ECE 252:Analogue Electronics
Lecture: DC and AC Analysis of PNP BJT Circuits
Voltage Gain Calculation
Introduction to Bipolar Junction Transistors (BJTs)
A Bipolar Junction Transistor (BJT) is a three-terminal semiconductor device used for amplification and switching applications. It has two main types: NPN and PNP. In this lecture, we will focus on PNP transistors in two common configurations:
Common Base (CB) Configuration
Common Emitter (CE) Configuration
These configurations are used in analog circuits such as amplifiers and signal processing systems.
2. Prerequisite Knowledge
Before diving into the DC and AC analysis, you should be familiar with:
a) Semiconductor Basics
PN Junction: Understanding how current flows through a P-N junction is essential.
Doping: How semiconductors are modified with impurities to create P-type and N-type materials.
b) Transistor Operation
Active Region: The region where a BJT can amplify signals.
Cutoff and Saturation Regions: Used for switching applications.
c) Circuit Analysis Basics
Kirchhoff’s Voltage and Current Laws (KVL & KCL): Essential for analyzing circuits.
Ohm’s Law: Used for calculating voltages, currents, and resistances in a circuit.
3. Importance of DC and AC Analysis in BJTs
Analyzing BJTs under DC and AC conditions is crucial for designing stable and efficient circuits.
Why DC Analysis?
Determines the biasing conditions of the transistor.
Ensures the transistor operates in the correct region (Active Region for amplification).
Helps in designing circuits that work under different temperature and voltage variations.
Why AC Analysis?
Evaluates how the transistor responds to small input signals.
Determines gain, input impedance, and output impedance, which are key for amplifier performance.
Helps in designing high-frequency circuits for communication systems.
4. Common Base (CB) and Common Emitter (CE) Configurations
a) Common Base (CB) Configuration
The Base is the common terminal for both input and output.
Input is applied to the Emitter and output is taken from the Collector.
Provides low input impedance and high output impedance.
Mainly used in high-frequency applications.
DC Equivalent Circuit of CB Configuration
Determines the operating point of the transistor.
Capacitors are treated as open circuits.
Resistors and DC sources define the biasing conditions.
AC Equivalent Circuit of CB Configuration
Used to analyze the small-signal response of the transistor.
Capacitors are treated as short circuits.
DC voltage sources are replaced with ground.
b) Common Emitter (CE) Configuration
The Emitter is the common terminal for both input and output.
Input is applied to the Base, and output is taken from the Collector.
Provides moderate input impedance and high gain.
Widely used in audio and RF amplifiers.
DC Equivalent Circuit of CE Configuration
Establishes the DC operating point.
Shows how the transistor is biased to function in the active region.
AC Equivalent Circuit of CE Configuration
Helps in understanding how the circuit amplifies signals.
Shows the transistor’s gain, impedance, and response to AC signals.
5. Biasing in DC Analysis
For a PNP transistor, we must ensure proper biasing to keep the transistor in the active region:
Emitter-Base Junction: Forward biased (Emitter more negative than Base).
Collector-Base Junction: Reverse biased (Collector more positive than Base).
Biasing methods include:
Fixed Bias: Simple but lacks stability.
Voltage Divider Bias: Provides better stability.
Emitter Bias: Helps in temperature stability.
6. Small-Signal Model for AC Analysis
For AC analysis, the transistor is replaced with a small-signal model:
h-parameter model: Uses h_FE (current gain) to describe behavior.
Hybrid-Pi Model: More accurate for high-frequency applications.
Important parameters:
Voltage Gain (Av) = VoutVin\frac{V_{\text{out}}}{V_{\text{in}}}VinVout
Input Impedance (Z_in): Resistance seen by the input source.
Output Impedance (Z_out): Resistance seen by the load.
7. Applications of Common Base and Common Emitter Circuits
Common Base (CB)
Used in high-frequency amplifiers and RF circuits.
Common Emitter (CE)
Used in audio amplifiers, oscillators, and signal processing.
8. Conclusion
DC Analysis is used to set up the transistor’s operating point.
AC Analysis helps in understanding amplification and signal response.
Common Base (CB) is used for high-frequency applications.
Common Emitter (CE) is widely used in amplifiers and signal processing.
9. Further Reading
Sedra & Smith – Microelectronic Circuits
Millman & Grabel – Microelectronics
Analysis and Design of Analog Integrated Circuits by Gray, Hurst, Lewis & Meyer
DC Equivalent of a Common Base PNP BJT Circuit
A DC equivalent circuit is obtained by:
Replacing capacitors with open circuits (since they block DC).
Replacing AC sources with short circuits.
Keeping DC voltage sources and biasing resistors as they are.
For a common base PNP transistor, the base is the common terminal for both input and output signals. The DC equivalent circuit mainly consists of:
A PNP transistor with proper DC biasing.
A current source (representing collector current).
Voltage sources to establish proper emitter-base and collector-base junction biases.
Diagram (DC Equivalent – Common Base PNP)
2. AC Equivalent of a Common Base PNP BJT Circuit
The AC equivalent circuit is obtained by:
Replacing capacitors with short circuits (since they act as short circuits for AC signals).
Replacing DC voltage sources with ground.
Replacing the transistor with its small-signal equivalent model (h-parameter or hybrid-pi model).
In the AC equivalent circuit, the behavior of the transistor is analyzed in terms of small-signal parameters such as input resistance, output resistance, and gain.
Diagram (AC Equivalent – Common Base PNP)
3. DC Equivalent of a Common Emitter PNP BJT Circuit
In a common emitter configuration, the emitter is the common terminal for both input and output.
For the DC equivalent, the capacitors are replaced with open circuits, and the transistor is analyzed in its DC biasing state.
Diagram (DC Equivalent – Common Emitter PNP)
4. AC Equivalent of a Common Emitter PNP BJT Circuit
The AC equivalent circuit replaces the transistor with its small-signal equivalent, and capacitors are treated as short circuits.
Diagram (AC Equivalent – Common Emitter PNP)
Explanation of Terms
DC Equivalent Circuit:
Used to analyze the transistor’s operating point (biasing).
Shows how the transistor behaves with DC voltage and currents.
Ignores capacitors because they block DC.
AC Equivalent Circuit:
Used to analyze signal amplification and response.
Shows how the circuit behaves with AC signals.
Capacitors act as short circuits since they allow AC to pass.
Transistor is replaced with small-signal models.
Common Base Configuration:
The base is the common terminal for input and output.
Has low input impedance and high output impedance.
Used in high-frequency applications.
Common Emitter Configuration:
The emitter is the common terminal.
Provides high gain and is widely used in amplifiers.
Has moderate input impedance and high output impedance.
Additional Explanations and Problem-Solving Examples for PNP BJT Circuits
Now that we have covered the theoretical aspects, let’s apply the knowledge to some practical problems and examples related to DC and AC analysis of PNP BJTs in Common Base (CB) and Common Emitter (CE) configurations.
1. Example: DC Biasing Analysis of a Common Base PNP BJT Circuit
Problem Statement:
Given the following Common Base PNP BJT circuit, determine the DC operating point
Voltage gain ( A_V ): How much amplification is needed?
Power supply ( V_{CC} ): The available DC voltage.
Collector current ( I_C ): Set based on the desired power level.
Impedances: Choose suitable values for input and output matching.
Example Specifications:
Voltage gain ( A_V = -10 ) (10× amplification, inverted signal).
Power supply ( V_{CC} = 12V ).
Collector current ( I_C = 2mA ).
Input impedance ( Z_{in} > 10k\Omega ).
Load resistor ( R_L = 2k\Omega ).
(IE,IC,IB,VBE,VCBI_E, I_C, I_B, V_{BE}, V_{CB}IE,IC,IB,VBE,VCB).
Circuit Parameters:
V_CC = 12V
V_EE = -5V
R_B = 100kΩ
R_C = 2kΩ
R_E = 1kΩ
β\betaβ (current gain) = 50
V_{BE} = 0.7V (PNP transistor assumption)
Step 1: Calculate the Emitter Current IEI_EIE
Using Kirchhoff’s Voltage Law (KVL) around the Emitter-Base Loop:
VEE+IERE+VBE=0V_EE + I_E R_E + V_{BE} = 0VEE+IERE+VBE=0
Substituting values:
−5V+IE(1kΩ)+0.7V=0-5V + I_E (1kΩ) + 0.7V = 0−5V+IE(1kΩ)+0.7V=0 IE=5V−0.7V1kΩ=4.3V1kΩ=4.3mAI_E = \frac{5V - 0.7V}{1kΩ} = \frac{4.3V}{1kΩ} = 4.3mAIE=1kΩ5V−0.7V=1kΩ4.3V=4.3mA
Step 2: Calculate the Collector Current ICI_CIC
Since IC≈IEI_C \approx I_EIC≈IE for large β\betaβ:
IC≈IE=4.3mAI_C \approx I_E = 4.3mAIC≈IE=4.3mA
Step 3: Calculate the Base Current IBI_BIB
IB=ICβ=4.3mA50=0.086mAI_B = \frac{I_C}{\beta} = \frac{4.3mA}{50} = 0.086mAIB=βIC=504.3mA=0.086mA
Step 4: Calculate VCBV_{CB}VCB
Applying Kirchhoff’s Voltage Law in the Collector Circuit:
VCB=VC−VBV_{CB} = V_C - V_BVCB=VC−VB
First, calculate VCV_CVC:
VC=VCC−ICRCV_C = V_{CC} - I_C R_CVC=VCC−ICRC VC=12V−(4.3mA×2kΩ)V_C = 12V - (4.3mA \times 2kΩ)VC=12V−(4.3mA×2kΩ) VC=12V−8.6V=3.4VV_C = 12V - 8.6V = 3.4VVC=12V−8.6V=3.4V
For VBV_BVB, using VB=VE+VBEV_B = V_E + V_{BE}VB=VE+VBE:
VB=(−5V)+(0.7V)=−4.3VV_B = (-5V) + (0.7V) = -4.3VVB=(−5V)+(0.7V)=−4.3V
Thus:
VCB=VC−VB=3.4V−(−4.3V)=7.7VV_{CB} = V_C - V_B = 3.4V - (-4.3V) = 7.7VVCB=VC−VB=3.4V−(−4.3V)=7.7V
Since VCBV_{CB}VCB is positive, the transistor is operating in the active region, confirming the design is correct.
2. Example: AC Gain Calculation of a Common Emitter PNP Amplifier
Problem Statement:
Given a Common Emitter PNP amplifier, determine:
Voltage gain (AVA_VAV)
Input impedance (ZinZ_{in}Zin)
Output impedance (ZoutZ_{out}Zout)
Circuit Parameters:
R_C = 2kΩ
R_E = 500Ω
h_FE (β\betaβ) = 100
Internal resistance of transistor re=25mVIEr_e = \frac{25mV}{I_E}re=IE25mV (thermal voltage approximation)
Step 1: Calculate rer_ere (Small-Signal Emitter Resistance)
Using the thermal voltage approximation:
re=25mVIEr_e = \frac{25mV}{I_E}re=IE25mV
Assume I_E = 1mA:
re=25mV1mA=25Ωr_e = \frac{25mV}{1mA} = 25Ωre=1mA25mV=25Ω
Step 2: Calculate Voltage Gain AVA_VAV
For a Common Emitter Amplifier:
AV=−RCre+REA_V = -\frac{R_C}{r_e + R_E}AV=−re+RERC AV=−2kΩ25Ω+500ΩA_V = -\frac{2kΩ}{25Ω + 500Ω}AV=−25Ω+500Ω2kΩ AV=−2000525=−3.8A_V = -\frac{2000}{525} = -3.8AV=−5252000=−3.8
So, the amplifier has a gain of -3.8, meaning it inverts the signal and amplifies it 3.8 times.
Step 3: Calculate Input Impedance ZinZ_{in}Zin
Zin=(β+1)×(re+RE)Z_{in} = (\beta + 1) \times (r_e + R_E)Zin=(β+1)×(re+RE) Zin=(100+1)×(25Ω+500Ω)Z_{in} = (100 + 1) \times (25Ω + 500Ω)Zin=(100+1)×(25Ω+500Ω) Zin=101×525Ω=53.03kΩZ_{in} = 101 \times 525Ω = 53.03kΩZin=101×525Ω=53.03kΩ
Step 4: Calculate Output Impedance ZoutZ_{out}Zout
For a Common Emitter Amplifier, ZoutZ_{out}Zout is approximately R_C:
Zout≈RC=2kΩZ_{out} \approx R_C = 2kΩZout≈RC=2kΩ
3. Summary of Key Takeaways
Common Base (CB) Circuit
Low input impedance, high output impedance.
Used in high-frequency amplifiers.
Voltage gain is greater than 1.
Common Emitter (CE) Circuit
Moderate input impedance, high gain.
Used in most amplifier circuits.
Inverts the signal (negative gain).
4. Further Exercises
Try solving these problems to strengthen your understanding:
Design a Common Emitter PNP Amplifier with a gain of -10. Choose suitable resistor values.
Modify the first example: What happens to IE,IC,IBI_E, I_C, I_BIE,IC,IB if RER_ERE increases?
For an amplifier with AV=−5A_V = -5AV=−5 and Zin=40kΩZ_{in} = 40kΩZin=40kΩ, determine the values of RCR_CRC and RER_ERE.
5. Conclusion
DC Analysis determines the operating point (Q-point).
AC Analysis helps in gain calculation and impedance matching.
Understanding these concepts is crucial for designing stable transistor amplifiers.
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