter that goes through the following Q₁Q₀ sequence $$00 \to 01 \to 11 \to 10 \to 00 \to ......$$
The inputs D₀ and D₁ respectively should be connected as

A 4-bit D/A converter is connected to a free-running 3-bit UP counter, as shown in the following figure. Which of the following waveforms will be observed at V₀=?

In the figure shown above, the ground has been shown by the symbol $$\nabla $$

The point p in the following figure is stuck- at-1. The output f will be

The number of product terms in the minimized sum-of-product expression obtained through the following k-map is ( where , "d" denotes don't care states)

The electric field of an electromagnetic wave propagating in the positive z-direction is given by $$$E = {\widehat a_x}\sin \left( {\omega t - \beta z} \right) + {\widehat a_y}\sin \left( {\omega t - \beta z + \pi /2} \right)$$$

The wave is

A transmission line is feeding 1 Watt of power to a horn antenna having gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is

$$\nabla \times \nabla \times P$$, where P is a vector, is equal to

A medium is divided into regions $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ about $$x = 0$$ plane, as shown in the Fig. below. An electromagnetic wave with electric field $${\overrightarrow E _1} = 4{\widehat a_x} + 3{\widehat a_y} + 5{\widehat a_z}$$ is incident normally on the interface form region-$${\rm I}$$ . The electric field $${E_2}$$ in region-$${\rm I}$$$${\rm I}$$ at the interface is

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

A medium of relative permittivityb $${\varepsilon _r} = 2$$ forms an interface with free-space. A point source of electromagnetic 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 interface is given by

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

A rectangular waveguide having $$T{E_{10}}$$ mode as dominant mode is having a cutoff frequency of 18 GHz for the $$T{E_{30}}$$ mode. The inner broad-wall dimension of the rectangular waveguide is

$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to

An n-channel depletion MOSFET has following two points on its I_D − V_GS curve:
(i) V_GS = 0 at I_D = 12 mA and
(ii) V_GS = - 6 Volts at I_D = 0
Which of the following Q-points will give the highest trans-conductance gain for small signals?

Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the

The concentration of minority carriers in an extrinsic semiconductor under equilibrium is:

Consider the function $$f(t)$$ having laplace transform
$$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2}},\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0.$$ The final value of $$f(t)$$ would be ____________.

For the function of a complex variable w = lnz (where w = u + jv and z = x + jy) the u = constant lines get mapped in the z-plane as

The value of the counter integral $$$\int\limits_{\left| {z - j} \right| = 2} {{1 \over {{z^2} + 4}}\,} dz\,\,in\,the\,positive\,sense\,is$$$

For the differential equation $${{{d^2}y} \over {d{x^2}}} + {k^2}y = 0,$$ the boundary conditions are
(i) $$y=0$$ for $$x=0$$ and
(ii) $$y=0$$ for $$x=a$$
The form of non-zero solution of $$y$$ (where $$m$$ varies over all integrals ) are

For the matrix $$\left[ {\matrix{ 4 & 2 \cr 2 & 4 \cr } } \right].$$ The eigen value corresponding to the eigen vector $$\left[ {\matrix{ {101} \cr {101} \cr } } \right]$$ is

The eigen values and the correspondinng eigen vectors of a $$2 \times 2$$ matrix are given by

Eigen value
$${\lambda _1} = 8$$
$${\lambda _2} = 4$$

Eigen vector
$${V_1} = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$
$${V_2} = \left[ {\matrix{ 1 \cr -1 \cr } } \right]$$

The matrix is

The rank of the matrix $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr } } \right]$$ is

Following is the segment of a 8085 assembly Language program:
LXI SP, EFFF H
CALL 3000 H
3000H: LXI H, 3CF4H
PUSH PSW
SPHL
POP PSW
RET

On completion of RET execution, the contents of SP is

An I/O peripheral device shown in figure (b) below is to be interfaced to an 8085 microprocessor. To select the I/O device in the I/O address range D4H – D7H, its chip-select (CS) should be connected to the output of the decoder shown in figure (a) below:

A two-port network is represented by ABCD parameters given by

$$\left[ {\matrix{ {{V_1}} \cr {{I_1}} \cr } } \right] = \,\left[ {\matrix{ A & B \cr C & D \cr } } \right]\,\left[ {\matrix{ {{V_2}} \cr { - \,{I_2}} \cr } } \right]$$

If port-2 is terminated by $${R_L}$$, the input impedance seen at port-1 is given by

A 2mH inductor with some initial current can be represented as shown below, where s is the Laplace Transform variable. The value of initial current is:

In the figure shown below, assume that all the capacitors are initially uncharged. If ν_i(t) = 10 u(t) Volts, ν₀(t) is given by

In the two port network shown in the figure below, z₁₂ and z₂₁ are, respectively

A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where $$g(t)\, = \,\,\sum\limits_{k = - \infty }^\infty {{{( - 10)}^k}\,\delta (t - 0.5x{{10}^{ - 4}}k)} $$
The resulting signal is then passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be

As x is increased from $$ - \infty \,\,to\,\infty $$, the function $$f(x) = {{{e^x}} \over {1 + {e^x}}}$$

A solution for the differential equation $$\mathop x\limits^. $$(t) + 2 x (t) = $$\delta (t)$$ with intial condition $$x({0^ - }) = 0$$ is

A low-pass filter having a frequency response $$H(j\omega )$$ = $$A(\omega ){e^{j\Phi (\omega )}}$$, does not product any phase distortion if

The Dirac delta function $$\delta (t)$$ is defined as

The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without distortion $$x(t) = 5{\left( {{{\sin \,\,2\,\pi \,1000\,t)} \over {\pi \,t}}} \right)^3} + 7{\left( {{{\sin \,\,2\,\pi \,1000\,t} \over {\pi \,t}}} \right)^2}$$

would be

A system with input $$x\left( n \right)$$ and output $$y\left( n \right)$$ is given as $$y\left( n \right)$$ $$ = \left( {\sin {5 \over 6}\,\pi \,n} \right)x\left( n \right).$$ The system is

In the system shown below,
x(t) = (sint)u(t). In steady-state, the response y(t) will be

Let g(t) = p(t) * p(t), where * denotes convolution and p(t) = u(t) - (t-1) with u(t) being the unit step function. The impulse response of filter matched to the singal s(t) = g(t) - $$[\delta (t - 2)*g(t)]$$ is given as

If the region of convergence of $${x_1}\left[ n \right]$$ + $${x_2}\left[ n \right]$$ is 1/3< $$\left| {z\,} \right|$$<2/3, then the region of convergence of $${x_1}\left[ n \right]$$ - $${x_2}\left[ n \right]$$ includes

Consider the function f(t) having Laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}\,\,\,\,\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0$$

The final value of f(t) would be:

Let x(t) $$ \leftrightarrow $$ X($$(j\omega )$$ BE Fourier transform pair. The Fourier Transform of the signal x(5t - 3) in terms of X($$(j\omega )$$ is given as