Voltage Divider Bias

Voltage Divider Configuration in Biasing Schemes

Introduction to Voltage Divider Configuration

• The lecture focuses on the voltage divider configuration, which is a widely used biasing scheme in electronic circuits.

• The circuit includes resistances R1 and R2 instead of resistance RB, necessitating the use of Thevenin's theorem for analysis.

Understanding Thevenin's Theorem

• The potential at two points in the circuit is equal to VCC, allowing for modifications to simplify calculations.

• In applying Thevenin's theorem, the equivalent circuit consists of a Thevenin resistance (Rth) and a Thevenin voltage (Vth), with load resistance included.

Calculating Equivalent Circuit Parameters

• To find Rth and Vth, the circuit is modified by replacing ground with a negative terminal and VCC with a positive terminal.

• For calculating Rth, all voltage sources are short-circuited; this results in resistors R1 and R2 being connected in parallel.

Deriving Resistance Values

• The formula for calculating Rth is given as R_th = R_1 cdot R_2/R_1 + R_2.

• After determining Rth, Vth can be calculated by finding current through the loop using Kirchhoff’s laws.

Current Calculation and Circuit Analysis

• Current I through the loop is expressed as I = fracV_CCR_1 + R_2, leading to voltage drop across resistor R2.

• Vth can be calculated using V_TH = I cdot R_2, resulting in an expression that incorporates both resistances.

Collector Current and Emitter Bias Configuration

• Analyzing closely reveals that this setup resembles emitter bias configuration but substitutes RB with Rth and VCC with Vth.

• Base current IB is derived from Kirchhoff’s law applied to the input loop: V_TH - I_B cdot R_TH - V_BE - I_E cdot r_E = 0.

Final Expressions for Currents

• Rearranging yields IB as IB = fracV_TH - V_BER_TH + (beta + 1)cdot r_E.

• Collector current IC can then be expressed as IC = beta cdot IB, showing dependence on parameters like beta and resistances involved.

Conditions for Beta Independence

Calculating VCE and Understanding Voltage Divider Configuration

Calculation of VCE

• The equation for calculating the voltage V_CE is derived from the drop across resistance R_C . It involves terms like -V_CE and emitter current I_E , leading to a simplified expression.

• The final expression for V_CE is given by:

[

V_CE = V_CC - I_C(R_C + r_e)

]

This represents the output voltage, where once the base current I_B is known, the collector current can be calculated using the relationship with beta.

• To find I_C , multiply the base current I_B by beta. Once you have this value, it can be substituted back into the equation to determine V_CE .

Advantages of Voltage Divider Configuration

• The voltage divider configuration utilizes resistances R_1 and R_2 , represented as equivalent resistance R_th = (R_1 || R_2) . This setup helps in making collector current ( I_C ) independent of beta.

• A critical condition for biasing schemes states that:

• The base resistance ( R_B ) must be smaller than:

• Beta + 1 times input resistance ( R_I).

• The difference between using parallel combination resistance ( R_th ) versus single resistance ( R_B) is highlighted. Using R_th < min(R_1, R_2), allows flexibility in design without needing excessively small values for individual resistors.