- 2073 Chaitra · 3+5 marks
Why divider bias is beta independent; design (IBQ 10 μA)
Short answer
Divider bias fixes VB, so IE = (VB-0.7)/RE is independent of β. Design: IC=1 mA, VE=2.4 V, RE≈2.38 kΩ, VCE=12 V, RC≈9.6 kΩ, R1≈190 kΩ, R2≈31 kΩ; with bypassed RE, Av=-384, Rin≈2.26 kΩ.
Why voltage divider biasing is called β independent? Design CE amplifier using β independent dc biasing method with appropriate guideline. Given: Vcc = 24 V, IBQ = 10μA and β = 100
Why divider bias is β independent
Voltage divider bias is called β independent because the divider (with I2 ≫ IB) fixes the base voltage VB = VCC R2/(R1+R2) regardless of β. Then IE = (VB - 0.7)/RE and IC ≈ IE contain no β, so a change in β (or temperature) does not move the Q-point.
Design (VCC = 24 V, IBQ = 10 µA, β = 100)
Here IC = β IBQ = 1 mA.
Design guidelines used:
- Emitter voltage VE ≈ VCC/10 (large enough for thermal and bias stability, small enough to leave room for the output swing).
- Collector-emitter voltage VCE ≈ VCC/2, so the output can swing equally up and down (Q-point at the centre of the load line).
- Divider current I2 = 10 IB, much greater than IB, so the base voltage is fixed and the bias is independent of β.
- VB = VE + 0.7 V.
Calculations
IC = 1 mA IB = IC/β = 1 mA/100 = 10 µA
IE = IC + IB = 1.01 mA
VE = VCC/10 = 2.4 V RE = VE/IE = 2.4/1.01 mA = 2.38 kΩ
VCE = VCC/2 = 12 V
RC = (VCC - VE - VCE)/IC = (24 - 2.4 - 12)/1 mA = 9.6 kΩ
VB = VE + 0.7 = 3.1 V
I2 = 10 IB = 100 µA
R2 = VB/I2 = 3.1/100 µA = 31 kΩ
R1 = (VCC - VB)/(I2 + IB) = 20.9/110 µA = 190 kΩ
Calculated values: R1 ≈ 190 kΩ, R2 ≈ 31 kΩ, RE ≈ 2.38 kΩ, RC ≈ 9.6 kΩ (in practice, use the nearest standard resistor values). The emitter resistor RE is bypassed by a large capacitor CE; C1 and C2 are the coupling capacitors.
Check and small-signal results (RE bypassed)
re = VT/IE = 25 mV/1.01 mA = 24.8 Ω
rπ = β re = 2475 Ω gm = IC/VT = 40 mA/V
R1 || R2 = 26.7 kΩ
Rin = R1 || R2 || rπ = 2.26 kΩ
Av = -gm RC = -40 mA/V × 9.6 kΩ = -384
Ro ≈ RC = 9.6 kΩ.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Design divider-bias CE amplifier (24 V, 2 mA, beta 90) · Electronics Devices and Circuit, chapter 2
- Why divider bias is beta independent; design (24 V) · Electronics Devices and Circuit, chapter 2 · asked 4×
- Design CE divider bias (12 V, 2 mA, beta 150) · Electronics Devices and Circuit, chapter 2 · asked 4×
- Design CE amplifier with divider bias (20 V, 10 mA) · Electronics Devices and Circuit, chapter 2
- Design CE voltage divider bias, beta 200 · Electronics Devices and Circuit, chapter 2
- Design beta independent CE amplifier (20 V, 2 mA) · Electronics Devices and Circuit, chapter 2 · asked 6×
- Voltage divider bias, DC load line, Q point (20 V) · Basic Electronics Engineering, chapter 3 · asked 2×
- Voltage divider bias, DC load line, Q point (15 V) · Basic Electronics Engineering, chapter 3 · asked 2×
- Voltage-divider bias load line and Q point · Fundamental of Electrical and Electronics Engineering, chapter 5