1. PE-Electrical Review Course - Class 4 (Transistors)
Objectives:
This review session is designed to review material and provide practical examples such that the student will be able to:
1) Be familiar with transistor symbols, characteristics, terminology, and typical values.
2) Be familiar with basic transistor biasing circuits and be able to calculate the Q-point.
3) Determine the Q-point is stable with respect to variations in transistor specifications.
4) Be familiar with different small-signal transistor models, including the h-parameter model and the hybrid- p model.
5) Be familiar with different transistor amplifier configurations, including CE, CB, and CC for BJT’s and CS, CG, and CD for FET’s.
6) Be able to calculate gains (voltage, current, and power) and impedances (input and output) for each amplifier configuration and to be familiar with typical values for each configuration.
7) Be able to calculate gains and impedances for multi-stage amplifiers.
8) Be familiar with the causes of frequency response limitation in amplifiers and be able to find the bandwidth of an amplifier.
9) Be familiar with resources available in the review book for specialized amplifier circuits, such as power, Darlington, cascode, and differential amplifiers.
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8, Chapter 10 (Section 1)

2. Transistors: Background:
PE-Electrical Review Course - Class 4 (Transistors)
Transistors:
Discuss how reviewing this area might be more difficult than other areas in Electrical Engineering due to the great familiarity required with symbols, characteristics, typical values, common circuits, and a huge number of formulas which can easily be misused if not understood in their proper context. (Note that Ch. 8 in the review text begins with a list of definitions for well over 100 variables and symbols.)
Background:
In reviewing the large amount of material in this area, the student may want to focus on the areas which are most useful (i.e., most commonly occur on the PE exam). As a result, this review course will focus on transistors and will not review semiconductor physics (n-type material, p-type materials, doping, majority and minority carriers, physical construction, etc) or diodes and diode circuits. If students wishes to review this material on their own, the following sections in the review text will be useful:
Reference: EE Ref. Manual, 5th Ed., Yarborough,
Chapter 8, Section 1 - PN Junction Characteristics
Chapter 10, Section 1 - Diode Circuits

3. PE-Electrical Review Course - Class 4 (Transistors)
Types of transistors:
The following 8 types of transistors are commonly encountered:
1) Bipolar Junction Transistor (BJT)
A) npn B) pnp
2) Field-Effect Transistor (FET)
A) Junction Field-Effect Transistor (JFET)
a) n-channel b) p-channel
B) Metal-Oxide-Semiconductor FET (MOSFET) (or Insulated-Gate FET (IGFET))
a) Depletion-mode MOSFET
1) n-channel 2) p-channel
b) Enhancement-mode MOSFET
1) n-channel 2) p-channel

4. JFETs PE-Electrical Review Course - Class 4 (Transistors)
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8 - Section 2
Symbol: n-channel JFET
D = Drain
G = Gate
S = Source
(Note: the circle around the transistor is optional)
Discuss:
Current relationship using KCL
Voltage relationship using KVL
Typical values
n-channel vs. p-channel

5. PE-Electrical Review Course - Class 4 (Transistors)
Output characteristics: n-channel JFET (typical)
Note:
Two key specifications for the JFET are IDSS and VP
JFET’s have two
regions of operation:
1) Ohmic (VDS < VGS - VP)
2) Saturation
(or Beyond Pinchoff)
(VDS > VGS - VP)

6. PE-Electrical Review Course - Class 4 (Transistors)
Ohmic Region: n-channel JFET (typical)
Ohmic Region defined by: VDS < VGS - VP
In the ohmic region the JFET acts like a voltage-controlled resistance
(called a Voltage Variable Resistor or VVR), where
Notes:
1) Not the most commonly used region
2) Discuss applications

7. PE-Electrical Review Course - Class 4 (Transistors)
Saturation Region (or Beyond Pinchoff Region): n-channel JFET (typical)
Saturation Region defined by: VDS > VGS - VP
The behavior of the JFET in the saturation region is modeled by the transfer characteristic (see graph below) and by the transfer characteristic equation.
Note:
The saturation region is the most common region (JFET used as an amplifier)

8. Depletion-mode MOSFETs
PE-Electrical Review Course - Class 4 (Transistors)
Depletion-mode MOSFETs
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8 - Section 3
Symbol: n-channel depletion-mode MOSFET
(Current and voltage designations and relationships are the same as for a JFET)
Depletion-mode MOSFETs are very similar to JFETs except for one key difference:
The depletion-mode MOSFET can operate in two modes:
A) depletion-mode:
- operates almost exactly as a JFET
- defined by VGS < 0 for an n-channel device
- current flows through a physical channel in the device
B) enhancement-mode:
- defined by VGS > 0 for an n-channel device
- the physical channel is “enhanced” by VGS to allow for increased ID

9. PE-Electrical Review Course - Class 4 (Transistors)
Output characteristics: n-channel depletion-mode MOSFET (typical)
As with JFET’s,
MOSFET’s have two regions of operation:
1) Ohmic: VDS < VGS - VP
2) Saturation (or Beyond Pinchoff): VDS > VGS - VP
Ohmic Region
As with JFET’s, in the ohmic region the MOSFET acts like a Voltage Variable Resistor (VVR), and is described by the ohmic region equation (below):

10. PE-Electrical Review Course - Class 4 (Transistors)
Saturation Region: n-channel depletion-mode MOSFET
Saturation Region defined by: VDS > VGS - VP
As with the JFET, the behavior of the depletion-mode MOSFET in the saturation region is modeled by the transfer characteristic (see graph below) and by the transfer characteristic equation.
Two key specifications for the depletion-mode MOSFET are IDSS and VP

11. Enhancement-mode MOSFETs
PE-Electrical Review Course - Class 4 (Transistors)
Enhancement-mode MOSFETs
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8 - Section 4
Symbol: n-channel enhancement-mode MOSFET
Enhancement-mode MOSFET’s lack the physical channel of the depletion-mode devices, so they can only operate in the enhancement mode.
Some minimum amount of VGS must be applied before a significant channel can be created and significant drain currents developed. This minimum voltage is called:
VT = threshold voltage = minimum VGS needed to enhance a significant channel for |ID|>0

12. PE-Electrical Review Course - Class 4 (Transistors)
Output characteristics: n-channel enhancement-mode MOSFET (typical)
As with JFET’s,
MOSFET’s have two regions of operation:
1) Ohmic: VDS < VGS - VP
2) Saturation (or Beyond Pinchoff): VDS > VGS - VP
Ohmic Region
As with JFET’s, in the ohmic region the MOSFET acts like a Voltage Variable Resistor (VVR), and is described by the ohmic region equation (below). Note that this equation is different from the equations for other FET’s.

13. PE-Electrical Review Course - Class 4 (Transistors)
Saturation Region: n-channel enhancement-mode MOSFET
Saturation Region defined by: VDS > VGS - VT
As with other FET’s, the behavior of the enhancement-mode MOSFET in the saturation region is modeled by the transfer characteristic (see graph below) and by the transfer characteristic equation. Note that this equation is different from the equations for other FET’s.
Two key specifications for the enhancement-mode MOSFET are K and VT.
(IDSS and VP do not exist for the enhancement-mode MOSFET.)

14. PE-Electrical Review Course - Class 4 (Transistors)
FET Biasing Circuits
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8 - Sections 3-5
The purpose of the biasing circuit is to insure that the FET is operating in the saturation region so that it can be used as an amplifier. The biasing circuit establishes a Q-point (or quiescent point or operating point) in the saturation region (for amplifier use).
For example, two possible Q points are shown below.
Q1 : Ohmic Region
ID = 2.6 mA
VDS = 0.4 V
VGS = -0.5 V
Q2 : Saturation Region
ID = mA
VDS = 10 V
VGS = -0.5 V

15. PE-Electrical Review Course - Class 4 (Transistors)
FET Biasing Circuits
There are various types of biasing circuits for FET’s. Several are shown below.
A) Fixed-bias B) Fixed-bias C) Self-bias D) Fixed- + Self-bias
Comments:
A) Fixed-bias:
B) Fixed-bias: (This biasing circuit works in the enhancement mode only.)
C) Self-bias:
D) Fixed- + Self-bias:

16. PE-Electrical Review Course - Class 4 (Transistors)
Find the Q-point for the biasing circuit shown below.
The JFET has the following specifications:
IDSS = 4 mA
VP = V
Example 1:

17. PE-Electrical Review Course - Class 4 (Transistors)
Find the Q-point for the biasing circuit shown below.
The JFET has the following specifications:
IDSS = 4 mA
VP = V
Example 2:
Note: The addition of RS makes the analysis
more difficult. KVL around the input loop
combined with the transfer characteristic
will yield the Q-point. An alternative is to
use a “Universal JFET Curve” (not covered).

18. BJT’s (Bipolar Junction Transistors)
PE-Electrical Review Course - Class 4 (Transistors)
BJT’s (Bipolar Junction Transistors)
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8 - Section 7
Symbol: n-channel BJT
C = Collector
B = Base
E = Emitter
(Note: the circle around the transistor is optional)
Discuss:
Current relationship using KCL
Voltage relationship using KVL
Typical values
npn vs. pnp

19. PE-Electrical Review Course - Class 4 (Transistors)
Output characteristics: npn BJT (typical)
Note: The PE review text often uses a less common but related parameter:
Find the approximate values of bdc and adc from the graph.
Input characteristics: npn BJT (typical)
The input characteristics look like the characteristics of a forward-biased diode. Note that VBE varies only slightly, so we often ignore these characteristics and assume:
Common approximation: VBE = Vo = V
Note: Two key specifications for the BJT are Bdc and Vo (or assume Vo is about 0.7 V)

20. PE-Electrical Review Course - Class 4 (Transistors)
BJT’s have three regions of operation:
1) Active - BJT acts like an amplifier (most common use)
2) Saturation - BJT acts like a short circuit
3) Cutoff - BJT acts like an open circuit
BJT is used as a switch by switching
between these two regions.
When analyzing a DC BJT circuit, the BJT is replaced by one of the DC circuit models shown below.
DC Models for a BJT:

21. PE-Electrical Review Course - Class 4 (Transistors)
BJT Biasing Circuits
The purpose of the biasing circuit is to insure that the BJT is operating in the active region so that it can be used as an amplifier. The biasing circuit establishes a Q-point (or quiescent point or operating point) in the active region (for amplifier use).
For example, three possible Q points are shown below.
Q1 : Active Region
IB = 150 mA
IC = 22.5 mA
VCE = 15 V
bdc = IC/IB =
= 22.5mA/150mA
= 150
Q2 : Saturation Region
IB = 150 mA
IC = 17 mA
VCE = 0.5 V
rsat = 0.5V/17mA
= 29.4 W
Q3 : Cutoff Region
IB = 0
IC = 0
VCE = 10 V

22. PE-Electrical Review Course - Class 4 (Transistors)
BJT Biasing Circuits
There are various types of biasing circuits for BJT’s. Several are shown below.
A) Base-bias B) Collector-bias C) Base-bias with D) Voltage-divider bias
emitter feedback with emitter feedback
(most popular)
Analysis Procedure:
A) Assume a region of operation (generally the active region for amplifier use)
B) Replace the BJT with the active region model
C) Analyze the circuit to determine the Q-point
Note: If unreasonable values are found it typically means that the wrong region was used. For example, if RC is too large, the BJT may be in saturation. Analysis with the active region model might yield a value of VCE that is negative.

23. PE-Electrical Review Course - Class 4 (Transistors)
Find the Q-point for the biasing circuit shown below.
The BJT has the following specifications:
bdc = 100, rsat = 100 W (Vo not specified, so assume Vo = 0.7 V)
Example 3:
Example 4:
Repeat Example 3 if RC is changed from 1k to 2.2k.

24. Voltage-Divider Biasing Circuit with Emitter Feedback
PE-Electrical Review Course - Class 4 (Transistors)
Voltage-Divider Biasing Circuit with Emitter Feedback
Most popular biasing circuit. Why?
Problem: bdc can vary over a wide range for BJT’s (even with the same part number)
Solution: Adding the feedback resistor RE. How large should RE be? Let’s see.
Substituting the active region model into the circuit to the left and analyzing the circuit yields the following well known equation:
ICEO has little effect and is often neglected yielding the simpler relationship:
Voltage divider biasing circuit with emitter feedback
Replacing the input circuit by a Thevenin equivalent circuit yields:
Test for stability: For a stable Q-point w.r.t. variations in bdc choose:
Why? Because then

25. PE-Electrical Review Course - Class 4 (Transistors)
Find the Q-point for the biasing circuit shown below.
The BJT has the following specifications:
bdc varies from 50 to 400, Vo = 0.7 V, ICBO = 10 nA
Solution:
Case 1: bdc = 50
Example 5:
Case 2: bdc = Similar to Case 1 above. Results are: IC = mA, VCE = 6.14 V
Summary:
Is the biasing circuit stable? Discuss.
Ex 8.1 and Eq on p. 8-19:
Uses adc and Q-point is unstable.

26. Small-Signal BJT Amplifiers
PE-Electrical Review Course - Class 4 (Transistors)
Small-Signal BJT Amplifiers
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8 - Section 8
BJT Amplifier Models: Once the DC Q-point has been established in the active region, the BJT can be used as an amplifier to amplifier small (AC) signals. New small-signal circuit models are needed to model the BJT. There are several types of models:
1) mid-frequency models - used to find voltage, current, and power gain and Zin and Zout.
2) low- and high-frequency models - used to find frequency response information
Mid-frequency small-signal models
There are several possible models. Textbooks vary in which model they prefer. The models are, however, closely related. Some of the most common are:
1) h-parameter model
2) hybrid-p model
3) re (or re’) model

27. Mid-frequency small-signal models Notes:
PE-Electrical Review Course - Class 4 (Transistors)
Mid-frequency small-signal models Notes:
Note: The hybrid-p model will be used in this presentation.

28. Determining hybrid-p parameter values
PE-Electrical Review Course - Class 4 (Transistors)
Determining hybrid-p parameter values
hybrid-p values may be provided (for example, from a specification sheet),
but they vary with the Q-point and are often calculated using Q-point values.

29. BJT Mid-frequency Analysis using the hybrid-p model:
PE-Electrical Review Course - Class 4 (Transistors)
BJT Mid-frequency Analysis
using the hybrid-p model:
A common emitter (CE) amplifier is shown to the right.
The mid-frequency circuit is drawn as follows:
the coupling capacitors (Ci and Co) and the
bypass capacitor (CE) are short circuits
short the DC supply voltage (superposition)
replace the BJT with the hybrid-p model
The resulting mid-frequency circuit is shown below.

30. Procedure: Analysis of a BJT amplifier at mid-frequency:
PE-Electrical Review Course - Class 4 (Transistors)
Procedure: Analysis of a BJT amplifier at mid-frequency:
1) Find the DC Q-point. This will insure that the BJT is operating in the active region and these values are needed for the next step.
2) Find the hybrid-p values. If the values are not given, use the relationships on the previous page.
3) Calculate the required values (typically Avi, Avs, AI, AP, Zi, and Zo. Use the formulas for the appropriate amplifier configuration (CE, CB, CC, partially-bypassed CE, etc).

31. PE-Electrical Review Course - Class 4 (Transistors)
Example 6:
Find the mid-frequency values for Avi, Avs, AI, AP, Zi, and Zo for the amplifier shown below. Assume that Ci, Co, and CE are large.
Note that this is the same biasing circuit used in Ex. 5, so IC = mA.
The BJT has the following specifications:
bdc = 50, Vo = 0.7 V, ICBO = 10 nA, bo = 40,
n = 1, VA = 30 V

32. BJT Amplifier Configurations and Relationships:
PE-Electrical Review Course - Class 4 (Transistors)
BJT Amplifier Configurations and Relationships:
Using the hybrid-p model.
Note: The biasing circuit is the same for each amplifier.

33. Small-Signal FET Amplifiers
PE-Electrical Review Course - Class 4 (Transistors)
Small-Signal FET Amplifiers
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8 - Section 8
FET Amplifier Models: FET amplifier models are very similar to BJT amplifiers with only a few differences:
1) The hybrid-p model is used almost exclusively.
2) Many formulas for calculating gains and impedances are similar to those for BJT’s. However, FET’s have very high input resistances so rp is infinite.
3) FET amplifiers in general tend to have lower voltage gains and higher input impedances.
4) The hybrid-p model parameters (particularly gm) are calculated differently.
Mid-frequency FET small-signal model:

34. FET Mid-frequency Analysis:
PE-Electrical Review Course - Class 4 (Transistors)
FET Mid-frequency Analysis:
A common source (CS) amplifier is shown to the right.
The mid-frequency circuit is drawn as follows:
the coupling capacitors (Ci and Co) and the
bypass capacitor (CSS) are short circuits
short the DC supply voltage (superposition)
replace the FET with the hybrid-p model
The resulting mid-frequency circuit is shown below.

35. Procedure: Analysis of an FET amplifier at mid-frequency:
PE-Electrical Review Course - Class 4 (Transistors)
Procedure: Analysis of an FET amplifier at mid-frequency:
1) Find the DC Q-point. This will insure that the FET is operating in the saturation region and these values are needed for the next step.
2) Find gm. If gm is not specified, calculate it using the DC values of VGS as follows:
3) Calculate the required values (typically Avi, Avs, AI, AP, Zi, and Zo. Use the formulas for the appropriate amplifier configuration (CS, CG, CD, etc).

36. PE-Electrical Review Course - Class 4 (Transistors)
Example 7:
Find the mid-frequency values for Avi, Avs, AI, AP, Zi, and Zo for the amplifier shown below. Assume that Ci, Co, and CSS are large.
Note that this is the same biasing circuit used in Ex. 2, so VGS = V.
The JFET has the following specifications:
IDSS = 4 mA, VP = V, rd = 50 k

37. FET Amplifier Configurations and Relationships:
PE-Electrical Review Course - Class 4 (Transistors)
FET Amplifier Configurations and Relationships:
Note: The biasing circuit is the same for each amplifier.

38. Which amplifier should be used?
PE-Electrical Review Course - Class 4 (Transistors)
Which amplifier should be used?
In order to answer this question, it is necessary to be familiar with typical values for each of the amplifier configurations. The tables below list some typical values. However, note that each value might vary considerably.
Highlight some of the key features that distinguish each amplifier configuration.
Point out the similarities between the BJT and FET amplifier configurations.

39. Multi-stage Amplifiers
PE-Electrical Review Course - Class 4 (Transistors)
Multi-stage Amplifiers
In general, multistage amplifiers are used when a single-stage amplifier cannot deliver all of the desired features. Keep in mind the following principles:
1) Avi = (Avi1)(Avi2)
2) Rs for stage 2 = Zo stage 1
3) RL for stage 1 = Zi for stage 2
Stage 1
Stage 2
Label the type of amplifier to be used in each case below in order to satisfy the design specifications?
Example 8:
A) Design specifications:
Avi = 100, Zo = 30
B) Design specifications:
Avi = 100, Zi = 100 k

40. PE-Electrical Review Course - Class 4 (Transistors)
Find Avi1 = v2/v1 , Avi2 = v3/v2 , Avi = v3/v1 , Zi1, Zi2, Zo1, and Zo2 for the CE-CE multistage amplifier shown below.
Example 9:
Note that the biasing circuits are identical and are from Ex. 5, so IC = mA. Each BJT has the same specifications: bdc = 50, Vo = 0.7 V,
ICBO = 10 nA, bo = 40,
n = 1, VA = 30 V

41. Frequency Response of Amplifiers
PE-Electrical Review Course - Class 4 (Transistors)
Frequency Response of Amplifiers
The voltage gain of an amplifier is typically flat over the mid-frequency range, but drops drastically for low or high frequencies. A typical LM response is shown below.
For a CE BJT: (shown on lower left)
low-frequency drop-off due to CE, Ci and Co
high-frequency drop-off due to Cp and Cm
(combined for form Ctotal)
Each capacitor forms a break (simple pole or zero)
with a break frequency of the form f = 1/(2pREqC),
where REq is the resistance seen by the capacitor
CE usually yields the highest low-frequency break
which establishes fLow.
For a CS FET: (not shown - similar to BJT)
low-frequency drop-off due to CSS, Ci and Co
low-frequency drop-off due to Cds, Cgs and Cgd

42. BJT High-frequency model
PE-Electrical Review Course - Class 4 (Transistors)
BJT High-frequency model
The BJT high-frequency hybrid-p model is shown to the right.
The capacitance Cm is replaced by a “Miller capacitance” so that the two capacitors can be added in parallel.
I.e., Ctotal = Cp + CMiller
The break frequencies can now be calculated using the following:

43. PE-Electrical Review Course - Class 4 (Transistors)
Example 10:
Find fHigh, fLow, and the bandwidth, BW, for the amplifier used in Example 6 if Ci = 10 mF, Co = 10 mF, CE = 50 mF, Cp = 20 pF, Cm = 2 pF, and rx = 20 ohms.

44. Special Amplifiers PE-Electrical Review Course - Class 4 (Transistors)
The focus of this review has been basic BJT and FET amplifiers. There are also a number of special amplifiers that would require considerable time to present. It would be difficult for the student to prepare adequately to be able to handle all special amplifiers. The best approach seems to be to review the basics well and then use a good reference book, such as the one for this course, if a special amplifier is encountered on the exam.
Special amplifiers would include:
Differential amplifiers
Darlingtons
Cascode amplifiers
Power amplifiers
Push-pull amplifiers
Reference: EE Ref. Manual, 5th Ed., Yarborough, Chapter 8 - Sections 9-13