**GATE 1990**

1.
Figure shows an RC phase shift oscillator.

Solve the network to find the minimum value of h

Solve the network to find the minimum value of h

_{fe}for the transistor for oscillations to be possible. Also determine the frequency of such oscillations. Take C = 0.01 µF and h_{ie}= 2 KΩ.
2.
A pick up signal is power amplified using a
complementary symmetry push pull amplifier and fed to a 5 Ω
loud speaker as shown.

The specifications of power transistors are as follows:

The specifications of power transistors are as follows:

I

_{Cmax}= Maximum collector current = 2 Amps and P_{Cmax}= Maximum power dissipation = 1 Watt.
Find the maximum power delivered to the loud speaker, if the maximum
output voltage subject to OP-AMP voltage limitations is 15 volts.

If the transistors are mounted on a heat sink, so that P

_{Cmax}changes to 3 Watts. What will be the new value of the maximum power delivered?**GATE 1991**

3.
In the figure, the operational amplifier is
ideal and its output can swing between – 15 and + 15 volts.

The input V

The input V

_{i}, which is zero for t<0, is switched to 5 volts at the instant t = 0. Given that the output V_{o}is + 15 volts for t<0, sketch the waveforms of V_{o}and V_{i}. You must give the values of important parameters of the sketch.
4.
In figure, the operational amplifier are ideal
and their output can swing between – 15 and + 15 volts.

Sketch the waveform of
voltages of V

_{1}and V_{2}as a function of time. You must give the values of important parameters of this sketch.**GATE 1992**

5.
The Two Port Darlington impedance booster of
figure uses identical transistors (h

Calculate the Z – parameters of the network. Use
relevant approximations.

_{ie}= 1 KΩ, h_{fe}= 100, h_{re}= h_{oe}= 0).
6.
The transistors in the differential amplifier
shown in figure are identical with h

a.
What is the differential gain of the circuit?

_{fe}= 100 and r_{e}= 25 Ω at 1 mA collector current. The circuit has a CMRR of 100.
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 V

_{o}?
7.
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 V

Assuming that the impedance's at nodes A and B do not load the preceding bridge circuit, calculate the output voltage V

_{o}. When (a) R_{A}= R_{B}= R_{C}= R_{D}= 100 Ω and (b) R_{A}= R_{B}= R_{C}= 100 Ω and R_{D}= 120 Ω.**GATE 1993**

8. A JFET with the following parameters is used in a single stage common source amplifier with a load resistance of 100 kΩ. Calculate the high frequency cutoff (upper 3dB frequency) of the amplifier. Given g

_{m}= 2 mA/V, C

_{gd}= 2 pF, C

_{ds}= 2 pF, r

_{d}= 100 kΩ and C

_{gs}= 1 pF.

9.
Find the output voltage V

_{o}in the following circuit, assuming that the operational amplifier is ideal.**Solution:****https://www.youtube.com/watch?v=PEruik14S0I****GATE 1994**

10. 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

**Solution:**

**https://www.youtube.com/watch?v=F5u_wKdvZYI**

11.
Calculate the frequency at which zero
transmission is obtained from the Wien-bridge shown below.

12.
Find the output voltage of the following circuit
shown below, assuming ideal operational amplifier behavior.

13.
In the MOSFET amplifier shown in the figure
below, the transistor has µ = 50, r

Draw a small signal equivalent circuit for the amplifier for mid band calculate its mid band voltage gain.

_{d}= 10 kΩ, C_{gs}= 5 pF, C_{gd}= 1 pF and C_{ds}= 2 pF.Draw a small signal equivalent circuit for the amplifier for mid band calculate its mid band voltage gain.

**GATE 1995**

14. 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.

**Solution:**

**https://www.youtube.com/watch?v=ulb3JFwnZDs**

15.
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 V

a. Draw the waveform V

_{o}(t), in relation to the input
b.
Specify V

_{o}(t) determine the voltage levels and the time constants involved.
16.
In the JFET circuit shown, assume that R

Determine the upper cutoff frequency of the amplifier.

_{1}//R_{2}= 1 MΩ and the total stray capacitance at the output to be 20 pF.Determine the upper cutoff frequency of the amplifier.

17.
Show that the circuit shown in figure is double
integrator. In other words, prove that the transfer gain is given by V

_{o}(s)/V_{s}(s) = 1/(CR_{s})^{2}, assume ideal operational amplifier.**Solution:****https://www.youtube.com/watch?v=kIlrli8NFJ0**
18.
In the amplifier circuit shown, determine the
value of R such that Q

Also determine the small signal input impedance of Q

_{2}is biased at V_{CE2}= 7.5 volts. Assume Q_{1}and Q_{2}to be identical with V_{BE}= 0.7 volts and neglect base currents.Also determine the small signal input impedance of Q

_{1}and Q_{2}, if both of them have β = 200. Use V_{T}= 26 mV.**GATE 1996**

19.
A common emitter amplifier with an external
capacitors C

a. Determine the ac small signal mid band voltage gain, V

_{C}connected across the base and the collector of the transistor is shown. Given g_{m}= 5 mA/V, r_{π}= 20 kΩ, C_{π}= 1.5 pF and C_{µ}= 0.5 pF.a. Determine the ac small signal mid band voltage gain, V

_{o}/V_{s}.
b.
Determine the upper cutoff frequency f

_{H}of the amplifier.
20.
A resistively loaded and resistively biased
differential amplifier circuit is shown. Neglect base current and assume
matched transistors with V

a. Determine the values of R

_{A}-> ∞ and β = 100. Use V_{T}= 26 mV, V_{BE(on)}= 0.7 volts and V_{CE(sat)}= 0.1 volts.a. Determine the values of R

_{C}and R_{2}to meet the following specifications: double ended differential mode gain = 500, CMRR = 500 and differential mode input resistance of 2 MΩ.
b.
Determine the minimum values of V

_{CC}and V_{EE}such that the transistors remain in the forward active region under zero signal condition. Assume that the DC common mode input is zero.
21.
Assuming ideal operational amplifiers, show that
the circuit shown simulates in inductor i.e. show that V

_{i}(S)/I_{i}(S) is inductive and write the expression for the effective inductance.**GATE 1997**

6. The transistor in the circuit shown is so biased (dc biasing
network is not shown) that the dc collector current, I

Evaluate small signal voltage gain A

_{C}= 1 mA and V_{CC}= 5 volts. The network components have following values: R_{C}= 2 kΩ, R_{S}= 1.4 kΩ and R_{E}= 100 Ω. The transistor has β = 100 and a base spreading resistance, r_{bb}’ = 100Ω. Assume V_{T}= 25 mV.Evaluate small signal voltage gain A

_{VS}at a frequency of 10 kHz, and input resistance R_{i}for two cases:
a.
C

_{E}, the bypass capacitor across R_{E}is 25 µF
b.
The bypass capacitor C

_{E}is removed leaving RE unbypassed
7. Consider the circuit given in the figure is using an ideal
operational amplifier. The characteristics of the diode are given by the
relation I = I

a. Express V

_{S}(e^{qV/KT}– 1), where V is the forward voltage across the diode.a. Express V

_{o}as function of V_{i}, assuming V_{i}> 0
b.
If R = 100 kΩ, I

_{S}= 1 µA and V_{T}= 25 mV, find the input voltage V_{i}for which V_{o}= 0.
8. In circuit shown, assume that the operational amplifier is
ideal and that V

a. Calculate the charge transferred per second from node A to node B.

_{o}= 0 volts initially. The switch is connected first to ‘A’ charging C_{1}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 V

_{o}.
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 10

^{4}times per second, C_{1}= 100pF, C_{2}= 10pF and V= 10 mV. What is the average change of the output voltage?
9. 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 R

Evaluate values of R

_{A}and R_{B}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.**GATE 1998**

22.
For the circuit shown,

a. Draw the transfer characteristics if both diodes D

a. Draw the transfer characteristics if both diodes D

_{1}and D_{2}are ideal.
b.
How would the characteristics change, if D

_{2}is ideal but D_{1}is non-ideal? Assume D_{1}has forward resistance of 10 Ω and a reverse resistance of infinity.
23.
Determine the input impedance of the circuit
shown and investigate if it can be inductive.

24.
Find the value of R’ in the circuit shown for
generating sinusoidal oscillations. Find the frequency of oscillations.

25.
In the circuit shown, determine the resistance R

_{o}seen by the output terminals. Ignore the effect of R_{1}and R_{2}.
26.
Implement a monostable multivibrator using the
timer circuit shown in figure. Also determine an expression for ON time ‘T’ of
the output pulse.

**GATE 1999**

27.
A bipolar junction transistor amplifier is shown
below. Assume that the current source I

Determine the ac small signal mid band voltage gain (V

_{bias}is ideal, and the transistor has very large β, r_{b}= 0 and r_{0}-> ∞.Determine the ac small signal mid band voltage gain (V

_{o}/ V_{s}), input resistance (R_{i}) and output resistance (R_{o}) of the circuit. Assume V_{T}= 26 mV.
28.
A JFET having µ = 50 and r

Determine the ac small signal mid band voltage gain (V

_{d}= 10 kΩ is used in a common source configuration as shown. The JFET capaciances are C_{gs}= 5 pF, C_{gd}= 2 pF and C_{ds}= 2 pF.Determine the ac small signal mid band voltage gain (V

_{o}/V_{s}) and the upper 3 dB frequency of the circuit.
29.
Neatly sketch and label the DC transfer
characteristic (V

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

_{o}verses V_{in}) of the circuit shown, as V_{in}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.

30.
A transistor LC oscillator circuit is shown
below.

Assume that the transistor has very high value of β(so that you may neglect r

Assume that the transistor has very high value of β(so that you may neglect r

_{b}). Derive an equation governing the circuit operation, and find the frequency of oscillation. Also state the gain condition required for oscillation to start.**Solution:**This circuit is

**Colpitts Oscillator using BJT as amplifier**. Refer any text book of EDC to know the condition for oscillations. We dont expect this type of questions will come these days....... as it is a 5 mark question in GATE 1999.

**GATE 2000**

31. 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.

32.
For the amplifier circuit shown, I

a. What is the small signal voltage gain, V

_{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?
33.
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.**

34.
Below figure shown is a common base amplifier.

a. Write expressions for the time constants associated with the capacitances C

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?

**GATE 2001**

35. 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 R_{1}.
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}?**GATE 2002**

37.
A triangular voltage waveform V

a. Determine the output 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.
38.
Below figure shown is a 2 – stage amplifier.

The transistors Q

The transistors Q

_{1}and Q_{2}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 C_{1}and C_{2}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)**Solution:**

39.
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.

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.
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