The general form of the complementary function of a differential equation is given by where A and B are real constants determined by the initial condition. The corresponding differential equation is__________.
Based on the solution we can judge that the characteristic equation has repeated real roots
In the context of Bode magnitude plots. . decade is the same as
20 dB/ decade =6 dB/ octave
40 dB/ decade =12 dB/ octave
In the feedback control system shown in the figure below .
R(s), Y(s) and E(s) are the Laplace transforms of r(t), y(t), and e(t), respectively. If the input r(t) is a unit step function, then ________.
does not exist, e(t) is oscillatory
Here,
i.e inner product outer product
System is marginally stable.
oscillatory system
doesn't exist
Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances , and (indicated in the figure) are_______.
Normalized impedance
Let be the unit vectors along x and y axes, respectively and let A be a positive constant. Which one of the following statements is true for the vector fields
Both are electrostatic fields.
Only is an electrostatic field.
Only is an electrostatic field.
Neither is an electrostatic field.
For an electrostatic field,
Curl of result in 0 & curl of is not 0.
Hence, is electrostatic, is not electrostatic.
In the circuit below, assume that the long channel NMOS transistor is biased in saturation. The small signal trans-conductance of the transistor is . Neglect body effect, channel length modulation and intrinsic device capacitances. The small signal input impedance is________.
….(I)
Input impedance
Input impedance will depend on and combination of
For the closed loop amplifier circuit shown below, the magnitude of open loop low frequency small signal voltage gain is 40. All the transistors are biased in saturation. The current source is ideal. Neglect body effect, channel length modulation and intrinsic device capacitances. The closed loop low frequency small signal voltage gain (rounded off to three decimal places) is________.
Given open loop gain
For the given differential amplifier with current mirror as active load.
Closed Loop gain
For the Boolean function
the essential prime implicants are________
,13,14,15)
Given minterms can be plotted in K-Map as shown below,
EPI is a PI which contains at least one minterm which is not covered by any other PI
Two such PI are quad at the center and also the quad formed by minterms at the corners of the K-Map
A white Gaussian noise with zero mean and power spectral density , when applied to a first-order RC low pass filter produces an output . At a particular time , the variance of the random variable is _________.
For RC LPF
A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t). A signal x(0.5 t) is applied to another causal and stable LTI system with impulse response h(0.5t). The resulting output is_________.
For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (𝑇) dependence of free electron concentration (𝑛)
The graph of log(n) vs 1/T is mentioned.
In the circuit shown, the step-down transformer and the diodes are ideal. The diodes have no voltage drop in forward biased condition. If the input voltage (in Volts) is and the average value of load voltage (in Volts) is , the value of is ________.
Let peak of each half of secondary.
Peak voltage across complete secondary winding,
A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is______.
Given 32-bit architecture {1 word long instructions}
1 word =32-bits
Number of registers = 2, bits required
Number instructions = 40
Opcode bits would be
n = 6-bits
Each register field requires 5-bits.
Instruction format would be
Immediate value bits = 32 – (6 + 5 + 5 + 5)
= 32 – 21
= 11-bits
The range of unsigned values
Maximum unsigned integer = 2047
An amplitude modulator has output (in Volts)
The carrier power normalized to resistance is 50 Watts. The ratio of the total sideband power to the total power is . The value of (in Volts, rounded off to two decimal places) is_______.
Given:
In a number system of base , the equation has as one of its solutions. The value of is_______.
Convert to decimal
Let and denote the set of real numbers and the three-dimensional vector space over it, respectively. The value of for which the set of vectors
Dose not form a basis of is__________.
Basis set of vectors is a linearly independent set and hence if the set does not form a basis then the matrix formed by its vectors should have determinant to be 0.
For the set to not form a basis,
In the given circuit, the current (in mA) is _________.
By KCL at super node,
In the circuit given below, the switch was kept open for a sufficiently long time and is closed at time . The time constant (in seconds) of the circuit for is ________.
To calculate across L,
Current source OC
Suppose and are independent and identically distributed random variables that are distributed uniformly in the interval . The probability that is _________.
(Area of triangle from Z>0)
A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is _________.
As shown in the circuit, the initial voltage across the capacitor is , with the switch being open. The switch is then closed at . The total energy dissipated in the ideal Zener diode after the switch is closed (in , rounded off to three decimal places) is ________.
C will discharge till
Capacitor current is given by,
Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the N latitude circle, that contains the north pole in its interior is__________.
In spherical coordinate system for 60° latitude,
As
Consider a unity negative feedback control system with forward path gain as shown.
The impulse response of the closed-loop system decays faster than if
Impulse response
To decay faster than , poles must lie to the left of
Replace
If poles lie to the left of imaginary axis after transformation then poles will lie to the left of s=-1
For stability inner producer outer product
Option (a) satisfies
A satellite attitude control system, as shown below, has a plant with transfer function cascaded with a compensator , where K and are positive real constants.
In order for the closed-loop system to have poles at , the value of must be ________.
…(1)
This equation will have 3 roots out of which roots are complex lying at , the third pole will be real.
Assuming that the third pole lies at s = -p
Let be
…(2)
Comparing (1) and (2)
A uniform plane wave with electric field is travelling in the air (relative permittivity, and relative permeability, ) in the direction ( is a positive constant, is the unit vector along the axis). It is incident normally on an ideal electric conductor (conductivity, ) at . The position of the first null of the total magnetic field in the air (measured from , in metres) is
At perfect conductor,
We know that occurs at
Hance,
So,
So, for 1st value of for H-field to be zero
Now, form equation
Hence
If the reference is not at interference, then
A 4-bit priority encoder has inputs , and in descending order of priority. The two-bit output is generated as , and 11 corresponding to inputs , and , respectively. The Boolean expression of the output bit is_____.
B = 1 for second row 01xx which means 4 minterms (0100, 0101, 0110, 0111 i.e. 4,5,6,7)
B = 1 for third row 000x which means two minterms (0000, 0001)
The propagation delay of the MUX shown in the circuit is 10 ns. Consider the propagation delay of the inverter as .
If is set to 1 then the output is________.
a square wave of frequency
a square wave of frequency
constant at 0
constant at 1
As
This means that circuit is operating in toggle mode and hence the output inverts itself every time after propagation delay.
If initially, wave form
The sequence of states of the given synchronous sequential circuit is ________.
Based on the logic circuit given in the question,
and
As per the characteristic equation of T-flipflop
So,
Let z be a complex variable. If and C is the circle in the complex plane with __________.
Residue at [double pole]
Residue at z=2 (single pole)
By Residue Theorem
Consider two continuous time signals x(t) and y(t) as shown below
If X(f) denotes the Fourier transform of x(t), then the Fourier transform of y(t) is__________.
Marks To All
The width of y(t) is double of x(t) and hence there is a time scaling by a factor of ½.
Based on the waveforms of the signals given,
A source transmits a symbol , taken from with equal probability, over an additive white Gaussian noise channel. The received noisy symbol is given by , where the noise is zero mean with variance 4 and is independent of .
Using , the optimum symbol error probability is_______.
transmission of
transmission of
transmission of
Given,
where,
where,
A full scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1W, and the total noise and distortion normalized power is . The effective number of bits (rounded off to the nearest integer) of the ADC is ________.
Given:
Signal power , Noise power
Now,
The information bit sequence is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is . The encoded sequence of bits is ___________.
Given information bit sequence:
Generator Polynomial
Maximum power of generator polynomial is 4.
So append 4 zeros in d
d=11101 01 01 0000
Replace last 0000 in d with 1100
Encoded sequence = 11101 01 0111 00
The opamps in the circuit shown are ideal, but have saturation voltages of .
Assume that the initial inductor current is . The input voltage is a triangular signal with peak voltages of and time period of . Which one of the following statements is true?
is delayed by relative to , and is a triangular waveform.
is not delayed relative to , and is a trapezoidal waveform.
is not delayed relative to , and is a triangular waveform.
is delayed by relative to , and is a trapezoidal waveform.
OPA1non-inverting Schmitt trigger
By Voltage Division Rule,
At UTP and LTP, Inverting and Non-Inverting Terminals would have equal voltage
For
Hence, we can draw wave form like,
Hence, is delayed las w.r.t .
Only from here we can say option (d) is correct. But to complete analysis
Now, for OPA2,
As is a square wave, we can take it as constant in each period.
Initially .
If we take in ,
Now, if
Then,
Hence,
Now, at
Now, if
From to , is fixed
Hence, we get a trapezoidal waveform in steady state.
In the circuit below, the opamp is ideal
If the circuit is to show sustained oscillations, the respective values of and the corresponding frequency of oscillation are________.
and
and
and
and
Wien Bridge Oscillator
In the circuit shown below, the transistors and are biased in saturation. Their small signal transconductances are and respectively. Neglect body effect, channel length modulation and intrinsic device capacitances.
The small signal model for the circuit given in question is shown below,
By
By KVL
Let be a random process, where amplitude and phase are independent of each other, and are uniformly distributed in the intervals and , respectively. is fed to an 8 -bit uniform mid-rise type quantizer. Given that the autocorrelation of is , the signal to quantization noise ratio (in , rounded off to two decimal places) at the output of the quantizer is_________.
A lossless transmission line with characteristic impedance is terminated with an unknown load. The magnitude of the reflection co-efficient is . As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in ) is ________.
The relationship between any N-length sequence x[n] and its corresponding N-point discrete Fourier transform X[k] is defined as
Another sequence y[n] is formed as below
For the sequence x[n]={1,2,1,3}, the value of Y[0] is __________
According duality property of DFT
For the two port network shown below, the value of the parameter (in Siemens) is__________.
Port-2 must be short circuited
Also,
Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of , a fixed positive oxide charge of at the oxide-silicon interface, and a metal work function of . Assume that the relative permittivity of the oxide is 4 and the absolute permittivity of free space is . If the flatband voltage is , the work function of the -type silicon (in , rounded off to two decimal places) is________.
Oxide capacitance is given by
Flat band voltage =
Sin Q it is given
Positive
Negative
Work function energy of semiconductor.
In the network shown below, maximum power is to be transferred to the load .
The value of in is __________.
A non-degenerate n-type semiconductor has neutral dopant atoms. Its Fermi level is located at below the conduction band and the donor energy level has a degeneracy of 2. Assuming the thermal voltage to be . The difference between and (in , rounded off to two decimal places) is __________.
neutral donor atoms/dopant atoms means donor atoms are ionized. Concentration of electrons occupying the donor level is given as
and where is ionized donor atoms concentration.
according to question
An NMOS transistor operating in the linear region has of at of 0.1 V. Keeping constant, the is increased to 1.5 V.
Given that , the
transconductance at the new operating point
(in , rounded off to two decimal places) is________.
In linear region,
The photocurrent of a PN junction diode solar cell is . The voltage corresponding to its maximum power point is . If the thermal voltage is , the reverse saturation current of the diode (in , rounded off to two decimal places) is______.
Given voltage is in terms of maximum power
i.e.
is not given
A digital communication system transmits through a noiseless bandlimited channel . The received signal at the output of the receiving filter is given by where are the symbols and is the overall system response to a single symbol. The received signal is sampled at . The Fourier transform of is . The Nyquist condition that must satisfy for zero inter symbol interference at the receiver is _______.
Marks to All
For zero ISI, x(t) should have zero crossings at ………
or
A continuous time signal is sampled at a rate of 15 Hz. The sampled signal when passed through an LTI system with impulse response
Produces an output The expression for is __________.
Marks to All
After sampling,
Now,
Hence, and components won’t appear in output.
Only will be present.
For a causal discrete-time LTI system with transfer function
Which of the following statements is/are true?
Since, the system is given to be causal, ROC must lie outside the outermost pole and hence ROC is
Such ROC will include the unit circle and hence the system is stable.
pole is present in right half part of z-plane non-minimum phase system
Let and represent density and velocity, respectively, at a point and time t. Assume is continuous. Let be an arbitrary volume in space enclosed by the closed surface and be the outward unit normal of Which of the following equations is/are equivalent to ?
The free electron concentration profile in a doped semiconductor at equilibrium is shown in the figure, where the points , and mark three different positions. Which of the following statements is/are true?
For between B and C, the electron diffusion current is directed from to .
For between B and A, the electron drift current is directed from B to A.
For between B and C, the electric field is directed from B to C.
For between B and A, the electric field is directed from to .
- Density of is maximum at point and minimum at .
- will move from , and from to .
Which of the following statements is/are true for a BJT with respect to its DC current gain ?
Under high-level injection condition in forward active mode, will decrease with increase in the magnitude of collector current.
Under low-level injection condition in forward active mode, where the current at the emitter-base junction is dominated by recombination-generation process, will decrease with increase in the magnitude of collector current.
will be lower when the BJT is in saturation region compared to when it is in active region.
A higher value of will lead to a lower value of the collector-to-emitter breakdown voltage.
When increases then by relation
Collector current increases thus
(collector to emitter voltage) decreases.
In saturation
will be lower when. BJT is in saturation region compared to when it as in alive region.
Consider a system S represented in state space as
Which of the state space representations given below has/have the same transfer function as that of S?
Opt (a)
(a) and (c) are correct.
Let be functions of (x, y, z). Suppose that for every given pair of points A and B in space, the line integral evaluates to the same value along any path C that starts at A and ends at B. Then which of the following is/are true?
For every closed path T, we have
There exists a differentiable scalar function F(x,y,z) such that
is independent of C
is conservative.
Line Integral of conservative field over a closed curve is 0
is correct
For conservative field the curl is zero
Hence the conservative field can be expressed as gradient of a scalar field
We can write
is correct.
Also,
is correct
Consider the matrix where k is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?
If ,
=0
Similarly, if
The radian frequency value(s) for which the discrete time sinusoidal signal
has a period of 40 is/are__________.
For periodic signal,
where
For
For m=6, if , then
Hence, over here N=20
If N is any time period, (a,c,d) is correct.
If N is the fundamental time period, (a,d) is correct.