Electronic Circuits
Chapter 2: BJT Amplifiers
1
Content
1. Device Structure and Physical Operation (Session 6.1)
2. Current–Voltage Characteristics (Session 6.2)
3. BJT Circuits at DC (Session 6.3)
4. Small-Signal Operation and Models
5. BJT Amplifier Configurations
2
1. Device Structure and Physical Operation
Review
3
2. Current–Voltage Characteristics
Circuit Symbols and Conventions
Circuit symbols for BJTs.
Voltage polarities and current flow in
transistors operating in the active mode.
4
2. Current–Voltage Characteristics
Circuit Symbols and Conventions
5
2. Current–Voltage Characteristics
The Common-Emitter Current Gain β
6
2. Current–Voltage Characteristics
Graphical Representation of Transistor Characteristics
The iC–vBE characteristic for an npn
transistor.
7
2. Current–Voltage Characteristics
8
2. Current–Voltage Characteristics
Large-signal, equivalent-circuit models of an npn BJT operating in the active mode in the
common-emitter configuration with the output resistance ro included.
9
3. BJT Circuits at DC
A Note on Units Except when otherwise specified, throughout this book we use a consistent set
of units, namely, volts (V), milliamps (mA), and kilohms (k )
3. BJT Circuits at DC
6Example
Active mode (npn BJT)
For modern npntransistors, 𝛽 is in the range 50 to 200, but it can be as high as
1000 for special devices.
Example 1:
The transistor in the following circuit having 𝛽 = 100
and exhibits a 𝑣𝐵𝐸 of 0.7𝑉 at 𝑖𝐶 = 1 𝑚𝐴. Design the
circuit so that a current of 2𝑚𝐴 flows through the
collector and a voltage of +5 𝑉 appears at the collector.
12
Active mode (npn BJT)
Example 2: In the circuit shown in figure a, the voltage at the emitter was measured
and found to be – 0.7 𝑉. If 𝛽 = 50, find 𝐼𝐸 , 𝐼𝐵 , 𝐼𝐶 and 𝑉𝐶 .
Example 3: In the circuit shown
in figure b, measurement
indicates 𝑉𝐵 to be +1.0𝑉 and 𝑉𝐸
to be +1.7𝑉. What are 𝛼 and 𝛽
for this transistor? What voltage
𝑉𝐶 do we expect at the collector?
Figure a
Figure b
13
Transistor Characteristics
𝑖𝐶 - 𝑣𝐵𝐸 characteristic for an npn transistor.
14
Transistor Characteristics – Early Effect
𝑖𝐶 - 𝑣𝐶𝐵 characteristic for an npn transistor.
𝑽𝑨 : Early Voltage.
𝑽𝑨 ~ 10V – 100V.
15
Transistor Characteristics – Early Effect
In saturation region, it behaves as a closed switch with a small resistance 𝑅𝐶𝐸𝑠𝑎𝑡 .
The saturation I-V curve can be approximated by a straight line intersecting the
𝑣𝐶𝐸 axis at 𝑉𝐶𝐸𝑜𝑓𝑓 .
The
output
resistance
looking into the collector is
not infinite:
𝒓𝒐 =
𝑽𝑨 + 𝑽𝑪𝑬
𝑰𝑪
16
BJT Circuits at DC - npn
• Step 1: assume the operation mode.
• Step 2: use the conditions or model for circuit analysis.
• Step 3: verify the solution.
• Step 4: repeat the above steps with another assumption if necessary.
17
BJT Circuits at DC - npn
Example 4: Analyze the following circuit to
determine all node voltages and branch currents.
Assume that β is specified to be 100.
18
BJT Circuits at DC - npn
Example 5: Analyze the circuit in Example 1 to determine all node voltages and branch
currents. The voltage at the base is now +0V.
19
BJT Circuits at DC - npn
Example 6: Analyze the circuit in Example 1 to determine all node voltages and branch
currents. The voltage at the base is now +6V.
20
BJT Circuits at DC - pnp
21
BJT Circuits at DC
Example 7: Analyze the following circuit to
determine all node voltages and branch currents.
Assume that β is specified to be 100.
22
BJT Circuits at DC
Example 8: Analyze the following circuit to determine all node voltages and branch
currents. Assume that β is specified to be 100.
23
BJT Circuits at DC
Example 9: Analyze the following circuit to determine all node voltages and branch
currents.
24
BJT Circuits at DC
Example 10: Analyze the following circuit to determine all node voltages and branch
currents. Assume that β is specified to be 100.
25
DC Bias for BJT amplifier
❖ The amplifiers are operating at a proper dc bias point.
❖ The DC bias circuit is to ensure the BJT in active mode with a proper collector current IC.
Point Q is known as the bias point
or the dc operating point.
The signal to be amplified 𝑣𝑏𝑒 ,a
function of time 𝑡.
𝑉𝐶𝐸 = 𝑉𝐶𝐶 − 𝑅𝐶 𝐼𝑆
𝑉𝐵𝐸
ൗ𝑉
𝑇
𝑒
26
DC Bias for BJT amplifier
The signal to be amplified 𝑣𝑏𝑒 , a function of time 𝑡:
𝒗𝑩𝑬 𝒕 = 𝑽𝑩𝑬 + 𝒗𝒃𝒆 (𝒕)
27
DC
Bias
for
BJT
amplifier
❖ The classical discrete-circuit bias arrangement:
➢ A single power supply and resistors are needed.
28
DC Bias for BJT amplifier
❖ The classical discrete-circuit bias arrangement:
➢ The two-power-supply version.
29
DC Bias for BJT amplifier
❖ Biasing using a constant-current source:
➢ RC is chosen to operate the BJT in active mode.
➢ The current source is typically implemented by a BJT current mirror.
✓ Both BJT transistors Q1 and Q2 are in active mode.
✓Assume current gain  is very high.
I REF
VCC + VEE − VBE
=
R
30
DC Bias for BJT amplifier
❖ Biasing using a collector-to-base feedback resistor:
➢ RB ensures the BJT in active (VCE > VBE = 0.7V)
31
Obtaining a Voltage Amplifier
The output voltage 𝑣𝐶𝐸 is given by:
In active mode:
The result is:
𝒗𝑪𝑬 = 𝑽𝑪𝑪 − 𝒊𝑪 𝑹𝑪
𝒊𝑪 = 𝑰 𝑺
𝒗𝑩𝑬
ൗ𝑽
𝑻
𝒆
𝒗𝑪𝑬 = 𝑽𝑪𝑪 −
(Neglect the Early effect)
𝒗𝑩𝑬
ൗ𝑽
𝑻𝑹
𝑰𝑺 𝒆
𝑪
This is obviously a nonlinear relationship.
32
Biasing the BJT
A dc voltage is selected to obtain operation at a point Q: 𝑽𝑪𝑬 = 𝑽𝑪𝑪 −
𝑽𝑩𝑬
ൗ𝑽
𝑻𝑹
𝑰𝑺 𝒆
𝑪
Point Q is known as the Bias point or the DC operating point.
Since at Q no signal component is present, it is also known as the Quiescent point.
33
Biasing the BJT
The signal 𝑣𝑏𝑒 to be amplified a
function of time 𝑡 is superimposed on
the bias voltage 𝑉𝐵𝐸 :
𝒗𝑩𝑬 𝒕 = 𝑽𝑩𝑬 + 𝒗𝒃𝒆 (𝒕)
The resulting 𝑣𝐶𝐸 (𝑡) can be obtained
by substituting this expression for
𝒗𝑩𝑬 𝒕 into:
𝒊𝑪 = 𝑰 𝑺
𝒗𝑩𝑬
ൗ𝑽
𝑻
𝒆
34
Small-Signal Operation and Models
We consider the DC bias conditions by setting 𝒗𝒃𝒆 = 𝟎. Then:
𝑰 𝑪 = 𝑰𝑺
𝑰𝑬 =
𝑽𝑩𝑬
ൗ𝑽
𝑻
𝒆
𝑰𝑩 =
𝑰𝑪ൗ
𝜶
𝑰𝑪
ൗ𝜷
𝑽𝑪𝑬 = 𝑽𝑪𝑪 − 𝑰𝑪 𝑹𝑪
When 𝒗𝒃𝒆 ≠ 𝟎 , the total instantaneous base-emitter voltage
𝒗𝑩𝑬 becomes: 𝒗𝑩𝑬 = 𝑽𝑩𝑬 + 𝒗𝒃𝒆
The collector current becomes:
𝒊𝑪 = 𝑰𝑺 𝒆𝒗𝑩𝑬Τ𝑽𝑻 = 𝑰𝑺 𝒆𝑽𝑩𝑬Τ𝑽𝑻 𝒆𝒗𝒃𝒆 Τ𝑽𝑻 = 𝑰𝑪 𝒆𝒗𝒃𝒆 Τ𝑽𝑻
Small signal operation: 𝒗𝒃𝒆 ≪ 𝑽𝑻
𝒊𝑪 = 𝑰 𝑪 + 𝒊𝒄 ≈ 𝑰 𝑪 𝟏 +
𝒗𝒃𝒆
𝑰𝑪
= 𝑰𝑪 +
𝒗
𝑽𝑻
𝑽𝑻 𝒃𝒆
𝛛𝒊𝑪
𝑰𝑪
𝒈𝒎 =
|
=
𝛛𝒗𝑩𝑬 𝒊𝑪 =𝑰𝑪 𝑽𝑻
35
Small-Signal Operation and Models
gm is called the trans-conductance:
𝛛𝒊𝑪
𝑰𝑪
𝒈𝒎 =
|
=
𝛛𝒗𝑩𝑬 𝒊𝑪 =𝑰𝑪 𝑽𝑻
36
Small-Signal Operation and Models
❖ The base current and the input resistance at the base:
➢ Base current:
𝒊𝑪 𝑰𝑺 𝒗 Τ𝑽
𝒊𝑩 = = 𝒆 𝑩𝑬 𝑻 = 𝑰𝑩 𝒆𝒗𝒃𝒆 Τ𝑽𝑻
𝜷
𝜷
➢ Small-signal approximation: 𝑣𝑏𝑒 << 𝑉𝑇
𝒊𝑩 = 𝑰 𝑩 + 𝒊𝒃 ≈ 𝑰 𝑩 𝟏 +
𝒗𝒃𝒆
𝜷
𝑽𝑻
𝒓𝝅 =
=
=
𝒊𝒃
𝒈𝒎 𝑰 𝑩
𝒗𝒃𝒆
𝑰𝑩
= 𝑰𝑩 +
𝒗
𝑽𝑻
𝑽𝑻 𝒃𝒆
The small-signal input
resistance between base and
emitter (looking into the base)
37
Small-Signal Operation and Models
❖ The emitter current and the input resistance at the emitter:
➢ Emitter current:
𝒊𝑬 = 𝑰 𝑬 + 𝒊𝒆 =
𝒊𝑪 𝑰 𝑪 𝒊𝒄
= +
𝜶
𝜶 𝜶
➢ Small-signal approximation: 𝑣𝑏𝑒 << 𝑉𝑇
𝒊𝒄 𝒈𝒎
𝑰𝑬
=
𝒗𝒃𝒆 =
𝒗
𝜶
𝜶
𝑽𝑻 𝒃𝒆
𝒗𝒃𝒆 𝑽𝑻
𝜶
𝟏
𝒓𝒆 ≡
=
=
≈
𝒊𝒆
𝑰 𝑬 𝒈𝒎 𝒈𝒎
𝒊𝒆 =
𝒓𝝅 = 𝟏 + 𝜷 𝒓𝒆
The relation between resistance
at base and resistance at emitter
38
Small-Signal Operation and Models
There are two type of equivalent circuit model of and BJT in small-signal operation:
▪
The Hybrid-Pi model.
▪
The T model.
Two models are exchangeable and does not affect the analysis result.
The hybrid-π model: typically used as the emitter is grounded.
39
Small-Signal Operation and Models
The T model: typically used as the emitter is not grounded.
40
Small-Signal Operation and Models
The analysis above indicates that every current and voltage in the amplifier circuit
is composed of two components: a dc component and a small-signal component.
• DC analysis:
• Remove all ac sources (short for voltage source and open for current source).
• All capacitors are considered open-circuit.
• DC analysis of BJT circuits for all nodal voltages and branch currents.
• Find the dc current 𝑰𝑪 and make sure the BJT is in active mode.
• AC analysis:
• Remove all dc sources (short for voltage source and open for current source).
• All large capacitors are considered short-circuit.
• Replace the BJT with its small-signal model for ac analysis.
• The circuit parameters in the small-signal model are obtained based on the
value of 𝑰𝑪.
41
Small-Signal Operation and Models
Example 12:
a. Analyze the following transistor amplifier to determine its voltage gain 𝑣𝑜Τ𝑣𝑖.
Assume β = 100.
b. Assume that 𝑣𝑖 has a triangular waveform. Determine the maximum amplitude
that 𝑣𝑖 is allowed to have.
c. Set amplitude of 𝑣𝑖 to this value, give the waveforms of the total quantities
𝑖𝐵(𝑡), 𝑣𝐵𝐸 (𝑡), 𝑖𝐶 (𝑡), and 𝑣𝐶 (𝑡).
42
Small-Signal Operation and Models
Example 13: Analyze the following transistor amplifier to determine its voltage gain
𝑣𝑜
Τ𝑣𝑖. Assume β = 100.
43
Small-Signal Operation and Models
Example 14: Calculate the overall voltage gain (𝑣𝑜/𝑣𝑠𝑖𝑔) of the following circuit. What is
the input resistance 𝑅𝑖𝑛. Assume 𝛽 = 200.
44
Small-Signal Operation and Models
Example 15: Find the input resistance 𝑅𝑖𝑏 and 𝑅𝑖𝑛 and the overall voltage gain (𝑣𝑜/𝑣𝑠𝑖𝑔).
Assume 𝛽 = 200.
45
Small-Signal Analysis – Early Effect
Early effect: The collector current depends not only on 𝒗𝑩𝑬 but also on 𝒗𝑪𝑬.
The dependence on 𝑣𝐶𝐸 can be modeled by assigning a finite output resistance:
𝑟𝑜 = (𝑉𝐴 + 𝑉𝐶𝐸 )/𝐼𝐶 ≈ 𝑉𝐴 /𝐼𝐶 (𝑉𝐴 : the Early voltage).
46
Small-Signal Analysis – Early Effect
Early effect: The collector current depends not only on 𝒗𝑩𝑬 but also on 𝒗𝑪𝑬.
The dependence on 𝑣𝐶𝐸 can be modeled by assigning a finite output resistance:
𝑟𝑜 = (𝑉𝐴 + 𝑉𝐶𝐸 )/𝐼𝐶 ≈ 𝑉𝐴 /𝐼𝐶 (𝑉𝐴 : the Early voltage).
47
Small-Signal Analysis – Summary
48
▪
Basic BJT Amplifier Configurations
Three basic configurations
49
Basic BJT Amplifier Configurations
Characterizing amplifiers:
•
𝒗
𝒊𝒊
Input resistance: 𝑹𝒊𝒏 = 𝒊. Together
with the resistance 𝑹𝒔𝒊𝒈 forms a
voltage divider that reduces 𝒗𝒔𝒊𝒈 .
𝑣𝑖 = 𝑣𝑠𝑖𝑔
•
𝑅𝑖𝑛
𝑅𝑖𝑛 + 𝑅𝑠𝑖𝑔
Open circuit voltage gain:
𝑨𝒗𝟎 =
𝒗𝒐
ቤ
𝒗𝒊 𝑹
𝑳 =∞
50
Basic BJT Amplifier Configurations
•
Output resistance: 𝑹𝟎 =
𝒗𝒙
𝒊𝒙
The output voltage can be found from:
The overall voltage gain 𝑮𝒗 :
𝑹𝑳
𝒗𝟎 =
𝑨 𝒗
𝑹𝑳 + 𝑹𝒐 𝒗𝒐 𝒊
𝒗𝒐
𝑹𝒊𝒏
𝑹𝑳
𝑮𝒗 ≡
=
𝑨
𝒗𝒔𝒊𝒈 𝑹𝒊𝒏 + 𝑹𝒔𝒊𝒈 𝒗𝒐 𝑹𝑳 + 𝑹𝒐
51
Basic BJT Amplifiers - CE Amplifier
•
Input resistance: 𝑹𝒊𝒏 = 𝒓𝝅
•
OC voltage gain: 𝑨𝒗𝒐 = −𝒈𝒎 𝑹𝑪 ∥ 𝒓𝒐
•
Output resistance: 𝑹𝒐 = 𝑹𝑪 ∥ 𝒓𝒐
•
Overall voltage gain: 𝑮𝒗 =
𝒗𝒐
𝒗𝒔𝒊𝒈
=−
𝒓𝝅
𝒈
𝒓𝝅 +𝑹𝒔𝒊𝒈 𝒎
𝑹𝑪 ∥ 𝑹𝑳 ∥ 𝒓 𝒐
52
Basic BJT Amplifiers - CE Amplifier
Alternative Gain expression:
•
Voltage gain:
𝐴𝑣 = −𝑔𝑚 𝑅𝐿 ∥ 𝑅𝐶 ∥ 𝑟𝑜 = −𝛼
•
𝑅𝐿 ∥ 𝑅𝐶 ∥ 𝑟𝑜
𝑡𝑜𝑡𝑎𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑖𝑛 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟
= −𝛼
𝑟𝑒
𝑡𝑜𝑡𝑎𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑖𝑛 𝑒𝑚𝑖𝑡𝑡𝑒𝑟
Overall voltage gain:
𝐺𝑣 = −
𝑟𝜋
𝑅𝐿 ∥ 𝑅𝐶 ∥ 𝑟𝑜
𝑡𝑜𝑡𝑎𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑖𝑛 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟
𝑔𝑚 𝑅𝐿 ∥ 𝑅𝐶 ∥ 𝑟𝑜 = −𝛽
= −𝛽
𝑟𝜋 + 𝑅𝑠𝑖𝑔
𝑅𝑠𝑖𝑔 + 𝑟𝜋
𝑡𝑜𝑡𝑎𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑖𝑛 𝑏𝑎𝑠𝑒
Example 16: A CE amplifier utilizes a BJT with 𝛽 = 100 and 𝑉𝐴 = 100𝑉, is biased at
𝐼𝐶 = 1mA and has a collector resistance 𝑅𝐶 = 5𝑘Ω. Find 𝑅𝑖𝑛 , 𝑅𝑜 and 𝐴𝑣𝑜 . If the
amplifier is fed with a signal source having a resistance of 5𝑘Ω and a load resistance
𝑅𝐿 = 5𝑘Ω is connected to the output terminal, find the resulting 𝐴𝑣 and 𝐺𝑣 If 𝑣ො𝜋 is to
be limited to 5 mV, what are the corresponding 𝑣ො𝑠𝑖𝑔 and 𝑣ො𝑜 with the load connected?
53
Basic BJT Amplifiers - CE Amplifier
CE Amplifier with Emitter Resistance:
•
Input resistance:
𝑹𝒊𝒏 = 𝜷 + 𝟏 𝒓𝒆 + 𝑹𝒆
•
OC voltage gain:
𝑨𝒗𝒐
•
𝑹𝑪
= −𝜶
𝒓𝒆 + 𝑹𝒆
Overall voltage gain:
𝑮𝒗 = −
𝑹𝒊𝒏
𝑹𝑪 ∥ 𝑹𝑳
𝜶
𝑹𝒊𝒏 + 𝑹𝒔𝒊𝒈 𝒓𝒆 + 𝑹𝒆
1.
𝑹𝒊𝒏 is increased by 𝟏 + 𝒈𝒎 𝑹𝒆
2.
𝑨𝒗 is decreased by 𝟏 + 𝒈𝒎 𝑹𝒆
54
Basic BJT Amplifiers - CE Amplifier
Example 17: For the CE amplifier specified in Example 16, what value of 𝑅𝑒 is needed to
raise 𝑅𝑖𝑛 to a value four times that of 𝑅𝑠𝑖𝑔 ? With included 𝑅𝑒 , find 𝐴𝑣𝑜 , 𝑅𝑜 and 𝐴𝑣 and
𝐺𝑣 . Also, if 𝑣ො𝜋 is limited to 5 mV, what are the corresponding values of 𝑣ො𝑠𝑖𝑔 and 𝑣ො𝑜 ?
55
Basic BJT Amplifiers - CB Amplifier
•
Input resistance: 𝑅𝑖𝑛 = 𝑟𝑒
•
OC voltage gain: 𝐴𝑣𝑜 = 𝑔𝑚 𝑅𝐶
•
Output resistance: 𝑅𝑜 = 𝑅𝐶
•
Overall voltage gain: 𝐺𝑣 =
𝑣𝑜
𝑣𝑠𝑖𝑔
=
𝑟𝑒
𝑔
𝑟𝑒 +𝑅𝑠𝑖𝑔 𝑚
𝑅𝐶 ∥ 𝑅𝐿
56
Basic BJT Amplifiers - CC Amplifier
The need for voltage buffers: the amplifier has
•
High input resistance.
•
Low output resistance.
57
Basic BJT Amplifiers - CC Amplifier
•
Input resistance: 𝑅𝑖𝑛 = 𝛽 + 1 𝑟𝑒 + 𝑅𝐿
•
Voltage gain:
•
Output resistance: 𝑅𝑜 = 𝑟𝑒
•
Overall voltage gain: 𝐺𝑣 =
𝐴𝑣 =
𝑅𝐿
𝑅𝐿 +𝑟𝑒
𝑣𝑜
𝑣𝑠𝑖𝑔
≈1
=
𝛽+1 𝑅𝐿
𝛽+1 𝑅𝐿 + 𝛽+1 𝑟𝑒 +𝑅𝑠𝑖𝑔
58
Basic BJT Amplifiers - CC Amplifier
Example 18: It is required to design an emitter follower to implement the buffer
amplifier of following figure. Specify the required bias current 𝐼𝐸 and the minimum
value 𝛽 the transistor must have. Determine the maximum allowed value of 𝑣𝑠𝑖𝑔 if 𝑣𝜋 is
to be limited to 5𝑚𝑉 in order to obtain reasonably linear operation. With 𝑣𝑠𝑖𝑔 =
200𝑚𝑉, determine the signal voltage at the output if 𝑅𝐿 is changed to 2𝑘Ω and to
0.5𝑘Ω.
59
Basic BJT Amplifiers - Summary
60
Basic BJT Amplifiers
Example 19: For the following
circuit, let 𝑉𝐶𝐶 = 9V, 𝑅1 =
27𝑘Ω , 𝑅2 = 15𝑘Ω , 𝑅𝐸 =
1.2𝑘Ω, and 𝑅𝐶 = 2.2𝑘Ω. The
transistor has 𝛽 = 100 .
Calculate the DC bias current
𝐼𝐸 . If the amplifier operates
between a source for which
𝑅𝑠𝑖𝑔 = 10𝑘Ω and a load
of 2𝑘Ω. Find the value of 𝑅𝑖𝑛,
the voltage gain 𝑣𝑜/𝑣𝑠𝑖𝑔.
61
Graphical analysis
62
DC Load Line
63
DC Load Line
64
AC Load Line
65
AC Load Line
•
Max swing condition:
𝑰𝑪𝑸
𝑽𝑪𝑪
=
𝑹𝑫𝑪 + 𝑹𝒂𝒄
66
Exercises
Exercise 1: In the following circuit, 𝑣𝑠𝑖𝑔 is a small sine wave signal with zero average.
The transistor β is 100.
a. Find the value of 𝑅𝐸 to establish a dc emitter current of about 0.5 mA.
b. Find 𝑅𝐶 to establish a dc collector voltage of about +5 V.
c. For𝑅𝐿 = 10 𝑘Ω and 𝑟𝑜 = 200𝑘Ω, draw the
small-signal equivalent circuit of the amplifier
and determine its overall voltage gain.
67
Exercises
Exercise 2: Using the topology of following circuit, design an amplifier to operate
between a 10𝑘Ω source and a 2𝑘Ω load with a gain of −8𝑉/𝑉. The power supply
available is 9𝑉. Use an emitter current of approximately 2𝑚𝐴 and a current of about
one-tenth of that in the voltage divider that feeds the base, with the dc voltage at the
base about one-third of the supply. The transistor available has 𝛽 = 100 and 𝑉𝐴 =
100𝑉. Use standard 5% resistor.
68
Exercises
Exercise 3: The following amplifier consists of two identical common-emitter
amplifiers connected in cascade. Observe that the input resistance of the second
stage, 𝑅𝑖𝑛2, constitutes the load resistance of the first stage.
a. For 𝑉𝐶𝐶 = 15𝑉, 𝑅1 = 100𝑘Ω, 𝑅2 = 47𝑘Ω, 𝑅𝐸 = 3.9𝑘Ω, 𝑅𝐶 = 6.8𝑘Ω, and 𝛽 =
100, determine the DC collector current and voltage of each transistor.
b. Draw the small-signal equivalent circuit of the entire amplifier and give the values
of all its components.
c. Find 𝑅𝑖𝑛1 and
𝑣𝑏1
ൗ𝑣𝑠𝑖𝑔 for 𝑅𝑠𝑖𝑔 =
5𝑘Ω.
d. Find 𝑅𝑖𝑛2 and
𝑣𝑏2
Τ𝑣𝑏1
e. For 𝑅𝐿 = 2 𝑘Ω,
find 𝑣𝑜Τ𝑣𝑏2
f. Find the overall
voltage gain 𝑣𝑜ൗ𝑣𝑠𝑖𝑔
69
Exercises
Exercise 4: For the following emitter-follower circuit, the BJT used is specified to have
β values in the range of 40 to 200 (a distressing situation for the circuit designer). For
the two extreme values of β (β = 40 and β = 200), find:
a. 𝐼𝐸 , 𝑉𝐸 , and 𝑉𝐵 .
b. The input resistance 𝑅𝑖𝑛 .
c. The voltage gain 𝑣𝑜ൗ𝑣𝑠𝑖𝑔 .
70
Q&A
71