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  • Electronics EECE2412 — Spring 2013 Exam #2 with Solutions

    Prof. Charles A. DiMarzio Department of Electrical and Computer Engineering

    Northeastern University File:11785/exam2

    23 April 2013

    1 BJT Amplifier

    The following figure shows a BJT amplifier, which we are going to analyze. The transistor has β = 160, and VA = 100 Volts. RS is part of the source. The input and output voltages are at the indicated locations, vin and vout, respectively.

    1

  • 1 BJT AMPLIFIER 1.1 Amplifier Type

    1.1 Amplifier Type

    What type of amplifier is it? Common Collector or Emitter Follower

    What is the typical situation in which this amplifier is used?

    Used when unity voltage gain is needed

    and source alone cannot supply current.

    1.2 Small–Signal Parameters

    What are the small–signal parameters?

    DiMarzio 11785/exam2, Apr 2013 Page 2DiMarzio 11785/exam2, Apr 2013 Page 2DiMarzio 11785/exam2, Apr 2013 Page 2

  • 1 BJT AMPLIFIER 1.3 AC Circuit

    gm = I DC C /VT =

    1 mA

    25 mV = 0.04 A/V

    rπ = β/gm = 160

    0.04 A/V = 4000 Ω

    re = I DC E /VT =

    rπ β + 1

    = 24.8 Ω

    R0 = VA IDCC

    = 100 Volts

    10−3 Amperes = 105 Ω

    gm = 0.04 A/V

    rπ = 4 kΩ

    re = 24.8 Ω

    R0 = 100 kΩ

    1.3 AC Circuit

    Draw the AC circuit, using a T model for the transistor.

    DiMarzio 11785/exam2, Apr 2013 Page 3DiMarzio 11785/exam2, Apr 2013 Page 3DiMarzio 11785/exam2, Apr 2013 Page 3

  • 1 BJT AMPLIFIER 1.4 Amplifier Characteristics

    AC circuit in the following figure:

    1.4 Amplifier Characteristics

    What are the AC characteristics of this amplifier?

    Voltage Gain: Look at the voltage divider. Neglect

    R0 in comparison to R:.

    AV = Vout Vin

    = 5000 ω

    5025 ω

    Current Gain: Note that the dependent source gm (vin − vout) can also be written as iacc = βi

    ac b . The current going to

    re and thus mostly to RL is the sum of i (ac) b and i

    (ac) c or

    β + 1 times the input current.

    Output resistance:

    vout:oc ≈ vin DiMarzio 11785/exam2, Apr 2013 Page 4DiMarzio 11785/exam2, Apr 2013 Page 4DiMarzio 11785/exam2, Apr 2013 Page 4

  • 1 BJT AMPLIFIER 1.4 Amplifier Characteristics

    iout:sc ≈ vin/25 Ω

    Rout = vout:oc2 iout:sc

    5 Ω

    Voltage Gain (With Load) 0.995

    Current Gain 161

    Output Resistance 25 Ω

    DiMarzio 11785/exam2, Apr 2013 Page 5DiMarzio 11785/exam2, Apr 2013 Page 5DiMarzio 11785/exam2, Apr 2013 Page 5

  • 2 DISCRETE FET AMPLIFIER

    2 Discrete FET Amplifier

    The following figure shows an amplifier using a discrete FET and a resistor. The transistor has a drain current of 250 µAmp when VGS = 5 Volts, and the threshold voltage is zero. The Early Voltage is VA = 70 Volts.

    What type of amplifier is it? Common Drain

    What is the typical situation in which this amplifier is used?

    Unity Voltage gain is desired

    and source cannot provide current

    DiMarzio 11785/exam2, Apr 2013 Page 6DiMarzio 11785/exam2, Apr 2013 Page 6DiMarzio 11785/exam2, Apr 2013 Page 6

  • 2 DISCRETE FET AMPLIFIER 2.1 Circuit Design

    2.1 Circuit Design

    We want a drain current of 250 µAmperes in this circuit. What resistance do we need for RS?

    I (DC) D = 250 µAmperes → V

    (DC) GS = 5 Volts

    V (DC) G = 0 → V

    (DC) S = −5 Volts

    RS = 10 Volts

    250× 10−6 Amperes = 4× 104 Ω

    RS =40 kΩ

    2.2 Small–Signal Parameters

    What are the small–signal parameters?

    gm = 2I

    (DC) D

    V (DC) GS

    = 250× 10−6 Amperes

    5 Volts = 10−4 A/V

    R0 = VA

    I (DC) D

    = 70 Volts

    250 µA = 2.8× 10−5 Ω

    gm = 100 µA/V

    R0 = 280 kΩ

    2.3 AC Circuit

    Draw the AC circuit, using a Pi model for the transistor.

    DiMarzio 11785/exam2, Apr 2013 Page 7DiMarzio 11785/exam2, Apr 2013 Page 7DiMarzio 11785/exam2, Apr 2013 Page 7

  • 2 DISCRETE FET AMPLIFIER 2.4 Amplifier Characteristics

    AC circuit is shown below

    2.4 Amplifier Characteristics

    What are the AC characteristics of this amplifier?

    v (AC) out:oc = gm

    ( v (AC) in − v

    (AC) out:oc

    ) (R0 ‖ Rs)

    v (AC) out:oc [1 + gm (R0 ‖ Rs)] = gmv

    (AC) in (R0 ‖ Rs)

    v (AC) out:oc =

    gm (R0 ‖ Rs) 1 + gm (R0 ‖ Rs)

    v (AC) in

    Neglect R0 in comparison to RS.

    v (AC) out:oc =

    10−4 A/V × 4× 104 Ω 1 + 10−4 A/V × 4× 104 Ω

    v (AC) in = 0.80v

    (AC) in

    DiMarzio 11785/exam2, Apr 2013 Page 8DiMarzio 11785/exam2, Apr 2013 Page 8DiMarzio 11785/exam2, Apr 2013 Page 8

  • 2 DISCRETE FET AMPLIFIER 2.4 Amplifier Characteristics

    Input resistance is infinite because of the oxide between

    the gate and the channel.

    Output resistance is RS ‖ R0 ≈ RS.

    Open–Circuit Gain 0.80

    Input Resistance Infinite

    Output Resistance 40 kΩ

    DiMarzio 11785/exam2, Apr 2013 Page 9DiMarzio 11785/exam2, Apr 2013 Page 9DiMarzio 11785/exam2, Apr 2013 Page 9

  • 3 CMOS AMPLIFIER

    3 CMOS Amplifier

    The figure below shows a CMOS amplifier. The transistors are all the same, and have a drain current of 250 µAmp when VGS = 5 Volts, and the threshold voltage is zero (This is the same as in Problem 2). However, in this case, VA = 100 Volts.

    3.1 Amplifier Type

    What type of amplifier is it? Common Drain

    What is the typical situation in which this amplifier is used?

    Unity Voltage gain is desired

    and source cannot provide current.

    DiMarzio 11785/exam2, Apr 2013 Page 10DiMarzio 11785/exam2, Apr 2013 Page 10DiMarzio 11785/exam2, Apr 2013 Page 10

  • 3 CMOS AMPLIFIER 3.2 Transistor Characteristics

    3.2 Transistor Characteristics

    What is the constant, µnCoxW/L for this transistor?

    In saturation,

    iD = µnCox W

    L

    (vGS − vthr)2

    2

    µnCox W

    L =

    2iD

    (vGS − vthr)2 =

    2× 250× 10−6 A (5 V2)

    = 2×10−5 A/V2.

    20 µA/V2

    3.3 Small–Signal Parameters

    What are the small–signal parameters?

    I (DC) D = 0.1 mA

    gm = I (DC) D

    V (DC) GS

    =

    √ 2I

    (DC) D µnCox

    W

    L = 6.3× 10−5 AV

    R0 = VA

    I (DC) D

    = 100 V

    10−4 A = 106 Ω

    gm = 63 µA/V

    R0 = 1 MΩ

    DiMarzio 11785/exam2, Apr 2013 Page 11DiMarzio 11785/exam2, Apr 2013 Page 11DiMarzio 11785/exam2, Apr 2013 Page 11

  • 3 CMOS AMPLIFIER 3.4 AC Circuit

    3.4 AC Circuit

    Draw the AC circuit, using a Pi model for the transistor.

    3.5 Amplifier Characteristics

    What are the AC characteristics of this amplifier?

    vout:oc = R0 2 gm (vin − vout:oc)

    vout:oc

    ( 1 +

    R0 2 gm

    ) =

    R0 2 gmvin

    vout:oc = R0 2

    1 + R02 gm gmvin =

    32

    33 vin

    Again, the input resistance is infinite because the input

    is on the gate.

    Open–Circuit Gain 0.97

    Input Resistance Infinite

    DiMarzio 11785/exam2, Apr 2013 Page 12DiMarzio 11785/exam2, Apr 2013 Page 12DiMarzio 11785/exam2, Apr 2013 Page 12

  • 4 CMOS LOGIC

    4 CMOS Logic

    The following figure shows a CMOS digital logic circuit. As usual, +5 Volts represents “true,” and zero represents “false.” There are two inputs, V A and V B, and one output, Vout at the voltage probe shown in the figure.

    4.1 Truth Table

    Construct the truth table for this circuit, for all possible combinations of inputs V A and V B being “true” or “false.”

    A B M1 M2 M3 M4 Out

    H H O O X X L

    H L X O O X L

    L H O X X O L

    L L X X O O H

    What is the function of this circuit?

    NOR

    DiMarzio 11785/exam2, Apr 2013 Page 13DiMarzio 11785/exam2, Apr 2013 Page 13DiMarzio 11785/exam2, Apr 2013 Page 13

  • 4 CMOS LOGIC 4.2 Output Voltages

    4.2 Output Voltages

    The following figure shows output voltage as a function of input voltage, V A. In the figure, the bottom curve (along the Vout = 0 axis) is for V B = 5, the next curve is for V B = 2.5 Volts and the top curve is for V B = 0 Volts. Explain these curves in terms of what you know about FETs.

    VB = 5 V: Output Always Low

    VB = 0 V: Output changes with VA.

    Similar to VB = 0 V but M4 is only partially on.

    4.3 Current

    Draw a plot of the current, iD as a function of V A for V B = 5 Volts. You don’t need to provide a correct current axis, because I have not given you

    DiMarzio 11785/exam2, Apr 2013 Page 14DiMarzio 11785/exam2, Apr 2013 Page 14DiMarzio 11785/exam2, Apr 2013 Page 14

  • 4 CMOS LOGIC 4.4 Alternative Output

    the transistor parameters.

    4.4 Alternative Output

    With the addition of two transistors at the output, you can convert this to either an “AND” or “OR” gate. Which one? Draw the additional circuit.

    Add an inverter.

    “AND” or ”OR?” OR

    DiMarzio 11785/exam2, Apr 2013 Page 15DiMarzio 11785/exam2, Apr 2013 Page 15DiMarzio 11785/exam2, Apr 2013 Page 15