Pre-Lab Design and Calculations

This section provides the essential parameters needed for designing a BJT voltage divider bias circuit. It specifies the type of transistor (NPN BJT, such as BC547), the supply voltage (12V), and the target operating conditions (Q-point with collector current IC of 2mA and collector-emitter voltage VCE of 6V). The parameters define how the circuit will be set up, ensuring that it operates correctly within the desired specifications, with βDC (beta) being the transistor's current gain.

To ensure stability in the BJT circuit design, we calculate the emitter voltage (VE) and emitter resistor (RE). The target emitter voltage is set at approximately 15% of the supply voltage (VCC), which translates to 1.8V in this case. RE is calculated from the desired collector current (IC) and VE. A standard resistor value is chosen for practical compatibility. This step ensures that the BJT operates in the active region by providing sufficient voltage and current levels.

In this step, we calculate the voltage at the collector (VC) by adding the collector-emitter voltage (VCE) with the emitter voltage (VE). This sets the working point of the amplifier. The collector resistor (RC) is calculated next, which is crucial for controlling the amount of current flowing through the collector circuit. Choosing a standard resistor value helps ensure easy assembly and allows for practical circuit-building.
- Chunk Title: Calculating Base Voltage and Resistor Values
- Chunk Text: 4. Calculate VB :
○ VB =VE +VBE =1.64V+0.7V=2.34V.
5. Calculate R1 and R2 (Voltage Divider):
○ Calculate IB : IB =βmin IC =1002mA =20μA.
○ Choose IR2 =10×IB =10×20μA=200μA.
○ R2 =IR2 VB =200μA2.34V =11.7kΩ.
○ Choose Standard Resistor Value for R2 : [Write down chosen standard value].
■ Let's proceed with R2 =12kΩ.
○ R1 =IR2 +IB VCC −VB =200μA+20μA12V−2.34V =220μA9.66V =43.9kΩ.
○ Choose Standard Resistor Value for R1 : [Write down chosen standard value].
■ Let's proceed with R1 =43kΩ.
- Detailed Explanation: Here, we calculate the base voltage (VB), which is crucial for setting the base current (IB) that controls the overall operation of the transistor. To achieve desired stability, we also design a voltage divider (using resistors R1 and R2) for biasing. The ratio of the resistors determines how much current flows into the base and ensures that it isn't overly dependent on changes in β (the current gain). Choosing values based on initial calculations ensures practical implementation.
- Chunk Title: Summary of Designed Resistor Values
- Chunk Text: Summary of Designed Resistor Values (for BJT Voltage Divider Bias):
● R1 =[ChosenR1 Value]
● R2 =[ChosenR2 Value]
● RC =[ChosenRC Value]
● RE =[ChosenRE Value]
- Detailed Explanation: This section summarizes all the resistor values chosen for the circuit. These selections are the culmination of previous calculations and ensure that the circuit meets the desired specifications. Summarizing these values is important for implementation and checking the design against theoretical expectations.
- Chunk Title: Theoretical Q-point Calculation
- Chunk Text: Theoretical Q-point (using chosen standard values and Exact Analysis for precision):
● Using R1 =43kΩ, R2 =12kΩ, RC =2.2kΩ, RE =820Ω, βDC =100, VBE =0.7V, VCC =12V.
● RTH =R1 +R2 R1 R2 =43k+12k43k×12k =55516 kΩ≈9.38kΩ.
● VTH =VCC ×R1 +R2 R2 =12V×55k12k ≈2.618V.
● IB =RTH +(βDC +1)RE VTH −VBE =9.38kΩ+(101×820Ω)2.618V−0.7V =9.38kΩ+83.22kΩ
1.918V =92.6kΩ1.918V ≈20.71μA.
● IC =βDC IB =100×20.71μA=2.071mA.
- Detailed Explanation: Here, the theoretical Q-point is calculated using the previously designed resistor values. RTH (Thevenin resistance) and VTH (Thevenin voltage) are determined to understand the behavior of the voltage divider bias circuit. The analysis continues to calculate base current (IB) and collector current (IC), crucial for realizing the expected performance of the amplifier circuit.
- Chunk Title: Theoretical Q-point Results
- Chunk Text: Calculated Theoretical Q-point for Voltage Divider Bias:
● IC =[2.071mA]
● VCE =[5.7288V]
- Detailed Explanation: This is where we conclude the calculations with the results for the theoretical Q-point. The collector current (IC) and the collector-emitter voltage (VCE) are provided. These results are critical as they will be compared to the actual measurements taken during the experiment to evaluate the performance and predictability of the designed circuit.
- Chunk Title: BJT Fixed Bias Design Overview
- Chunk Text: Design Steps:
1. Calculate IB :
○ IB =βDC IC =1002mA =20μA.
2. Calculate RB :
○ RB =IB VCC −VBE =20μA12V−0.7V =20μA11.3V =565kΩ.
- Detailed Explanation: In the design of a fixed bias circuit, the first step is to calculate the base current (IB) based on the specified collector current (IC) and the transistor’s current gain (βDC). The second step calculates the base resistor (RB), which manages how much current enters the base. It is essential to ensure that this biasing method functions correctly and to determine the appropriate resistance value needed for stability.
- Chunk Title: Fixed Bias Circuit Resistor Values
- Chunk Text: Summary of Designed Resistor Values (for BJT Fixed Bias):
● RB =[ChosenRB Value]
● RC =[ChosenRC Value]
Theoretical Q-point for Fixed Bias (using chosen standard values):
● Using RB =560kΩ, RC =3kΩ, βDC =100, VBE =0.7V, VCC =12V.
- Detailed Explanation: This segment summarizes the existing calculations and values used for the fixed bias design. It reflects the importance of maintaining thorough records of selected resistor values as they directly influence the operational characteristics of the bias circuit. Choosing appropriate component values ensures that the circuit performs as intended, which is crucial for reliable amplifier operation.
- Chunk Title: Fixed Bias Theoretical Q-point Calculation
- Chunk Text: ● IB =RB VCC −VBE =560kΩ12V−0.7V =560kΩ11.3V ≈20.18μA.
● IC =βDC IB =100×20.18μA=2.018mA.
- Detailed Explanation: This segment continues the calculations for the theoretical Q-point of the fixed bias design. Here, the calculated base current (IB) is used to find the collector current (IC) based on the gain parameter (βDC). This step is essential for understanding the operational capability of the transistor under biasing conditions, allowing for a deeper exploration of expected performance versus actual performance during practical implementation.
- Chunk Title: BJT Fixed Bias Q-point Results
- Chunk Text: Calculated Theoretical Q-point for Fixed Bias:
● IC =[2.018mA]
● VCE =[5.946V]
- Detailed Explanation: Now we see the calculated theoretical Q-point for the fixed bias circuit, including values for IC and VCE. This data serves as the expected performance benchmark against which you will compare actual measurements taken during the experiment. It is critical for determining how closely the design matches reality and identifying potential issues in the biasing configuration.
- Chunk Title: JFET Self-Bias Design Overview
- Chunk Text: Design Steps:
1. Target ID =1mA.
2. Calculate VGS using Shockley's Equation:
○ VGS =VP (1−IDSS ID )
○ VGS =−1V(1−2mA1mA )=−1V(1−0.5 )
- Detailed Explanation: This section marks the beginning of the design for the JFET self-bias circuit. The design steps entail selecting a target drain current (ID) and then calculating the gate-source voltage (VGS) using Shockley's Equation. This calculation is necessary because the VGS value directly affects the operation of the JFET and determines the stability and bias conditions for successful amplification.
- Chunk Title: Calculating RS and Drain Resistor Values
- Chunk Text: 3. Calculate RS :
○ RS =−ID VGS =−1mA−0.293V =293Ω.
○ Choose Standard Resistor Value for RS : [Write down chosen standard value, e.g., 270Ω or 330Ω].
■ Let's proceed with RS =270Ω.
- Detailed Explanation: In this segment, we calculate the source resistor (RS), which is fundamental for self-biasing the JFET. This resistor helps set the operating point of the JFET by determining the source voltage, which in turn affects the gate-source voltage (VGS) and the drain current (ID). Selecting a standard value ensures the manufactured component fits the design without complications.
- Chunk Title: Calculating Drain Resistor Values
- Chunk Text: 4. Calculate RD :
○ Aim for VD ≈VDD /2=15V/2=7.5V.
○ RD =ID VDD −VD =1.066mA15V−7.5V =1.066mA7.5V ≈7.03kΩ.
○ Choose Standard Resistor Value for RD : [Write down chosen standard value, e.g., 6.8kΩ].
■ Let's proceed with RD =6.8kΩ.
- Detailed Explanation: This part focuses on calculating the drain resistor (RD), which is critical for determining the drain voltage (VD). By choosing an RD value that positions VD around half the supply voltage, it allows for maximum signal swing without distortion. Ensuring standard resistor values helps in practical applications of the design, avoiding discrepancies during construction.