1. Physical Structure and Modes of Operation
n-type
Emitter
region
p-type
Base
Collecter
Emitter
(E)
Collecter
(C)
Metal
contact
Emitter-base
junction
(EBJ)
Collecter-base
junction
(CBJ)
Base
(B)
Mode EBJ CBJ
Cutoff Reverse Reverse
Active Forward Reverse
Saturation Forward Forward

2. Operation of the npn Transistor in the Active Mode
Injected Diffusing Collected
electrons electrons electrons C
Injected holes (iB1) B

3. Carrier concentration
Current Flow
Only diffusion-current components are considered
Profiles of minority-carrier concentrations in the base and in the emitter of an npn transistor operating in the active mode; vBE > 0 and vCB  0.
Collector
(n)
Effective base
width W
Carrier concentration
Emitter
EBJ
depletion
region
Base
(p)
CBJ
Hole
concentration
Electron
np (ideal)
np (with
recombination)
np(0)
pn(0)
pn0
Distance (x)

4. The Collector Current
Most of the diffusing electrons will reach the boundary of the collector-base depletion region
These successful electrons will be swept across the CBJ depletion region into the collector
By convention, the direction of iC is opposite to that of electron flow
saturation current

5. Two components of base current, iB1 and iB2.
The Base Current
Two components of base current, iB1 and iB2.
Hole diffusivity
in the emitter
Hole diffusion length
in the emitter
minority-carrier
lifetime
Doping concentration
of the emitter
common-emitter
current gain

6. The Emitter Current
common-base
current gain

7. First Order Equivalent Circuit Models
The externally controlled signals for this model are the three currents shown outside the gray box.
The voltage VBE, exists internally as a result of the currents and can be externally measured. We can force a current and measure a voltage.
The diode in the model is designated as DE since the current flowing through the diode is the same as the emitter current. The collector current is dependent on the base-emitter voltage VBE.
The model is a non-linear voltage controlled current source
Voltage Controlled Current Source Model C B C DE
The externally controlled signals for this model are two currents and the voltage VBE shown outside the gray box.
The current iE exists internally as a result of the voltage VBE and can be externally measured.
The collector current is dependent on the emitter current iE. B E DE
Current Controlled Current Source E

8. Equivalent Circuit Models, cont’d
In this version of the model the diode conducts the BASE current which is beta times smaller.
In one version the dependent current source is voltage controlled (vBE), in the other version the dependent current source is current controlled (b). E B C E B C
Note connection point is now
on the opposite side of the diode
Current Controlled Current Source
Voltage Controlled Current Source Model

9. Two Port Model of the Common-Base Configuration
Network B B E B
The base lead is common to both ports DE E C E B B
If we switch the leads within the network
the common base aspect is more apparent E C B B
Two-Port representation of a BJT Transistor
symbol in a common-base configuration
The common-base current gain is a

10. Two Port Model of the Common-Emitter ConfigurationB C B C
Two port
Network E E
The emitter lead is common to both ports
iC is out of phase with iB C B E E
Two-Port representation of a BJT Transistor
symbol in a common-emitter configuration
The common-emitter current gain is a

11. Operation of the pnp Transistor in the Active Mode
Injected Diffusing Collected
holes holes holes C
Injected electrons (iB1) B

12. Equivalent pnp Circuit ModelsB B C C

13. Circuit Symbols and Conventions - npn
Voltage polarities and current flow in a
transistor biased in the active mode.
npn BJT

14. Circuit Symbols and Conventions - pnp
Voltage polarities and current flow in a
transistor biased in the active mode.
pnp BJT

15. Example 4.1
The transistor in the circuit below has b = 100 and exhibits a vBE of 0.7V at iC = 1 mA. Design the circuit so that a current of 2 mA flows through the collector and a voltage of +5V appears at the collector.

16. Graphical Representation of Transistor Characteristics
Similar to diodes, except we talk about the voltage across one junction VBE and the current through the other terminal iC.
For most of the conditions we will encounter in working with BJTs the ideality factor, n will be considered to be 1.
T1>T2>T3 T1 T3 T2
iC-vBE characteristics
Effect of temperature on iC-vBE characteristic.
At a constant current, vBE changes by –2mV/oC.

17. iC versus vCB Characteristics
npn transistor in active mode
saturation
Current controlled
current source
-Vnp = forward bias
+Vnp = reverse bias
saturation
See next page

18. iC=vCE Characteristics
The Early Voltage (typically Volts), also known as the Base-Width Modulation parameter.
As the base-collector junction reverse bias is increased the depletion layer expands and consumes some of the base narrowing it and causing an increase in the collector current.
Saturation
region
Active

19. Example 4.2
We wish to analyze this circuit to determine all node voltages and branch currents. We will assume that b is specified to be 100.

20. Example 4.2, cont’d
We don’t know whether the transistor is in the active mode or not.
A simple approach would be to assume that the device is in the active mode, and then check our results at the end 1 3 2 4 5 1 3 2 4 5

21. Example 4.3
We wish to analyze the circuit shown below to determine the voltages at all nodes and the currents through all branches. Note that this circuit is identical to the previous circuit except that the voltage at the base is now +6 V.
Assuming active-mode: 3 4 1 2
Collector voltage > base voltage
saturation mode, not active mode

22. Example 4.4
We wish to analyze the circuit below to determine the voltages at all nodes and the currents through all branches. This circuit is identical to that considered in the previous two examples except that now the base voltage is zero. 1 2 3 4 5

23. Example 4.6
We will analyze the following circuit to determine the voltages at all nodes and currents through all branches. Assume b=100. 1 3 2 3 4 4 2 5 5

24. Example 4.7
We want to analyze the circuit shown below to determine the voltages at all nodes and currents through all branches. Assume b=100.

25. Example 4.7, cont’d

26. The BJT as an Amplifier Objectives 1. Biasing 2. DC equations
3. Transconductance
4. Input resistance looking into the base
5. Input resistance looking into the emitter
6. Voltage gain
7. Gummel plots
Lesson
1) For our amplifiers, the BJT must be biased in the FORWARD-ACTIVE
2) However, it’s a difficult challenge to establish a CONSTANT DC CURRENT
3) Our goal: A Q point insensitive to TEMPERATURE , ß , VBE .

27. The BJT as an Amplifier 2. DC Equations (learn ‘em now) 1) 2) 3) 4)
3. Transconductance (remember the small-signal approximation from before?)
- Valid only for vBE< 10 mV
- Defined as the incremental change in output current for an incremental change in input voltage at a DC operating point…..

28. The BJT as an Amplifier If vbe<< VT
Note that iC = IC at vBE = VBE, so…...

29. The BJT as an Amplifier
Input Resistance “ looking into “ the Base ( highlight this in your text & on this page!)
Defined as the incremental change input voltage for an incremental change in base current at a DC operating point…
Other important relationships ( be prepared to use any of these!)

30. The BJT as an Amplifier
Input Resistance “looking into “ the Emitter (hightlight this in your text & on this page)
Define as the incremental change in input voltage for an incremental change in emitter current at DC operating point…..
Other important relationship ( be prepared to use either of them!)

31. The BJT as an Amplifier Relationship between r and re
- The same input resistance just “ viewed from two different places ! “

32. The BJT as an Amplifier Out of phase with the input
Lets look at Voltage Gain again
A BJT senses vbe and causes a proportional current gm vbe
This is a VOLTAGE - CONTROLED CURRENT SOURCE
So How do we obtain an output voltage so that we get a voltage gain?
Out of phase with
the input

33. Voltage Gain
Signal voltage:
Voltage gain:

34. Small-signal equivalent circuit models
Every current and voltage in the amplifier circuit is composed of two components: a dc component and a signal component.
The dc components are determined from the dc circuit below on the left.
By eliminating the dc voltages, we are left with the signal components (on the right). The resulting circuit is equivalent to the transistor as far as small-signal operation is concerned. + - + -
Amplifier circuit with dc sources
Amplifier circuit with dc sources eliminated

35. The Hybrid-P Model B C B C E E voltage-controlled current-controlled
current source
current-controlled
current source B C E B C E

36. The T Model
These models explicitly show the emitter resistance re rather than the base resistance rp featured in the hybrid-p model. E B C B C E
voltage-controlled
current source
current-controlled
current source

37. Application of the Small-Signal Equivalent Circuits
The availability of the small-signal BJT circuit models makes the analysis of transistor amplifier circuits a systematic process consisting of the following steps:
Determine the dc operating point of the BJT and in particular the dc collector current IC.
Calculate the values of the small-signal model parameters:
Eliminate the dc sources by replacing each dc voltage source with a short circuit and each dc current source with an open circuit.
Replace the BJT with one of its small-signal equivalent circuit models. Although any one of the models can be used, one might be more convenient than the others for the particular circuit being analyzed. This point will be made clearer later in this chapter.
Analyze the resulting circuit to determine the required quantities (e.g., voltage gain, input resistance).

38. Example 4.9
We wish to analyze the transistor amplifier shown below to determine its voltage gain. Assume b = 100. 1 2 3 + - 2 1 3

39. Example 4.9, cont’d
Having determined the operating point, we now proceed to determine the small-signal model parameters B C E + -

40. A note about Output Signal Swing
The collector voltage (and vo) can have a maximum value of zero volts before the transistor goes from forward active mode to saturation mode since the base is grounded.
When no input (ac) voltage is applied the output (collector) was found to be at a DC level of -5.4V.
If we desire a symmetric output signal (about the -5.4V DC level) the signal would have to go to or Volts (this is a large output signal swing).
This causes a problem, since our lower voltage supply is only -10V.
In order to avoid possibly producing a distorted output signal the input signal range must be limited so that the output is not clipped as shown below. Limiting the input signal to smaller values to limit clipping is not the same as using a small signal to invoke the linear approximation as indicated in the next bullet item.
Another important point to be made about the output signal is that it is shown to be linear in the figure below but in fact the iC-vbe characteristic is not linear for a large output signal swing. t
-5.4
-10
clipping

41. Modifying the Hybrid-p Model to Include the Early Effect
The Early effect causes the collector current to depend on vBE as well as vCE.
The dependence on vCE is modeled by assigning a finite output resistance to the controlled current-source.
By including ro in the equivalent circuit shown below, the gain will be somewhat reduced.
voltage-controlled
current source
current-controlled
current source B C B C E E

42. Summary of the BJT Small-Signal Model Parameters
Keep these at your fingertips (I.e. formula sheet for an exam or homework or in lab)
See Table 4.3
Model parameters in terms of DC bias currents
Model parameters in terms of the transconductance, gm
Model parameters in terms of re
Relationships between the common-emitter current gain and the common-base gain

43. Graphical Analysis

44. Graphical Analysis (cont.)

45. Graphical Analysis (cont.)

46. Graphical Analysis (cont.)

47. Single Power Supply
Biasing the BJT involves establishing a constant dc current in the emitter which is calculable, predictable, and insensitive to temperature variations and to b (for transistors of the same type).
The bias point should allow for maximum output signal swing.
To design for a stable IE, the design constraints (shown below) must be satisfied.
Design constraints:
Circuit topology for
biasing a BJT amplifier

48. Single Power Supply, cont’d
From the previous page, our design constraints are as follows:
When biasing the BJT, we must make sure of the following:
VBB must not be too large, or it will lower the sum of voltages across RC and VCB
RC should be large enough to obtain high voltage gain and large signal swing
VCB (or VCE) should be large enough to provide a large signal swing
Rules of thumb:
We’d like for RB to be small, which is achieved by low values of R1 and R2. This could result in higher current drain from the power supply, hence lower input resistance (if the input signal is coupled to the base). This means that we want to make the base voltage independent of b and solely determined by the voltage divider. In order to achieve this, another rule of thumb is practiced: select R1 and R2 such that their current is in the range of

49. Example 4.12
We wish to design the bias network of the amplifier shown below to establish a current IE = 1mA using a power supply VCC = +12 V.
neglecting base current:
for voltage divider current = 0.1IE
for nonzero base current:
for voltage divider current = IE

50. Example 4.12, cont’d
Depending on what the emitter current is, we can have two designs:
Design 1: the voltage divider current = 0.1IE, and
Design 2: the voltage divider current = IE
Design 1
Design 2

51. Biasing Using Two Power Supplies
A somewhat simpler bias arrangement is possible if two power supplies are available.
If the transistor is to be used with the base grounded, then RB can be eliminated altogether.
If the input signal is to be coupled to the base, then RB is needed.
Design constraints:

52. An Alternative Biasing Arrangement

53. Biasing Using a Current Source
The BJT can be biased using a current source
The advantage is that the emitter current is independent of the values b and RB
Current-source biasing leads to significant design simplification

54. Common-Emitter Amplifier
Circuit
AC Hybrid p-based model

55. Common-Emitter Amplifier (cont.)
Input Resistance:
Current Gain:
Voltage Gain:
Output Resistance:

56. What is Av if a 5kW load resistor is added to the circuit:
Exercise 4.31
For a CE amplifier, let I=1 mA, RC=5kW, b=100, VA=100V, and Rs=5kW. Find Ri, Av, Ai, and Ro:
What is Av if a 5kW load resistor is added to the circuit:

57. Common-Emitter Amplifier with an Emitter Resistor

58. Common-Emitter Amplifier with an Emitter Resistor (cont.)
Input Resistance:
Voltage Gain:

59. Common-Emitter Amplifier with an Emitter Resistor (cont.)
Characteristics of CE amplifier with resistance Re:
Input resistance is increased by the factor of (1+gmRe)
An input signal of (1+gmRe) times larger can be applied to the input without inducing nonlinear distortion
The voltage gain is reduced
The voltage gain is less dependent on the value of b
The high frequency response is significantly improved
Output Resistance:
Current Gain:

60. Exercise 4.32
For a CE amplifier with Re, let I=1 mA, RC=5kW, b=100, and Rs=5kW. Find Re such that the amplifier has an input resistence of 4 times that of the source. Find Av, Ai, and Ro:

61. Exercise 4.32
For the same CE amplifier, find the maximum vs without Re and with Re if vp is to be limited to 5mV:

62. Common-Base Amplifier

63. Common-Base Amplifier (cont.)
Input Resistance:
Current Gain:
Voltage Gain:
Output Resistance:

64. Exercise 4.33
For a CB amplifier with Re, let I=1 mA, RC=5kW, b=100, and Rs=5kW. Find RiAv, Ai, and Ro:
Note that RiAv, Ai are much lower than the CE amplifier using the same components although the voltage gain of the CB amplifier can be almost equivalent if Rs is low.

65. Common-Collector Amplifier - Emitter Follower

66. Common-Collector Amplifier - Emitter Follower (cont.)

67. Common-Collector Amplifier - Emitter Follower (cont.)
Input Resistance:
Voltage Gain:
Current Gain:

68. Common-Collector Amplifier - Emitter Follower (cont.)
Output Resistance:

69. Common-Collector Amplifier - Emitter Follower (cont.)
Output Resistance (cont.):
Voltage Gain revisited:
Open-circuit voltage gain:

70. Exercise 4.34
For an emitter follower with a load resistence, RL=1kW, let I=5 mA, b=100, VA=100V, and Rs=10kW. Find :

71. Exercise 4.34 (cont.)
For an emitter follower with a load resistence, RL=1kW, let I=5 mA, b=100, VA=100V, and Rs=10kW. Find :

72. The BJT as a switch-cutoff and saturation
The BJT has 4 modes of operation:
Cutoff
Forward Active
Saturation
Inverse Active
So far, we have studied the forward active mode in great detail. Now we will look at the BJT in cutoff mode and at the BJT in saturation mode. These two extreme modes of operation are very useful if the transistor is used as a switch, such as in digital logic circuits.
Mode EBJ CBJ
Cutoff Reverse Reverse
Forward Active Forward Reverse
Saturation Forward Forward
Inverse Active Reverse Forward

73. Cutoff Region
Consider the circuit shown below. If voltage source vI is goes lesss than about 0.5V, the Emitter-Base Junction will conduct negligible current (reverse-biased). The CBJ is also reverse-biased since VCC is positive.
The device will be in the cutoff mode. It follows that: + -

74. Active Region
To turn the transistor on, vI must be increased to above 0.7V. This gives base current:
The collector current is given by which applies only if the device is in active mode. At this point, we don’t know for sure, therefore we assume active mode and calculate the collector current from + -
Next, we check whether or not. In our case, just check whether
or not . If so, then our original assumption is true. If not, the device is in saturation.

75. MAXIMUM BASE current in forward active
Saturation Region
Saturation occurs when we attempt to force a current in the collector higher than the collector circuit can support while maintaining active-mode operation.
Maximum collector current
MAXIMUM BASE current in forward active
Increasing above , the collector current will increase and the collector voltage will fall below that of the base.
This will continue until the CBJ becomes forward-biased. + -
Constant current
IB is usually higher than IB(EOS) by a factor of 2 to overdrive factor.
EOS=edge of saturation
This value can be set “at will.”

76. Model for the Saturated BJT
A simple model for the npn and pnp transistors in saturation mode is shown on the left.
For quick approximate calculations one may consider VBE and VCEsat to be zero and use the three-terminal short circuit shown on the right to model a saturated transistor. E C B E B C
npn E C B
approximate model
pnp

77. Example 4.13
We wish to analyze the circuit to determine the voltages at all nodes and currents in all branches. Assume the transistor b is specified to be at least 50.
Assuming saturation: 1 4 2 3 3 5 1 2 4 5

78. Example 4.14
The transistor shown below is specified to have b in the range 50 to Find the value of RB that results in saturation with an overdrive factor of at least 10.

79. Example 4.15
We want to analyze the circuit below to determine the voltages at all nodes and the currents through all branches. The minimum value of b is specified to be 30.

80. Example 4.15, cont’d
Substituting in the equations on the previous page, we obtain the following:

81. Introduction - Equation forms for use in SPICE
Consider the equation for the emitter current in an ideal pnp bipolar junction transistor
We can simplify the equations by collecting the terms into only a few constants, giving the coefficients different names, for example, half of the equation given above becomes;
The other half of the equation is similarly reduced
This allows the emitter current to be written in a much more compact form:

82. Equation forms for use in SPICE (continued)
Now consider the equation for the collector current in an ideal pnp bipolar junction transistor
The right half of the equation reduces to:
The left half of the equation is similarly reduced
This allows the collector current to be written in a much more compact form:
If we know two of the terminal currents we can find the current in the third terminal

83. The Ebers-Moll equations for an ideal PNP BJT
The key results are
The equivalent circuit (just another way to state the equations) C IC P C IC
aFIF IR IB B N B
aRIR IF IB IE IE E E P

84. Use in SPICE
The current sources illustrate the interaction of the two junctions due to the narrow base region
IS is one of the three required SPICE parameters for a BJT in SPICE2
The reduced equations can be manipulated to show that:
Only three numbers, bF , bR and IS are needed for the Ebers-Moll equations to be completely specified.
All other parameters can be calculated from these three
The equations can be applied to all regions of operation
Can be extended to the nonideal case by defining coefficients in front of the exponential terms
For NPN transistors the diodes, currents and voltage polarities are reversed

85. An Alternative form of the Ebers-Moll Model, the Transport Model
In this model the diodes DBE and DBC have saturation currents IS/bF and IS/bF respectively
The base current, ib can be written as
iT is the current component of iC which arises from the minority carrier diffusion (transport) across the base, hence the name of this model
The transport model is exactly equivalent to the Ebers-Moll model but it highlights different aspects of BJT behavior. It uses one less circuit element and one less parameter in SPICE C iC
DBC
IS/bR iB B iT
DBE
IS/bF iE E

86. Common-Base Characteristics
First-Order iC-vCB Characteristics
Second-Order iC-vCB Characteristics

87. Common-Emitter Characteristics
Second-Order iC-vCE Characteristics (refer to lesson 17)

88. DC and ac b “BETA DC” (spice) “BETAAC” (spice)
More accurate than bF, because its determined at Q
Common-emitter current gain at DC
“BETAAC” (spice)
Input ac signal results in DiB  DiC.
Thus changes, because
Since vCE is constant, bac=short-circuit current gain.
Typically, bac=bdc. Use bac in small-signal model.

89. “Complete” BJT Models Low-frequency model
rx=base resistance of bulk Si
r=

90. “Complete” BJT Models
High-frequency model