Let and be two vectors. The value of the coefficient in the expression , which minimizes the length of the error vector , is
From the given expression, we can write
The error vector can be calculated as.
Taking its magnitude, we get
at
stationary point
The rate of increase, of a scalar field in the direction at a point is
2
4
Given, scalar field,
finding the gradient of this Scalarfield.
By the formula.
Gradient of scalar field,
At point
Now finding the direction derivative,
Directional derivative,
Let . Which of the following cannot be a value of ?
Given equation is
On expanding the equation we get.
For
For
For
Option (a) is not Correct.
The value of the contour integral,
, where the contour is
, taken in the counter clockwise direction, is
Let the contour integral,
The given denominator equation can be written as
Poles are given
Only one poll is inside other is outside.
where lies outside ''
by Cauchy's residue theorem,
Let the sets of eigenvalues and eigenvectors of a matrix be and , respectively. For any invertible matrix , the sets of eigenvalues and eigenvectors of the matrix , where , respectively, are
and
and
and
and
Given input is
are called matrices similar.
Both have same set 7 eigen values
Matrix A & B has different eigen vector.
Let
Eigen vectors of are .
In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as
degenerate -type.
degenerate -type.
non-degenerate -type.
non-degenerate -type.
In degenerate semiconductor, fermi level lies inside conduction band or valence band.
As the Fermi lies inside the conduction band hence it is degenerate -type semiconductor.
For an intrinsic semiconductor at temperature , which of the following statement is true?
Intrinsic semiconductor at behaves as an insulator.
Hence, valence band is completely filled with electrons and conduction band is completely empty.
A series RLC circuit has a quality factor of 1000 at a center frequency of . The possible values of and are
and
and
and
and
Given: Quality factor, and center frequency
Quality factor for series RLC circuit is given by
Quality factor,
Also, center frequency,
So, and
For a MOS capacitor, and are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width for varying gate voltage is best represented by
We know then accumulation mode.
in accumulation mode because there is no depletion charge.
Now, then depletion and inversion mode.
Depletion width is available.
Strong inversion.
Depletion width Constant.
And and
But after strong inversion, remains constant.
Correction option is (b).
Consider a narrow band signal, propagating in a lossless dielectric medium , with phase velocity and group velocity . Which of the following statement is true?
( is the velocity of light in vacuum.)
- Phase velocity,
- Group velocity,
Here,
Hence,
In the circuit shown below, and are bias voltages. Based on input and output impedances, the circuit behaves as a
In the given circuit,
Transistor is common-gate amplifier and transistor behaves as an active load.
By using properties of common gate (CG) amplifier,
Input impedance is low
Output impedance is high
So, it is a current amplifier.
Current amplifier is a current controlled current source.
A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when
the closed loop gain is less than 1 and the phase shift is less than .
the closed loop gain is greater than 1 and the phase shift is less than .
the closed loop gain is less than 1 and the phase shift is greater than .
the closed loop gain is greater than 1 and the phase shift is greater than .
Marks to all
For sustained oscillation
(i) Loop gain magnitude
(ii) Phase of loop gain or
So, correct answer is option (d).
* In options, closes loop gain is mentioned technically it should be loop gain.
In the circuit shown below, and are the inputs. The logical function realized by the circuit shown below is
From the Y given
Output,
is 0, is 1 Put it in the equation of output
The synchronous sequential circuit shown below works at a clock frequency of . The throughput, in bits/s, and the latency, in ns, respectively, are
1000,3
2000,3
The given circuit is a type of serial input serial output.
The latency is given by the formula.. Latency where, number of flip flops
The Throughput is given by the formula. Throughput= Number of bits/sec
The open loop transfer function of a unity negative feedback system is , where and are positive constants. The phase cross-over frequency, in rad/s, is
We know phase crossover frequency is that frequency at which phase of the open loop transfer function is .
Now finding the phase of , we get
Phase of
Consider a system with input and output . The system is
For causality,
We have,
At
i.e. present value of output depends on future value of input, hence it is non-causal.
For Time Variant:
Delay the input,
…(i)
Delay the output,
…(ii)
i.e. equations (i) (ii)
Hence, it is time variant system.
So the system is Non causal & time varying option (b) is correct.
The Fourier transform of is
Note:
To find the Fourier transform of
1. Use the Fourier transform definition:
2. Complete the square in the exponent:
3. Substitute :
4. Use the given integral result:
5. Therefore:
So the answer is:
Which matches option (C).
In the table shown below, match the signal type with its spectral characteristics.
Signal Type
(i) Continuous, aperiodic
(ii) Continuous, periodic
(iii) Discrete, aperiodic
(iv) Discrete, periodic
Spectral Characteristics
(a) Continuous, aperiodic
(b) Continuous, periodic
(c) Discrete, aperiodic
(d) Discrete, periodic
(i) (a), (ii) (b), (iii) (c), (iv) (d)
(i) (a), (ii) (c), (iii) (b), (iv) (d)
(i) (d), (ii) (b), (iii) (c), (iv) (a)
(i) (a), (ii) (c), (iii) (d), (iv) (b)
The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 . The resolution of the ADC is __________ (rounded off to the nearest integer). bits.
We know that for sinusoidal input, the signal to noise ratio (SNR) is given as,
In the circuit shown below, the current I flowing through 200 Ω resistor is ________ mA.
(rounded off to two decimal places).
By applying source transformation between 1 mA current source and resistor in parallel we get
By applying nodal at node
We find current across resistor,
Put the value of in it.
For the two port network shown below, the [Y]-parameters is given as
The value of load impedance , in , for maximum power transfer will be _________.
(rounded off to the nearest integer).
For the Pi-network
Given,-parameters,
For the given -parameter the two-port network is
On solving,
The network becomes,
Converting the - network of Y-matrix which is in delta connection to star connection, we get
For maximum power transfer,
For the circuit shown below, the propagation delay of each NAND gate is . The critical path delay, in ns, is ________ (rounded off to the nearest integer).
Redrawing the circuit to simplify is as shown.
The critical path delay
In the circuit shown below, switch S was closed for a long time. If the switch is opened at t=0, the maximum magnitude of the voltage in volts, is ________ (rounded off to the nearest integer).
At steady state inductance behaves as short circuit
At , the switch was closed, hence the circuit is in steady state.
At , the switch is open, hence the circuit becomes,
Magnitude of voltage
A random variable , distributed normally as , undergoes the transformation , given in the figure. The form of the probability density function of is (In the options given below, are non-zero constants and is piecewise continuous function)
Given random variables,
X=N(0,1)
is taking discrete set of values and a continuous range of values, so it is mixed random variable. From the given options, density function of ' ' will be.
The value of the line integral along the straight line joining the points and is
Given line integral, along the line joining the points and is
Putting the values into the integration then integrating to the point. so
Let be an real column vector with length . The trace of the matrix is
Given the vector length is,
Let
let the Vector in expanding form.
Trace of
The of the circuit shown below is
Given circuit
Here, is an inverting amplifier and is a noninverting amplifier.
For , applying KCL at (-)ve node
In the circuit shown below, and are silicon diodes with cut-in voltage of . and are input and output voltages in volts. The transfer characteristic is
Case I:
For the + ve half cycle if input
For diode
Case II:
For the half cycle if input .
For diode
Case III:
Transfer characteristics,
A closed loop system is shown in the figure where and . The steady state error due to a ramp input is given by
Given, input is ,Taking its laplace we get
From the figure,
Now steady state error for Ramp input is
where is the magnitude of Ramp input
Velocity error constant is given by the formula,
Putting it in steady state error we get
In the following block diagram, and are two inputs. The output is expressed as
. and are given by
and
and
and
and
Given, block diagram,
Considering first R(s) only so making D(s) =0, then Y(s) is
So we get as follows
So option (a,d) will be one of the correction answer.
Now considering only making R(s)=0, then is
So we get as follows
Hence, and both are equal.
So correct option is (a)
The state equation of a second order system is is the initial condition.
Suppose and are two distinct eigenvalues of A and and are the corresponding eigenvectors. For constants and , the solution, , of the state equation is
The correct option is 1
Concept:
Given:
If is the eigenvalue of matrix A then .
As there are 2 eigenvalues and of matrix A , the solution of the state equation will be, Hence, the correct option is (a).
The switch was closed and was open for a long time. At , switch is opened and is closed, simultaneously. The value of , in amperes, is
At ; switch closed, switch opened, hence the circuit is in steady state.
At steady state inductance behaves as short circuit
At steady state capacitance behaves as open circuit
At ; switch opened, switch closed, the circuit can be redrawn as
By applying :
Let a frequency modulated (FM) signal , where is a message signal of bandwidth . It is passed through a non-linear system with output . Let denote the FM bandwidth. The minimum value of required to recover from is
Bandwidth
Bandwidth of
To recover
Compared to FM BW, message BW is very small. So, that it can be ignored.
The h-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain is
very high and
very high, very high and
very high, very high and
very high and very high
Marks to All
Dependent current source should have instead of according to -parameter.
Voltage gain,
To achieve maximum ,
Hence, answer should be (a) according to .
Consider a discrete-time periodic signal with period . Let the discrete-time Fourier series (DTFS) representation be , where
and . The value of the sum is
Let,
…(i)
As we know,
Put
Put
From equation (i),
Let an input having discrete time Fourier transform.
be passed through an LTI system. The frequency response of the LTI system is . The output of the system is
For an LTI system, output,
By taking DTFT,
Taking IDTFT;
Let be passed through an LTI system having impulse response . The output of the system is
Given is Real and Even. When sinusoidal input applied to LTI system having even impulse response, then output will also be sinusoidal.
here,
let,
(using Fourier transform property)
where,
Now;
Let and be two band-limited signals having bandwidth each. In the figure below, the Nyquist sampling frequency, in , required to sample , is
Given that, and are two bandlimited signals having bandwidth .
and
The S-parameters of a two port network is given as
with reference to . Two lossless transmission line sections of electrical lengths and are added to the input and output ports for measurement purposes, respectively. The Sparameters of the resultant two port network is
Let us evaluate and first at
(a) :
(b) :
Here,
Hence,
From previous discussion in ,
(looking at options (a) is correct)
The value of the integral over the region , given in the figure, is __________(rounded off to the nearest integer).
Given, integral,
Here we Break the integration limits into 2 parts.
Part-A varies from and
Part-B varies from x=y-2 to 2-y and y=1 to 2
In an extrinsic semiconductor, the hole concentration is given to be where is the intrinsic carrier concentration of . The ratio of electron to hole mobility for equal hole and electron drift current is given as _________(rounded off to two decimal places).
Given,
Given hold drift currentdrift current (In)
The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is , where and c are positive constants. The value of is __________. (rounded off to the nearest integer).
From the given Bode magnitude plot, it is clear that there is one pole at origin, so we get so
and at frequency
As the slope is decade previously to make it 0 slope we will need a zero at frequency , so system has a zero,
and at frequency ,
As the slope is decade previously to make it decade slope we will need 2 poles at frequency , so
Let and is shown in the figure below. For , the is _________. (rounded off to the nearest integer).
Given, signal
We draw as follows
Now,
Taking Fourier transform
We know,
From area property we know
Let be a white Gaussian noise with power spectral density . If is input to an LTI system with impulse response . The average power of the system output is __________ W. (Rounded off to two decimal place).
We know that,
Given: Input PSD
We know output PSD,
()
()
A transparent dielectric coating is applied to glass to eliminate the reflection of red light . The minimum thickness of the dielectric coating, in , that can be used is ________. (rounded off to two decimal places).
For no reflection, impedance must be matched. Hence, acts like a quarter wave impedance transformer.
So,
(i)
(ii) For impedance matching,
Here,
Hence, for minimum distance,
So,
In a semiconductor device, the Fermi-energy level is above the valence band energy. The effective density of states in the valence band at is . The thermal equilibrium hole concentration in silicon at is _________. (rounded off to two decimal places). Given KT at is .
Given,
[Considering it is given at ]
Also, at
Given, effective density of states in the valence band,
Now, hole concentration at is given as
A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of . The time for sampling switch to stay closed to charge a capacitor adequately to full scale voltage of with 12-bit accuracy is ________ .
(rounded off to two decimal places)
Given: Time constant of sec.
Full scale voltage
Steady state voltage of circuit is given by
…(i)
To calculate the voltage to stay closed to charge capacitor adequately to a full scale voltage with 12 -bit accuracy is given by
…(ii)
Comparing equations (i) and (ii), we get,
In a given sequential circuit, initial states are and . For a clock frequency of , the frequency of signal in , is ________. (rounded off to the nearest integer).
Given, initial states, and
Clock frequency,
As after 4 CLK pulses the sequential circuit repeats itself so its MOD no. 4.
The frequency of signal
In the circuit below, the voltage is _______V. (rounded off to two decimal places)
Given circuit,
drain current is proportional to ratio of width to length
The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of "yes/no" questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _______ (rounded off to two decimal places).
The average number of questions when asked in the most efficient sequence, to determine the chosen symbol possible number of questions per symbol
For a real signal, which of the following is/are valid power spectral density/densities?
(Graph always above x axis)
: even function
Hence, options (a) and (b) are valid power spectral densities.
The standing wave ratio on a lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. can be replaced by an equivalent length and terminating resistance of the same line. The value of and , respectively, are
Given
As we know that,
Now, distance between successive voltage minima
Also, for minima,
At , 1st minima,
Here,
Going through options,
satisfy this
identity, hence option (b) and (c) are correct.’
The electric field of a plane electromagnetic wave is
Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?
Given,
At
Going by options,
Option (a):
at
at
Hence, it is LHEP.
Option (b):
at
at
Hence, it is LHEP.
Option (c):
at
at
Hence, it is RHEP.
Option (d):
at
at
Hence, it is LHEP.
Option (a), (b) and (d) are correct.
The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are
