August 2014 | GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems

GATE 2000 ECE Video Solutions on Analog Circuits (Analog Electronics)

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

a. Zero
b. Infinite
c. Indeterminate
d. (V_in1 + V_in2) / 2V_T

Solution: https://www.youtube.com/watch?v=goC-ZRrr_Yw

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

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

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

3. Introducing a resistor in the emitter of a CE amplifier stabilizes the dc operating point against variations in
a. Only the temperature
b. Only the β of the transistor
c. Both temperature and β
d. None of the above

Solution: https://www.youtube.com/watch?v=Hj4RgZDwBwk

4. The current gain of a bipolar transistor drops at high frequencies because of
a. Transistor capacitances
b. High current effects in the base
c. Parasitic inductance effects
d. The Early Effect

Solution: https://www.youtube.com/watch?v=mZE9xTPfxjs

5. If the OP-AMP in the figure is ideal, then the output voltage V_o is

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

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

6. The configuration of the figure is a

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

Solution: https://www.youtube.com/watch?v=PxZImxr0h6Q

7. Assume that the OP-AMP of the figure is ideal. If V_i is a triangular wave, then V_o will be

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

Solution: https://www.youtube.com/watch?v=ZvsEb1Tpxaw

8. 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

Solution: https://www.youtube.com/watch?v=JFfOcIr8x7U

9. 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 V_o will be

a. 0 volts
b. 5 mV
c. + 15 volts or – 15 volts
d. + 50 volts or – 50 volts

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

10. a. For the circuit shown, plot V_o under steady state conditions, with and without capacitor C. Assume that the diode is ideal.

Solution: https://www.youtube.com/watch?v=GJXs26_62eE

b. Design a circuit using two ideal diodes, one resistor and two voltage sources that would convert the input voltage to the output voltage as shown in figure. The resistor value need not be specified.

Solution: https://www.youtube.com/watch?v=gXD0ms6S8iY

11. For the amplifier circuit shown, I_C = 1.3 mA, R_C = 2 kΩ, R_E = 500 Ω, V_T = 26 mV, β = 100, V_CC = 15 volts, V_S = 0.01 sin(ωt) volts and C_b = C_e = 10 µF.

a. What is the small signal voltage gain, V_o/V_S
b. What is the approximate voltage gain if C_e is removed?
c. What will be the output Vo, if C_b is short circuited?

Solution: https://www.youtube.com/watch?v=x75WPMXrTOg

12. For a feedback amplifier, the open loop transfer function has three poles at 100 k rad/sec, 1 M rad/sec and 10 M rad/sec. The low frequency open loop gain is 1000 and the feedback factor (β) is 1. Use Bode plots to determine the phase margin of the amplifier. Is the amplifier stable?

Solution: Amplifier is Unstable.

13. Below figure shown is a common base amplifier.

a. Write expressions for the time constants associated with the capacitances C_b and C_s.
b. What is the approximate lower cutoff frequency of the amplifier?

Solution: https://www.youtube.com/watch?v=wTtlORiy598

GATE 2001 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. The current gain of a BJT is
a. g_mr_o
b. g_m/ r_o
c. g_mr_π
d. g_m/ r_π

Solution: https://www.youtube.com/watch?v=NQcoEO5xLYk

2. 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 = ∞

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

3. Consider the following two statements :
Statement 1: Astable Multivibrator can be used for generating square wave.
Statement 2: Bistable Multivibrator can be used for storing binary information.
a. Only statement 1 is correct.
b. Only statement 2 is correct.
c. Both the statements 1 and 2 are correct.
d. Both the statements 1 and 2 are incorrect.

Solution: https://www.youtube.com/watch?v=HQUPS3pY2A8

4. An NPN BJT has g_m = 38 mA/volt, C_µ = 10^-14 F, C_π = 4x10^-13 F and DC current gain β = 90. For this transistor f_τ and f_β are
a. f_τ = 1.64 x 10⁸ Hz and f_β = 1.47 x 10¹⁰ Hz
b. f_τ = 1.47 x 10¹⁰ Hz and f_β = 1.64 x 10⁸ Hz
c. f_τ = 1.33 x 10¹² Hz and f_β = 1.47 x 10¹⁰ Hz
d. f_τ = 1.47 x 10¹⁰ Hz and f_β = 1.33 x 10¹² Hz

Solution: https://www.youtube.com/watch?v=VJJplixM0a8

5. The following circuit shown in the figure is

a. Hartley oscillator with f_osc = 79.6MHz
b. Colpitts oscillator with f_osc = 50.3MHz
c. Hartley oscillator with f_osc = 159.2MHz
d. Colpitts oscillator with f_osc = 159.2MHz

Solution: https://www.youtube.com/watch?v=U6V6gK9avGY

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

a. – 8
b. – 9
c. – 10
d. – 11

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

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

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

8. An emitter follower amplifier is shown below, where Z_i is the impedance looking into the base of the transistor and Z_o is the impedance looking into the emitter of the transistor.

a. Draw the small signal equivalent circuit of the amplifier.
b. Obtain an expression for Z_i.
c. Obtain an expression for Z_o.
d. Determine Z_i and Z_o, if a capacitor C is connected across R₁.

Solution: https://www.youtube.com/watch?v=UH5_EioJdxU

9. 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 ?

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

GATE 2002 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. In a negative feedback amplifier using voltage-series (Voltage sampling and series mixing) feedback,
a. R_i decreases and R_o decreases
b. R_i decreases and R_o increases
c. R_i increases and R_o decreases
d. R_i increases and R_o increases

Solution: https://www.youtube.com/watch?v=_22d9h7qEFU

2. 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

Solution: https://www.youtube.com/watch?v=jg0FBlbWzMU

3. Three identical RC coupled transistor amplifiers are cascaded. If each of the amplifiers has a frequency response as shown in the figure, the overall frequency response is as given in

Solution: https://www.youtube.com/watch?v=EtdsNaauT8g

4. 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

Solution: https://www.youtube.com/watch?v=E28FKsiD0cQ

5. 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

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

6. The voltage gain A_v = V_o/V_i of the JFET amplifier shown in the figure is I_DSS = 10 mA, V_P = 5 volts. Assume C₁, C₂ and C_s to be very large.

a. + 16
b. – 16
c. + 8
d. – 6

Solution: https://www.youtube.com/watch?v=9K_U1BcpZSI

7. A triangular voltage waveform V_i(t) is applied at the input to the circuit shown. Assume the diodes to be ideal.

a. Determine the output V_o(t)
b. Neatly sketch the output waveform superimposed on the input V_i(t) and label the key points.

Solution: https://www.youtube.com/watch?v=DwkF8O6Xlvw

8. Below figure shown is a 2 – stage amplifier.

The transistors Q₁ and Q₂ are identical with current gain β = 100, further β_DC = β_ac = β. The zener diode D_z has a break down region and its dynamic resistance r_z is zero. The capacitors C₁ and C₂ are large and provide negligible impedance at signal frequencies.
a. Identify the configuration in each of the amplifier stages. (i.e. whether CE, CC or CB)
b. Determine the quiescent quantities of I_C1 and V_C1.
c. Determine an expression for the voltage gain V_o/V_s and determine its value. (Assume V_BE = 0.7 volts, r_o = ∞ and thermal voltage V_T = 25mV)
Answer:
Solution:

9. 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.

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

GATE 2003 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. Choose the correct match of input resistance of various amplifier configurations shown below:

Solution: https://www.youtube.com/watch?v=KEJiSEq93hw

2. The circuit shown in the figure is best described as a

a. Bridge rectifier
b. Ring modulator
c. Frequency discriminator
d. Voltage doubler

Solution: https://www.youtube.com/watch?v=jINTo6uHBDA

3. 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

Solution: https://www.youtube.com/watch?v=c_SMIFD5g0w

4. 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

Solution: https://www.youtube.com/watch?v=OFD168On6wQ

5. Generally, the gain of a transistor amplifier falls at high frequencies due to the
a. Internal capacitance of the device
b. Coupling capacitor at the input
c. Skin effect
d. Coupling capacitor at the output

Solution: https://www.youtube.com/watch?v=Ent-TO_v21Q

6. An amplifier without feedback has a voltage gain of 50, input resistance of 1 KΩ and output resistance of 2.5 KΩ. The input resistance of the current-shunt negative feedback amplifier using the above amplifier with a feedback factor of 0.2 is
a. 1/11 KΩ
b. 1/5 KΩ
c. 5 KΩ
d. 11 KΩ

Solution: https://www.youtube.com/watch?v=t1yotRs_s5A

7. In the amplifier circuit shown in the figure, the values of R₁ and R₂ are such that the transistor is operating at V_CE = 3 volts and I_C = 1.5 mA, when its β is 150.for a transistor with β of 200, the operating point (V_CE, I_C) is

a. (2 volts, 2 mA)
b. (3 volts, 2 mA)
c. (4 volts, 2 mA)
d. (4 volts, 1 mA)

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

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

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

9. 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

Solution: https://www.youtube.com/watch?v=aYqrNc3c4KU

10. 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

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

11. Three identical amplifiers with each one having a voltage gain of 50, input resistance of 1 KΩ and output resistance of 250 Ω are cascaded. The open circuit voltage gain of the combined amplifier is
a. 49 dB
b. 51 dB
c. 98 dB
d. 102 dB

Solution: https://www.youtube.com/watch?v=Mv94EuUazrQ

12. An ideal saw-tooth voltages waveform of frequency of 500 Hz and amplitude 3 volts is generated by charging a capacitor of 2 µF in every cycle. The charging requires
a. Constant voltage source of 3 volts for 1 ms
b. Constant voltage source of 3 volts for 2 ms
c. Constant current source of 1 mA for 1 ms
d. Constant current source of 3 mA for 2 ms

Solution: https://www.youtube.com/watch?v=jA7LuPuKGFg

GATE 2004 ECE Video Solutions on Analog Circuits (Analog Electronics)

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

Solution: https://www.youtube.com/watch?v=-3pE3zjlc-I

2. Voltage series feedback (also called series-shunt feedback) results in
a. Increase in both input and output impedances
b. Decrease in both input and output impedances
c. Increase in input impedance and decrease in output impedance
d. Decrease in input impedance and increase in output impedance

Solution: https://www.youtube.com/watch?v=W1PMTIiCpuU

3. The circuit in the figure is a

a. Low pass filter
b. High pass filter
c. Band pass filter
d. Band reject filter

Solution: https://www.youtube.com/watch?v=hUwaNK0aINo

4. A bipolar transistor is operating in the active region with a collector current of 1 mA. Assuming that the β of the transistor is 100 and the thermal voltage (V_T) is 25 mV. The Transconductance (g_m) and the input resistance (r_π) of the transistor in the common emitter configuration are
a. g_m = 25 mA/V and r_π = 15.625 KΩ
b. g_m = 40 mA/V and r_π = 4.0 KΩ
c. g_m = 25 mA/V and r_π = 2.5 KΩ
d. g_m = 40 mA/V and r_π = 2.5 KΩ

Solution: https://www.youtube.com/watch?v=cK0KRkqCWVw

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

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

6. 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

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

7. In the full wave rectifier using two ideal diodes, V_dc and V_m are the dc and peak values of the voltage respectively across a resistive load. If PIV is the peak inverse voltage of the diode, then the appropriate relationships for this rectifier are

Solution: https://www.youtube.com/watch?v=bN5s61Q90RE

GATE 2005 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. The effect of current shunt feedback in an amplifier is to
a. Increase the input resistance and decrease the output resistance.
b. Increase both input and output resistances
c. Decrease both input and output resistances
d. Decreases the input resistance and increase the output resistance

Solution: https://www.youtube.com/watch?v=ZZ6rItV_wj8

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

a. 30/4 KΩ
b. 10 KΩ
c. 40 KΩ
d. Infinite

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

3. The cascode amplifier is a multistage configuration of
a. CC – CB
b. CE – CB
c. CB – CC
d. CE – CC

Solution: https://www.youtube.com/watch?v=srt3MdOny5g

4. A square pulse of 3 volts amplitude is applied to RC circuit shown in figure. The capacitor is initially uncharged. The output voltage V_o at time t = 2 sec is

a. 3 volts
b.– 3 volts
c. 4 volts
d. – 4 volts

Solution:

5. For an NPN transistor connected as shown in figure, V_BE = 0.7 volts. Given that reverse saturation current of the junction at room temperature 300^oK is 10^-13 amp, the emitter current is

a. 30 mA
b. 39 mA
c. 49 mA
d. 20 mA

Solution: https://www.youtube.com/watch?v=3HVbE9qCcH8

6. 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.

Solution: https://www.youtube.com/watch?v=OuIncy3Iz-w

7. 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

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

8. 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

Solution: https://www.youtube.com/watch?v=YH9E2xVqdv0

9. The circuit using a BJT with β = 50 and V_BE = 0.7 volts is shown in figure. The base current I_B and the collector voltage V_C are respectively.

a. 43 µA and 11.4 volts
b. 40 µA and 16 volts
c. 45 µA and 11 volts
d. 50 µA and 10 volts

Solution: https://www.youtube.com/watch?v=W8VHHTLp6Kg

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

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

Common Data Questions for 11, 12 and 13:
Given r_d = 20 KΩ, I_DSS = 10 mA, V_P = - 8 volts.

11. Z_i and Z_o of the circuit are respectively
a. 2 MΩ and 2 KΩ
b. 2 MΩ and 20/11 KΩ
c. Infinity and 2 KΩ
d. Infinity and 20/11 KΩ

12. I_D and V_DS under DC conditions are respectively
a. 5.625 mA and 8.75 Volts
b. 7.50 mA and 5.0 Volts
c. 4.50 mA and 11.0 Volts
d. 6.25 mA and 7.5 Volts

13. Transconductance in milli-siemens (mS) and the voltage gain of the amplifier are
a. 1.875 mS and 3.41
b. 1.875 mS and – 3.41
c. 3.30 mS and – 6
d. 3.30 mS and 6

Solution(11, 12, 13): https://www.youtube.com/watch?v=3EaSdIyGqME

GATE 2006 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. The input impedance(Z_i) and output impedance (Z_o) of an ideal Transconductance (voltage controlled current source) amplifier are
a. Z_i = 0, Z_o = 0
b. Z_i = 0, Z_o = ∞
c. Z_i = ∞, Z_o = 0
d. Z_i = ∞, Z_o = ∞

Solution: https://www.youtube.com/watch?v=ZF6_tDjeD-w

2. 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

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

Common Data for Questions (3, 4 and 5):
In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: β_DC = 60, V_BE = 0.7 volts, h_ie -> ∞, h_oe -> ∞. The capacitance C_C can be assumed to be infinite.

3. Under the DC conditions, the collector to emitter voltage drop is
a. 4.8 volts
b. 5.3 volts
c. 6.0 volts
d. 6.6 volts

4. If β_DC is increased by 10%, the collector to emitter voltage drop
a. Increases by less than or equal to 10%
b. Decreases by less than or equal to 10%
c. Increases by more than 10%
d. Decreases by more than 10%

5. The small signal gain of the amplifier V_o/V_s is
a. – 10
b. – 5.3
c. + 5.3
d. + 10

Solution(3, 4, 5): https://www.youtube.com/watch?v=qdpEHlqob00

Statement for Linked Answer Questions (6 and 7):
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.

6. 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

7. 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%

Solution(6 & 7): https://www.youtube.com/watch?v=_fx1s9uTcCw

GATE 2007 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. In a Transconductance amplifier, it is desirable to have
a. A large input resistance and a large output resistance
b. A large input resistance and a small output resistance
c. A small input resistance and a large output resistance
d. A small input resistance and a small output resistance

Solution: https://www.youtube.com/watch?v=XdHNm2Ly-Kc

2. 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

Solution: https://www.youtube.com/watch?v=GNXEesKW7VQ

3. 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

Solution: https://www.youtube.com/watch?v=_FEUmzL53hg

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

4. The Transfer function V_o(s)/ V_i(s) is

5. 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

Solution(4 & 5): https://www.youtube.com/watch?v=5BVus7UsCas

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