### GATE Study Materials for ECE, EIE, CSE, CSIT and EEE (Hand Written GATE Class Notes)

The following subjects with hand written notes will be useful for both
Electronics & Communication Engineering (ECE) and
Electrical & Electronics Engineering (EEE).
Few subjects will be used for
Electronics & Instrumentation Engineering (EIE)
Computer Science Engineering (CSE)

thanks to raghul.org......

 S.No: Subjects Links 1 Analog Electronics 2 Communication Systems 3 Control Systems 4 Digital Electronics 5 Electrical Machines 6 Electrical Measurements 7 Electromagnectic Theory 8 Electronic Devices & Circuits 9 Engineering Mathematics 10 Microprocessors 11 Network Theory 12 Power Electronics 13 Power Systems 14 Signals & Systems

### Previous GATE Questions on Shift Registers with Solutions (1987 - Till Date)

1992

4.       The initial contents of the 4 bit serial in serial out, right shift, shift register shown in figure, are 0110. After three clock pulses are applied, the contents of the shift register will be

a.       0000
b.      0101
c.       1010
d.      1111

Answer:     C

1996

2.       A pulse train can be delayed by a finite number of clock periods using a
a.       Serial In Serial Out shift register
b.      Serial In Parallel Out shift register
c.       Parallel In serial Out shift register
d.      Parallel In parallel Out shift register
Answer:    A
Solution :

11.    A 4 bit shift register, which shifts 1 bit to the right at every clock pulse, is initialized to values 1000 for (Q0Q1Q2Q3). The D input is derived from Q0, Q2 and Q3 through two XOR gates as shown in figure.

a.       Write the 4 bit values (Q0Q1Q2Q3) after each clock pulse till the pattern (1000)             reappears on (Q0Q1Q2Q3).
b.      To what values should the shift register be initialized so that the pattern (1001)            occurs after the first clock pulse?

1997

15.   Circuit shown in the figure is an NMOS shift register. All transistors are NMOS enhancement type with threshold voltage VT = 1 volt. Supply used is VDD = 5 volts.

Two non- overlapping clocks ø1 and ø2 are as shown in the figure is and have large pulse widths.
All capacitors are initially discharged and the Vin = 0 volts is applied. If values of capacitors are C1 = 2 pF and C2 = 1 pF. Find out voltage VC2 on capacitor C2 after ø2 goes low. Neglect body effect on VT in your evaluation.

2004

4.       Choose the correct one from among the alternatives A,B,C,D after matching an item from Group 1 with the most appropriate item in Group 2.
 Group 1 Group 2 P: Shift Register 1: Frequency division Q: Counter 2: Addressing in memory chips R: Decoder 3: Serial to Parallel data conversion

a.       P – 3, Q – 2, R – 1
b.      P – 3, Q – 1, R – 2
c.       P – 2, Q – 1, R – 3
d.      P – 1, Q – 2, R – 2
Answer:    B

2006

4.       For the circuit shown, two 4-bit parallel in serial out shift registers loaded with the data shown are used to fed the data to a full adder. Initially, all the flip-flops are in clear state. After applying two clock pulses, the outputs sum and carry of the full adder should be ……respectively.

a.       0, 0
b.      0, 1
c.       1, 0
d.      1, 1
Answer:    D

### Previous GATE Questions on Operational Amplifiers & Differential Amplifiers - II (2001 - Till Date)

2001

1.       The ideal OP-AMP has the following characteristics
a.       Ri = , AV= , Ro = 0
b.      Ri = 0, AV= , Ro = 0
c.       Ri = , AV= , Ro =
d.      Ri = 0, AV= , Ro =
Answer:       A

2.       The inverting OP-AMP shown in the figure has an open loop gain of 100. The closed loop gain Vo/Vs is

a.        – 8
b.      – 9
c.       – 10
d.      – 11
Answer:      B

3.       In the figure, assume the OP-AMPs to be ideal. The output Vo of the circuit is

Answer:      A
Solution:  https://www.youtube.com/watch?v=E4dxhaGLiOA

4.   In the circuit shown, assume that the OP-AMP is ideal.

a.       Obtain an expression for Vo in terms of Vs, R and the reverse saturation current Is of the transistor.
b.      If R = 1 , Is = 1 pA and the thermal voltage VT = 25 mV, then what is the value of the output voltage Vo for an input voltage Vs of 1 volt?
c.       Suppose that the transistor in the feedback path is replaced by a  PN junction diode with a reverse saturation current of Is. The P-side of the diode is connected to node A and the N-side to node B. then what is the expression for Vo in terms of Vs, R and Is ?

Answer:
(a) VO = – VT ln(VS/IOR)
(b) – 0.81 volts
(c) VO = – ηVT ln(VS/IOR)

2002

1.       A 741 OP-AMP has a gain-bandwidth product of 1 MHz. A non-inverting amplifier using this OP-AMP and having a voltage gain of 20 dB will exhibit a –3 dB bandwidth of
a.       50 kHz
b.      100 kHz
c.       100/17 kHz
d.      1000/7.07 kHz
Answer:      B
Solution:  https://www.youtube.com/watch?v=jg0FBlbWzMU

2.       The circuit in the figure employs positive feedback and is intended to generate sinusoidal oscillations. If at a frequency fo, β(f) = Vf(f)/Vo(f) = 1/6 0o, then to sustain oscillations at this frequency

a.       R2 = 6R1
b.      R2 = 5R1
c.       R2 = R1/6
d.      R2 = R1/5
Answer:     B
Solution: https://www.youtube.com/watch?v=E28FKsiD0cQ

3.       An amplifier using an OP-AMP with a slew rate SR = 1 V/µsec has a gain of 40 dB. If this amplifier has to faithfully amplify sinusoidal signals form dc to 20 kHz without any slew rate induced distortion, then the input signal level must not exceed
a.       795 mV
b.      395 mV
c.       79.5 mV
d.      39.5 mV

4.   Consider the circuit shown. Assume the operational amplifier is ideal.

a.       In which mode is the BJT operating (active or saturation or cutoff)? Justify your answer.
b.      Obtain an expression relating the output current Io and the input voltage Vi.
c.       Determine Io and Vop if Vi = 2 volt. Assume β = 99 and VBE = 0.7 volts.
Answer:
(a) Active region
(b) Vi = IORL – 15
(c) IO = 1.7 Amp, VOP = 5.25 volts

2003

1.       If the input to the ideal comparator shown in the figure is a sinusoidal signal of 8 volts peak to peak, without any DC component, then the output of the comparator has a duty cycle of

a.       1/2
b.      1/3
c.       1/6
d.      1/2
Answer:      B
Solution: https://www.youtube.com/watch?v=c_SMIFD5g0w

2.       If the differential voltage gain and the common mode voltage gain of a differential amplifier are 48 dB and 2 dB respectively, then common mode rejection ratio is
a.       23 dB
b.      25 dB
c.       46 dB
d.      50 dB
Answer:      C
Solution:  https://www.youtube.com/watch?v=OFD168On6wQ

3.       The oscillator circuit shown in the figure has an ideal inverting amplifier. Its frequency of oscillation in Hertz is

Answer:      A
Solution:   https://www.youtube.com/watch?v=BdULnwS91ts

4.       The output voltage of the regulated power supply shown in the figure is

a.       3 volts
b.      6 volts
c.       9 volts
d.      12 volts
Answer:      C
Solution:  https://www.youtube.com/watch?v=aYqrNc3c4KU

5.   If the OP-AMP in the figure is ideal, the output voltage VOUT will be equal to

a.       1 volt
b.      6 volts
c.       14 volts
d.      17 volts
Answer:      B
Solution:  https://www.youtube.com/watch?v=uUtCBwdwSjU

2004

1.       An ideal OP-AMP is an ideal
a.       Voltage Controlled Current Source
b.      Voltage Controlled Voltage Source
c.       Current Controlled Current Source
d.      Current Controlled Voltage Source
Answer:      B
Solution:  https://www.youtube.com/watch?v=-3pE3zjlc-I

2.       The circuit in the figure is a

a.       Low pass filter
b.      High pass filter
c.       Band pass filter
d.      Band reject filter
Answer:      A
Solution:  https://www.youtube.com/watch?v=hUwaNK0aINo

3.       The value of capacitor C required for sinusoidal oscillations of frequency 1 kHz in the circuit of the figure is

Answer:    A
Solution:  https://www.youtube.com/watch?v=dcCpebp-_Cs

4.       in the OP-AMP circuit given in the figure, the load current iL is

a.       – VS / R2
b.      VS / R2
c.       – VS / RL
d.      VS / R1
Answer:      A
Solution:    https://www.youtube.com/watch?v=TxVYCU-8ejQ

2005

1.       The input resistance Ri of the amplifier shown in figure is

a.       30/4 K
b.      10 K
c.       40 K
d.      Infinite
Answer:     B
Solution:  https://www.youtube.com/watch?v=N7D9lXz25dU

2.       The voltage eo indicated in figure has been measured by an ideal voltmeter, which of the following can be calculated?

a.       Bias current of the inverting input only
b.      Bias current of the inverting and non-inverting inputs only
c.       Input offset current only
d.      Both the bias currents and the input offset current.
Answer:      C
Solution:  https://www.youtube.com/watch?v=OuIncy3Iz-w

3.       The OP-AMP circuit shown in figure is a filter. The type of filter and its cut-off frequency are respectively.

a.       High pass, 1000 rad/sec
b.      Low pass, 1000 rad/sec
c.       High pass, 10000 rad/sec
d.      Low pass, 10000 rad/sec
Answer:     A
Solution:   https://www.youtube.com/watch?v=AykAekOV_Mg

4.       In the differential amplifier shown in figure, a large value of RE

a.       Increases both the differential and common mode gains
b.      Increases the common mode gain only
c.       Decreases the differential mode gain only
d.      Decreases the common mode gain only
Answer:      D
Solution:  https://www.youtube.com/watch?v=YH9E2xVqdv0

5.   Given the ideal operational amplifier circuit shown in figure indicate the correct transfer characteristics assuming ideal diodes with zero cut-in voltage.

Answer:      B
Solution:  https://www.youtube.com/watch?v=q_6bzIBuW7A

2006

1.       For the circuit shown in the following figure, the capacitor C is initially uncharged. At t = 0, the switch S is closed. The voltage VC across the capacitor at t = 1 ms is _____. Assume the OP – AMP is supplied with ± 15 volts.

a.       0 volts
b.      6.3 volts
c.       9.45 volts
d.      10 volts
Answer:        D

Statement for Linked Answer Questions (2 and 3):
A regulated power supply shown in the figure below has an unregulated input of 15 volts and generates a regulated output Vout. Use the component values shown in the figure.

2.       The power dissipation across the transistor Q1 shown in the figure is
a.       4.8 volts
b.      5.0 volts
c.       5.4 volts
d.      6.0 volts
Answer:  D
3.       If the unregulated voltage increases by 20%, then power dissipation across the transistor Q1
a.       Increases by 20%
b.      Increases by 50%
c.       Remains unchanged
d.      Decreases by 20%
Answer:      B
Solution:    https://www.youtube.com/watch?v=_fx1s9uTcCw

2007

1.       For the OP-AMP circuit shown in the figure, Vo is

a.       – 2 volts
b.      – 1 volts
c.       – 0.5 volts
d.      + 0.5 volts
Answer:     C
Solution:     https://www.youtube.com/watch?v=GNXEesKW7VQ

2.       In the OP-AMP circuit shown, assume that the diode current follows the equation I = ISexp(V/VT). For Vi = 2 Volts, Vo = V01, and for Vi = 4 Volts, Vo = V02. The  relationship between V01 and V02 is

a.       V02 = 2 V01
b.      V02 = e2 V01
c.       V02 = V01 ln2
d.      V02 -  V01 = VT ln2
Answer:      D
Solution:  https://www.youtube.com/watch?v=_FEUmzL53hg

Statement for Linked Answer Questions
Consider the OP-AMP circuit shown in the figure.

3.        The Transfer function Vo(s)/ Vi(s) is
Answer:      A

4.       If Vi = V1 sin(ωt) and Vo = V2 sin(ωt+ø), then the minimum and maximum values of ø (in radians) are respectively
a.       – π/2 and π/2
b.      0 and π/2
c.       – π and 0
d.      – π/2  and 0
Answer:      C
Solution:     https://www.youtube.com/watch?v=5BVus7UsCas

2008

1.       Consider the following circuit using an ideal OP-AMP. The I-V characteristic of the diode is described by the relation I = Io(exp(V/VT) - 1), where VT = 25 mV, Io = 1 µA and V is the voltage across the diode(taken as positive for forward bias). For an input voltage Vi = - 1 volts, the output voltage Vo is

a.       0 volts
b.      0.1 volts
c.       0.7 volts
d.      1.1 volts
Answer:      B
Solution:    https://www.youtube.com/watch?v=Hm-AQGstHH0

2.       The OP-AMP circuit shown below represents a

a.       High pass filter
b.      Low pass filter
c.       Band pass filter
d.      Band reject filter
Answer:      B
Solution:    https://www.youtube.com/watch?v=iNclgQhX8gs

3.       Consider the schmitt trigger circuit shown below.

A triangular wave which goes from –12 volts  to +12 volts is applied to the inverting input of OP-AMP. Assume that the output of the OP-AMP swings from +15 volts to –15 volts. The voltage at the non-inverting input switches between
a.       – 12 volts and +12 volts
b.      – 7.5 volts and +7.5 volts
c.       – 5 volts and +5 volts
d.      0 volts and +5 volts
Answer:      C
Solution:    https://www.youtube.com/watch?v=U1PM8Q0IT0o

2009

1.       In the following Astable Multivibrator circuit, which properties of Vo(t) depend  on R2 ?

a.       Only the frequency
b.      Only the amplitude
c.       Both the amplitude and the frequency
d.      Neither the amplitude nor the frequency
Answer:      A
Solution:    https://www.youtube.com/watch?v=CNrhstw1lQI

2.       In the circuit shown below, the OP-AMP is ideal, the transistor has VBE = 0.6 volts and β = 150. Decide whether the feedback in the circuit is positive or negative and determine the voltage V at the output of the OP-AMP.

a.       Positive feedback, V = 10 Volts
b.      Positive feedback, V = 0 Volts
c.       Negative feedback, V = 5 Volts
d.      Negative feedback, V = 2 Volts
Answer:      D
Solution:    https://www.youtube.com/watch?v=H6FpEgr7ZYI

2010

1.       Assuming the OP-AMP is ideal, the voltage gain of the amplifier shown below is

a.       - R2/R1
b.      - R3/R1
c.       - (R2 || R3) / R1
d.      - (R2 + R3)/R1
Answer:    A
Solution:    https://www.youtube.com/watch?v=-GMfvkT72y0

2.       The transfer characteristic for the precision rectifier circuit shown below is (Assume ideal OP-AMP and Practical Diodes)

Answer:      B
Solution:    https://www.youtube.com/watch?v=K2Rp0dv6Ll0

2011

1.       The circuit below implements a filter between the input current ii and the output voltage vo. Assume that the op-amp is ideal. The filter implemented is a

a.       Low pass filter
b.      Band pass filter
c.       Band stop filter
d.      High pass filter
Answer:      D
Solution:    https://www.youtube.com/watch?v=jH8CXKYc1No

2012

1.       The circuit shown is a

Answer:      B
Solution:    https://www.youtube.com/watch?v=tr13sXmjwH4

2013

1.       In the circuit shown below, what is the output voltage (Vout), if a silicon transistor Q and an ideal OP-AMP are used?

a.       - 15 volts
b.      - 0.7 volts
c.       + 0.7 volts
d.      + 15 volts
Answer:      B
Solution:

2.       In the circuit shown below, the OP-AMPs are ideal. Then Vout in volts is

a.       4
b.      6
c.       8
d.      10
Answer:      C
Solution:    https://www.youtube.com/watch?v=txQhRQhmZfE

2014

1.       In the low pass filter shown in the figure, for a cutoff frequency of 5 KHz, the value of R2 (in K) is ……..

Answer:     3.18

2.       In the voltage regulator circuit shown in the figure, the Op-Amp is ideal. The BJT has VBE = 0.7 volts, and β = 100, and the zener voltage is 4.7 volts. For a regulated output of 9 volts, the value of R (in ) is ……..

Answer:     1090

3.       In the circuit shown, the Op-Amp has finite input resistance, infinite voltage gain and zero input offset voltage. The output voltage Vout is …….

a.       – I2(R1 + R2)
b.      I2R2
c.       I1R2
d.      – I1(R1 + R2)
Answer:     C

4.       In the differential amplifier shown in the figure, the magnitude of the common mode and differential mode gains are Acm and Ad, respectively. If the resistance RE is increased, then

a.       Acm increases
b.      Common mode rejection ratio increases
c.       Ad increases
d.      Common mode rejection ratio decreases
Answer:     B

5.       Assuming that the Op-Amp in the circuit is ideal, then the output voltage is

Answer:     D

6.       The circuit represents

a.       A band pass filter
b.      A voltage controlled oscillator
c.       An Amplitude modulator
d.      A monostable multivibrator
Answer:     D

2015

1.       In the circuit shown, assume OP-AMP is ideal then the 3 dB cut off frequency (in Hz) is __________
Answer:      159.15

2.       In the circuit shown, assume that the OP-AMP is ideal. If the gain (Vo/Vin) is –12 , then the value of R (in kΩ) is _________________
Answer:      1 Kohm

3.       In the circuit shown, assume that the OP-AMP is ideal. The bridge output voltage Vo (in mV) for δ = 0.05 is _______________
Answer:     250

4.       The circuit shown in the figure has an ideal OP-AMP. The oscillation frequency and the condition to sustain the oscillations respectively are ________________
Answer:     D

5.       In the circuit shown, I1 = 80 mA and I2 = 4 mA. Transistors T1 and T2 are identical. Assume that thermal voltage is 26 mV at 27oC. At 50oC, the value of voltage V12 = V1 – V2 (in mV) is _______________
Answer:     83.4

6.       In the circuit shown, Vo = VOA for switch SW in position A and Vo = VOB for switch SW in position B. Assume that the OP-AMP is ideal. The value of VOB/VOA is ______________
Answer:     1.5

7.   In the bistable circuit shown, the ideal OP-AMP ahs saturation levels of ± 5 volts. The value of R1 (in kΩ) that gives a hysteresis width of 500 mV is _________________
Answer:      1 Kohm

8.   Assuming that the OP-AMP in the circuit shown is ideal, the output voltage Vo (inn volts) is __________
Answer:     12

9.   For the voltage regulator circuit shown,the input voltage (Vin) is 20 V ± 20% and the regulated output voltage (Vout) is 10 volts. Assume the OP-AMP is ideal. For a load RL drawing 200 mA, the maximum power dissipation in Q1 (in Watts) is _________________

Answer:     2.85

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