### Previous GATE Questions on BJT Small Signal Analysis (at Mid Frequencies) (1987 - Till Date)

1988

1.       The quiescent collector current IC, of a transistor is increased by changing resistances. As a result
a.       gm will not be effected
b.      gm will decrease
c.       gm will increase
d.      gm will increase or decrease depending upon bias stability

2.       The amplifier circuit shown below uses a composite transistor of a MOSFET and BIPOLAR in cascade. All capacitances are large. gm of the MOSFET is 2 mA/V, and hfe of the BIPOLAR is 99. The overall Transconductance gm of the composite transistor is
a.       198 mA/V
b.      9.9 mA/V
c.       4.95 mA/V
d.      1.98 mA/V

3.       The transistor in the amplifier shown below has following parameters: hfe = 100, hie = 2 k, hre = 0, hoe = 0.05 mhos. All capacitors are very large. The output impedance is
a.       20 k
b.      16 k
c.       5 k
d.      4 k

1990

1.       Which of the following statements are correct for biasing transistor amplifier configurations?
a.       CB amplifier has low input impedance and a low current gain
b.      CC amplifier has low output impedance and a low current gain
c.       CE amplifier has very poor voltage gain but has very high input impedance
d.      The current gain of CB amplifier is higher than the current gain of CC amplifier

1991

1.       In figure, both transistors are identical and have a high value of β. Take the DC base emitter voltage drop as 0.7 volts and KT/q = 25 mV. The small signal low frequency voltage gain (Vo/Vi) is equal to __________

2.       Two non-inverting amplifiers, one having a unity gain and the other having a gain of 20 are made using identical operational amplifiers. As compared to unity gain amplifier, the amplifier with gain 20 has
a.       Less negative feedback
b.      Greater negative feedback
c.       Less bandwidth
d.      None of the above

1993

1.       For the amplifier circuit of figure, the transistor has a β of 800. The mid band voltage gain Vo/V1 of the circuit will be
a.       0
b.      < 1
c.       = 1
d.      800

1994

1.       A common emitter transistor amplifier has a collector current of 1.0 mA when its base current is 25 µA at room temperature. Its input resistance is approximately equal to _______

1995

1.       An RC coupled amplifier is assumed to have a single pole low frequency transfer function. The maximum lower cutoff frequency allowed for the amplifier to pass 50 Hz square wave with no more than 10% tilt is ______________

2.       Match the following:
a)      CC amplifier                     1) provides voltage gain but no current gain
b)      CE amplifier                     2) provides current gain but no voltage gain
c)       CB amplifier                     3) provides neither voltage nor power gain
4) provides neither current nor power gain
5) provides both voltage and current gain

1996
1.       In the circuit shown, ‘N’ is a finite gain amplifier with a gain of K, large input impedance and very low output impedance. The input impedance of the feedback amplifier with the feedback impedance Z connected as shown will be ______________

2.   A common emitter amplifier with an external capacitors CC connected across the base and the collector of the transistor is shown. Given gm = 5 mA/V, rπ = 20 k, Cπ = 1.5 pF and Cµ = 0.5 pF.

a.       Determine the ac small signal mid band voltage gain, Vo/Vs.
b.      Determine the upper cutoff frequency fH of the amplifier.
Answer:    (a) -33.33 (b) 18.326 KHz

1997

1.       In the BJT amplifier shown in figure, the transistor is based in the forward active region. Putting a capacitor across RE will
a.       Decrease the voltage gain and decrease the input impedance
b.      Increase the voltage gain and decrease the input impedance
c.       decrease the voltage gain and increase the input impedance
d.      Increase the voltage gain and increase the input impedance

2.
The transistor in the circuit shown is so biased (dc biasing network is not shown) that the dc collector current, IC = 1 mA and VCC = 5 volts. The network components have following  values: RC = 2 kΩ, RS = 1.4 kΩ and RE = 100 Ω. The transistor has β = 100 and a base spreading resistance, rbb’ = 100Ω. Assume VT = 25 mV.
Evaluate small signal voltage gain AVS at a frequency of 10 kHz, and input resistance Ri for two cases:
a.       CE, the bypass capacitor across RE is 25 µF
b.      The bypass capacitor CE is removed leaving RE unbypassed
Answer:    (a) -50, 2.5 kΩ (b) -14.2, 12.6 KΩ

1998
1.   In the circuit shown, determine the resistance Ro seen by the output terminals. Ignore the effect of R1 and R2.

1999

1.       An amplifier is assumed to have a single pole high frequency transfer function. The rise time of its output response to a step function input is 35 nsec. The upper -3 dB frequency (in MHz) for the amplifier to a sinusoidal input is approximately at
a.       4.55
b.      10
c.       20
d.      28.6

2.   A bipolar junction transistor amplifier is shown below. Assume that the current source Ibias is ideal, and the transistor has very large β, rb = 0 and r0 -> ∞.
Determine the ac small signal mid band voltage gain (Vo / Vs), input resistance (Ri) and output resistance (Ro) of the circuit. Assume VT = 26 mV.

Answer:    (a) 10 (b) 52 Ω (c) 100 KΩ

2000

1.       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

2.   For the amplifier circuit shown, IC = 1.3 mA, RC = 2 k, RE = 500 , VT = 26 mV, β = 100, VCC = 15 volts, VS = 0.01 sin(ωt) volts and Cb = Ce = 10 µF.
a.       What is the small signal voltage gain, Vo/VS
b.      What is the approximate voltage gain if Ce is removed?
c.       What will be the output Vo, if Cb is short circuited?

Answer:     (a) -100, (b) -4, (c) - sinwt

3.   Below figure shown is a common base amplifier.
a.       Write expressions for the time constants associated with the capacitances Cb and Cs.
b.      What is the approximate lower cutoff frequency of the amplifier?
τCb = 2π(re + RE//RS),
τCs = 2π(re//RE +RS)CS,
fCb = 1/τCb , fCs = 1/ τCs ,
overall fL = Max{ fCb , fCs }

2001

1.       The current gain of a BJT is
a.       gmro
b.      gm / ro
c.       gmrπ
d.      gm / rπ

2.   An emitter follower amplifier is shown below, where Zi is the impedance looking into the base of the transistor and Zo 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 Zi.
c.       Obtain an expression for Zo.
d.      Determine Zi and Zo, if a capacitor C is connected across R1.

(b) Zi = rπ + (1 + β)RL
(c) Zo = (RS + rπ)/(1 + β)
(d) Zi = rπ + (1 + β)ZL and Zo = (RS + rπ)/(1 + β)

2003
1.       Choose the correct match of input resistance of various amplifier configurations shown below:
Configuration                                    Input resistance
CB : Common Base                            LO :   Low
CC : Common Collector                     MO : Moderate
CE : Common Emitter                         HI :  High

a.       CB – LO,  CC – MO,      CE – HI
b.      CB – LO,  CC – HI,         CE – MO
c.       CB – MO, CC – HI,         CE – LO
d.      CB – HI,    CC – LO,        CE – MO

2004

1.       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 (VT) is 25 mV. The Transconductance (gm) and the input resistance (rπ) of the transistor in the common emitter configuration are
a.       gm =  25 mA/V and rπ = 15.625 K
b.      gm =  40 mA/V and rπ = 4.0 K
c.       gm =  25 mA/V and rπ = 2.5 K
d.      gm =  40 mA/V and rπ = 2.5 K

2006

Common Data for Questions (1, 2 and 3):
In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: βDC = 60, VBE = 0.7 volts, hie -> , hoe -> ∞. The capacitance CC can be assumed to be infinite.
1.       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
2.       If βDC  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%
3.       The small signal gain of the amplifier Vo/Vs is
a.       – 10
b.      – 5.3
c.       + 5.3
d.      + 10

2008

In the following transistor circuit, VBE = 0.7 volts, re = 25 mV/IE, β and all the capacitances are very large.
1.       The value of DC current IE is
a.       1 mA
b.      2 mA
c.       5 mA
d.      10 mA
2.       The mid-band voltage gain of the amplifier is approximately
a.       – 180
b.      – 120
c.       – 90
d.      – 60

2009

1.       A small signal source Vi(t) = Acos20t + Bsin106t is applied to a transistor amplifier as shown below. The transistor has β = 150 and hie = 3 KΩ. Which expression best approximate Vo(t).
a.       Vo(t) = - 1500 (Acos20t + Bsin106t)
b.      Vo(t) = - 150 (Acos20t + Bsin106t)
c.       Vo(t) = - 1500 (Bsin106t)
d.      Vo(t) = - 150 (Bsin106t)

2010

1.       The amplifier circuit shown below uses a silicon transistor. The capacitors CC and CE can be assumed to be short at signal frequency and effect of output resistance ro can be ignored. If CE is disconnected from the circuit, which one of the following statements is TRUE.
a.       The input resistance Ri increases and magnitude of voltage gain AV decreases
b.      The input resistance Ri decreases and magnitude of voltage gain AV increases
c.       The input resistance Ri decreases and magnitude of voltage gain AV decreases
d.      The input resistance Ri increases and magnitude of voltage gain AV increases

Common Data Questions:
Consider the common emitter amplifier shown below with the following circuit parameters.

β = 100, gm = 0.3861 A/V, ro = 259 , RS = 1 K, RB = 93 K, RC = 250 , RL = 1 K, C1 = and C2 = 4.7 µF.
2.       The resistance seen by the source VS is
a.       258
b.      1258 Ω
c.       93 KΩ
d.
3.       The lower cutoff frequency due to C2 is
a.       33.9 Hz
b.      27.1 Hz
c.       13.6 Hz
d.      16.9 Hz

2011

1.       In the circuit shown below, capacitors C1 and C2 are very large and are shorts at the  input frequency . vi is a small signal input. The gain magnitude |V0/Vi| at 10 M rad/sec is
a.       Maximum
b.      Minimum
c.       Unity
d.      Zero

2012

1.       The current ib through the base of a silicon NPN transistor is 1+0.1cos (10000πt) mA. At 300oK, the rπ in the small signal model of the transistor is ________ (in Ohms).
a.       250
b.      27.5
c.       25
d.      22.5

2.       The impedance looking into nodes 1 and 2 in the given circuit is________ (in Ohms).
a.       50
b.      100
c.       5K
d.      10.1 K

3.       The voltage gain Av, of the circuit shown below is
a.       |Av|   200
b.      |Av|    100
c.       |Av|    20
d.      |Av|    10

2014

1.       A BJT is biased in forward active mode. Assume VBE = 0.7 volts, KT/q = 25 mV and reverse saturation current IS = 10-13 Amp. The Transconductance of the BJT (in mA/volt) is…..

2.       For the amplifier shown in the figure, the BJT parameters are VBE = 0.7 volts, β = 200, and thermal voltage VT = 25 mV. The voltage gain (vo/vi) of the amplifier is ……..

3.       If the emitter resistance in a common emitter voltage amplifier is not bypassed, it will
a.       Reduce both the voltage gain and the input impedance
b.      Reduce the voltage gain and increase the input impedance
c.       Increase the voltage gain and reduce the input impedance
d.      Increase both the voltage gain and the input impedance

4.       Consider two BJTs biased at the same collector current with area A1 = 0.2 µm x 0.2 µm and A2 = 300 µm x 300 µm. assuming that all other device parameters are identical, KT/q = 26 mV, the intrinsic carrier concentration is 1 x 1010 cm-3, and q = 1.6 x 10-19C, the difference between the base emitter voltages (in mV) of the two BJTs (i.e. VBE1 – VBE2) is …………….

5.       A BJT in a common base configuration is used to amplify a signal received by a 50 antenna. Assume KT/q = 25 mV, the value of collector bias current (in mA) required to match the input impedance of the amplifier to the impedance of the antenna is ………..

6.       Consider the common collector amplifier in the figure (bias circuitry ensures that the transistor operates in forward active region, but has been omitted for simplicity). Let IC be the collector current, VBE be the base emitter voltage and VT be the thermal voltage. Also, gm and ro are the small signal Transconductance and output resistance of the transistor, respectively. Which one of the following conditions ensures a nearly constant small signal voltage gain for a wide range of values of RE?

2015

1.       Consider the bode plot shown in figure. Assume that all the poles and zeros are real valued. The value of fH – fL (in Hz) is _____________

2.   In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical parameters with β>>1. The open circuit small signal voltage gain is approximately is _________________