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

2001

1.       The ideal OP-AMP has the following characteristics

           a.       R_i = ∞, A_V= ∞, R_o = 0

           b.      R_i = 0, A_V= ∞, R_o = 0

           c.       R_i = ∞, A_V= ∞, R_o = ∞

           d.      R_i = 0, A_V= ∞, R_o = ∞

Answer:       A

https://www.youtube.com/watch?v=mtUl2BzGphU

 

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

           a.        – 8

           b.      – 9

           c.       – 10

           d.      – 11

Answer:      B

https://www.youtube.com/watch?v=JMZCkiOUJDI

 

3.       In the figure, assume the OP-AMPs to be ideal. The output V_o 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 V_o in terms of V_s, R and the reverse saturation current I_s of the transistor.

      b.      If R = 1 Ω, I_s = 1 pA and the thermal voltage V_T = 25 mV, then what is the value of the output voltage V_o for an input voltage V_s 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 I_s. The P-side of the diode is connected to node A and the N-side to node B. then what is the expression for V_o in terms of V_s, R and I_s ?

Answer:       
(a) V_O = – V_T ln(V_S/I_OR)
(b) – 0.81 volts
(c) V_O = – ηV_T ln(V_S/I_OR)
 Solution:  https://www.youtube.com/watch?v=3YOkRQGOWbg

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 f_o, β(f) = V_f(f)/V_o(f) = 1/6 ∟0^o, 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

Answer:     C
Solution: https://www.youtube.com/watch?v=vG62ly43ziE

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 I_o and the input voltage V_i.

      c.       Determine Io and V_op if V_i = 2 volt. Assume β = 99 and V_BE = 0.7 volts.

Answer:      
(a) Active region
(b) V_i = I_OR_L – 15
(c) I_O = 1.7 Amp, V_OP = 5.25 volts

Solution:  https://www.youtube.com/watch?v=F4ZuatGRJO0

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 V_OUT 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 i_L is 

           a.       – V_S / R₂ 

           b.      V_S / R₂ 

           c.       – V_S / R_L 

           d.      V_S / R₁ 

Answer:      A
Solution:    https://www.youtube.com/watch?v=TxVYCU-8ejQ

2005

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

           a.       30/4 KΩ

           b.      10 KΩ

           c.       40 KΩ

           d.      Infinite

Answer:     B
Solution:  https://www.youtube.com/watch?v=N7D9lXz25dU

2.       The voltage e_o 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 R_E

           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 V_C 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

Solution:  https://www.youtube.com/watch?v=XbVKE5nEOPI

  

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 V_out. 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, V_o 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 = I_Sexp(V/V_T). For V_i = 2 Volts, V_o = V₀₁, and for V_i = 4 Volts, V_o = V₀₂. The  relationship between V₀₁ and V₀₂ is

           a.       V₀₂ = √2 V₀₁ 

           b.      V₀₂ = e² V₀₁

           c.       V₀₂ = V₀₁ ln2

           d.      V₀₂ -  V₀₁ = V_T 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 V_o(s)/ V_i(s) is

Answer:      A

 

4.       If V_i = V₁ sin(ωt) and V_o = 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 = I_o(exp(V/V_T) - 1), where VT = 25 mV, I_o = 1 µA and V is the voltage across the diode(taken as positive for forward bias). For an input voltage V_i = - 1 volts, the output voltage V_o 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 V_o(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 V_BE = 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 i_i and the output voltage v_o. 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 (V_out), 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:     https://www.youtube.com/watch?v=vR9F9Cmapog

  

2.       In the circuit shown below, the OP-AMPs are ideal. Then V_out 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 KΩ) is ……..

         Answer:     3.18

               Solution :    https://www.youtube.com/watch?v=BjcHUWQA4TQ

2.       In the voltage regulator circuit shown in the figure, the Op-Amp is ideal. The BJT has V_BE = 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 Ω) is ……..

              Answer:     1090

               Solution :   https://www.youtube.com/watch?v=B5rropdO8jA

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

           a.       – I₂(R₁ + R₂)

           b.      I₂R₂

           c.       I₁R₂

           d.      – I₁(R₁ + R₂)

Answer:     C

               Solution :   https://www.youtube.com/watch?v=DAEuj8Z-ncY

4.       In the differential amplifier shown in the figure, the magnitude of the common mode and differential mode gains are A_cm and A_d, respectively. If the resistance R_E is increased, then

           a.       A_cm increases

           b.      Common mode rejection ratio increases

           c.       A_d increases

           d.      Common mode rejection ratio decreases

Answer:     B

               Solution :   https://www.youtube.com/watch?v=AhxODnKBU5Y

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

Answer:     D

               Solution :   https://www.youtube.com/watch?v=Q7DUP4Rz58o

6.       The circuit represents 

           a.       A band pass filter

           b.      A voltage controlled oscillator

           c.       An Amplitude modulator

           d.      A monostable multivibrator

Answer:     D

               Solution :  https://www.youtube.com/watch?v=oi_nPP2yd4k

2015

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

Answer:      159.15

Solution:       https://www.youtube.com/watch?v=68aTpkiHA6c       

           

2.       In the circuit shown, assume that the OP-AMP is ideal. If the gain (V_o/V_in) is –12 , then the value of R (in kΩ) is _________________

Answer:      1 Kohm

Solution:      https://www.youtube.com/watch?v=tK6-rhSk62w        

           

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

Answer:     250

Solution:          https://www.youtube.com/watch?v=j3isPwGHe_8               

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

Solution:      https://www.youtube.com/watch?v=SA30jnkdunM                   

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 27^oC. At 50^oC, the value of voltage V₁₂ = V₁ – V₂ (in mV) is _______________

Answer:     83.4

Solution:       https://www.youtube.com/watch?v=vltaQSRU2KE                  

6.       In the circuit shown, V_o = V_OA for switch SW in position A and V_o = V_OB for switch SW in position B. Assume that the OP-AMP is ideal. The value of V_OB/V_OA is ______________

Answer:     1.5

Solution:      https://www.youtube.com/watch?v=c4GkgCOXgLQ    

               

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

Solution:      https://www.youtube.com/watch?v=Q6RQWfpg_6c      

   

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

Answer:     12

Solution:      https://www.youtube.com/watch?v=3RL9Dy8Xxco                   

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

Answer:     2.85

Solution:         https://www.youtube.com/watch?v=cKkJa1-Kl_U