### Previous GATE Questions on Operational Amplifiers & Differential Amplifiers - 1 (1987 - 2000)

1987

1.       In the figure, if the CMRR of the operational amplifier is 60 dB, then the magnitude of the output voltage is

1988

1.       The OP-AMP shown in figure below is ideal and R = (L/C)1/2. The phase angle between Vo and Vi at ω = 1/(LC)1/2 is

a.       π/2
b.      π
c.       3π/2
d.      2π

1989

1.       Referring to the figure shown,

1990

1.       The operational amplifier has a very poor open loop gain of 45, otherwise is ideal. The gain of the amplifier is

a.       5
b.      20
c.       4
d.      4.5

2.       The CMRR of the differential amplifier shown is

a.       Infinity
b.      Zero
c.       900
d.      1800

3.       If the input to the circuit shown is a sine wave, the output will be

a.       Half wave rectified sine wave
b.      Full wave rectified sine wave
c.       Triangular wave
d.      Square wave

1991

1.       In order that the circuit of figure works properly as differentiator it should be modified to __________(draw the modified circuit)

2.       In the figure, the operational amplifier is ideal and its output can swing between – 15 and + 15 volts.

The input Vi, which is zero for t<0, is switched to 5 volts at the instant t = 0. Given that the output Vo is + 15 volts for t<0, sketch the waveforms of Vo and Vi. You must give the values of important parameters of the sketch.

Answer:   Vo(t) = - 5t x 103 + 15

3.       In figure, the operational amplifier are ideal and their output can swing between – 15 and + 15 volts. Sketch the waveform of voltages of V1 and V2 as a function of time. You must give the values of important parameters of this sketch.

1992

1.       An operational amplifier has an offset voltage of 1 mV and is ideal in all other respects. If this amplifier is used in the circuit shown in figure, the output voltage will be (select the nearest value)
a.       1 mV
b.      1 V
c.       ± 1 V
d.      0

2.       The circuit of figure uses an ideal operational amplifier. For small positive values of Vin, the circuit works as

a.       Half Wave Rectifier
b.      Differentiator
c.       Logarithmic amplifier
d.      Exponential amplifier

3.       Assume that the operational amplifier in figure is ideal. The current I through the 1 k resistor is _____________

4.       The transistors in the differential amplifier shown in figure are identical with hfe = 100 and re = 25 at 1 mA collector current. The circuit has a CMRR of 100.

a.       What is the differential gain of the circuit?
b.      What is the common mode gain of the circuit?
c.       If DC voltage of 1010 mV and 990 mV are applied to inputs 1 and 2 respectively       with reference to ground, what will be the output voltage Vo?

Answer:   (a) 20 (b) 0.2 (c) 600 mV

5.       Consider the circuit shown in figure. This circuit uses an ideal operational amplifier.

Assuming that the impedance's at nodes A and B do not load the preceding bridge circuit, calculate the output voltage Vo. When (a)  RA = RB = RC = RD = 100    and (b) RA = RB = RC = 100 Ω and RD = 120 Ω.

Answer:   (a) 0 volts (b) - 0.552 volts

1993

1.       For the ideal operational amplifier circuit shown, determine the output voltage Vo.

2.       Find the output voltage Vo in the following circuit, assuming that the operational amplifier is ideal.

1994

1.       The frequency compensation is used in operational amplifiers is to increase its ___________

2.   Assuming that the amplifier shown in the figure below is a voltage controlled voltage source.

Show that the voltage transfer function of the network is given by

3.   Calculate the frequency at which zero transmission is obtained from the Wien-bridge shown below.

4.   Find the output voltage of the following circuit shown below, assuming ideal operational amplifier behavior.

1995

1.       A change in the value of the emitter resistance, RE, in a differential amplifier
a.       affects the difference mode gain Ad
b.      affects the common mode gain Ac
c.       affects both Ad and Ac
d.      does not affect both Ad and Ac.

2.       In the given circuit, if the voltage V+ and V_ are to amplified by the same factor, the value of R should be _________

3.       An OP-AMP is used as a zero crossing detector. If the maximum output available from the OP-AMP is  ±12 volts peak to peak, and the slew rate of the OP-AMP is 12 V/µsec, then the maximum frequency of the input signal that can be applied without causing a reduction in the peak to peak output is _____________

4.   Sketch the output as a function of the input voltage (for negative values) for circuit shown below. Assume ideal operational amplifier and diode forward voltage drop as zero.

Answer:   (a) 0 Volts (b) -Vin

5.   The waveform input to the sweep generator circuit shown in figure, is a square wave of period 2 msec and amplitude varying between 0 and 12 volts.

a.       Draw the waveform Vo(t), in relation to the input
b.      Specify Vo(t) determine the voltage levels and the time constants involved.

6.   Show that the circuit shown in figure is double integrator. In other words, prove that the transfer gain is given by Vo(s)/Vs(s) =  1/(CRs)2, assume ideal operational amplifier.

1996

1.       The circuit shown in the figure is  that of

a.       A Non-inverting amplifier
b.      An Inverting amplifier
c.       An Oscillator
d.      A Schmitt trigger

2.       Value of R in the oscillator circuit shown in the given figure, so chosen that it just oscillates at an angular frequency of ω. The value of ω and the required value of R will respectively are

a.       105 rad/sec, 2 x 104
b.      2 x 104 rad/sec, 2 x 104
c.       2 x 104 rad/sec,  105

3.   A resistively loaded and resistively biased differential amplifier circuit is shown. Neglect base current and assume matched transistors with VA -> and β = 100. Use VT = 26 mV, VBE(on) = 0.7 volts and VCE(sat) = 0.1 volts.

a.       Determine the values of RC and R2 to meet the following specifications: double ended differential mode gain = 500, CMRR = 500 and differential mode input resistance of 2 M.
b.      Determine the minimum values of VCC and VEE such that the transistors remain in the forward active region under zero signal condition. Assume that the DC common mode input is zero.

Answer:   (a) 5 MΩ, 2.5 MΩ (b) 12.6 Volts, -13.83 Volts

4.   Assuming ideal operational amplifiers, show that the circuit shown simulates in inductor i.e. show that Vi(S)/Ii(S) is inductive and write the expression for the effective inductance.

1997

1.       The output voltage Vo of the circuit shown is

a.       – 4 volts
b.      6 volts
c.       5 volts
d.      – 5.5 volts

2.       Consider the circuit given in the figure is using an ideal operational amplifier. The            characteristics of the diode are given by the relation I = IS(eqV/KT – 1), where V is the      forward voltage  across the diode.

a.       Express Vo as function of Vi , assuming Vi > 0
b.      If R = 100 kΩ, IS = 1 µA and VT = 25 mV, find the input voltage Vi for which Vo = 0.

Answer:   (a) VD = ISR – VT ln(Vi/ISR) (b) 5.46 Volts

3.       In circuit shown, assume that the operational amplifier is ideal and that Vo = 0 volts initially.   The switch is connected first to ‘A’ charging C1 to the voltage V. it is then connected to      the  point ‘B’. This process is repeated 'f' times per second.

a.       Calculate the charge transferred per second from node A to node B.
b.      Derive the average rate of change of the output voltage Vo.
c.       If the capacitor and the switch are removed and a resistor is connected                                     between points  A and B, find the value of the resistor to get the same average rate                  of change of the output  voltage?
d.      If the repetition rate of the switching action is 104 times per second, C1 =                                 100pF, C2 = 10pF and V= 10 mV. What is the average change of the output                                voltage?

Answer:   (a) C1Vf (b) – (C1Vf)/C2 (c) R = 1/C1f (d) - 1000 V/sec

4.       An IC 555 chip has been used to construct a pulse generator. Typical pin connections with components are shown below. It is desired to generate a square pulse of 10 kHz.

Evaluate values of RA and RB if the capacitor C has the value of 0.01 µF for the                     configuration chosen. If necessary you can suggest modification in the external                       configuration.

Answer:   RA = RB = 5 kΩ

1998

1.       In a differential amplifier, CMRR can be improved by using an increased
a.       Emitter resistance
b.      Collector resistance
c.       Power supply voltages
d.      Source resistance

2.       From a measurement of the rise time of the output pulse of an amplifier, whose input is a small amplitude square wave, one can estimate the following parameter of the amplifier
a.       Gain-bandwidth product
b.      Slew rate
c.       Upper 3 dB frequency
d.      Lower 3 dB frequency

3.       The emitter coupled pair of BJT’s given a linear transfer relation between the differential output voltage and the differential input voltage Vid, only when the magnitude of Vid  is less α times the thermal voltage, where α is
a.       4
b.      3
c.       2
d.      1

4.   One input terminal of high gain comparator circuit is connected to ground and a sinusoidal voltage is applied to the other input. The output of comparator will be
a.       A sinusoid
b.      A full rectified sinusoid
c.       A half rectified sinusoid
d.      A square wave

5.   Determine the input impedance of the circuit shown and investigate if it can be inductive.

Answer:    Zi = - R2(1+SCR1)/(1+SCR2) and Zi is not Inductive.

6.   Find the value of R’ in the circuit shown for generating sinusoidal oscillations. Find the frequency of oscillations.
Answer:   R' = 2R, f = 1/2πRC

7.   Implement a monostable multivibrator using the timer circuit shown in figure. Also determine an expression for ON time ‘T’ of the output pulse.

Answer:   τp = RC ln(3) = 1.1 RC

1999

1.       The first pole encountered in the frequency response of a compensated OP-AMP is approximately at
a.       5 Hz
b.      10 kHz
c.       1 MHz
d.      100 MHz

2.   Neatly sketch and label the DC transfer characteristic (Vo verses Vin) of the circuit shown, as Vin varies from – 2 volts to + 2 volts.

Assume ideal operational amplifier and the diodes have a forward voltage of 0.6 volts and zero incremental resistance.

Answer:   Same as output of Half Wave Rectifier

2000

1.       In the differential amplifier of the figure, if the source resistance of the current source IEE is infinite, then the common mode gain is

a.       Zero
b.      Infinite
c.       Indeterminate
d.      (Vin1 + Vin2) / 2VT

2.       In the circuit shown in figure, the output voltage Vo is

a.       – 1 volts
b.       2  volts
c.       + 1 volts
d.      + 15 volts

3.       If the OP-AMP in the figure is ideal, then the output voltage Vo is

a.       Zero
b.      (V1 – V2) sinωt
c.       – (V1 + V2) sinωt
d.      (V1 + V2) sinωt

4.       The configuration of the figure is a

a.       Precision rectifier
b.      Hartley oscillator
c.       Butterworth high pass filter
d.      Wien-bridge oscillator

5.       Assume that the OP-AMP of the figure is ideal. If Vi is a triangular wave, then Vo will be

a.       Square wave
b.      Triangular wave
c.       Parabolic wave
d.      Sine wave

6.       The most commonly used amplifier in Sample and Hold circuits is
a.       Unity gain inverting amplifier
b.      Unity gain non-inverting amplifier
c.       An inverting amplifier with a gain of 10
d.      An inverting amplifier with a gain of 100

7.       If the OP-AMP in the figure has an input offset voltage of 5 mV and an open loop voltage gain of 10,000. Then the output Vo will be
a.       0 volts
b.      5 mV
c.       + 15 volts or – 15 volts
d.      + 50 volts or – 50 volts

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