--- title: "Design CE divider bias (12 V, 2 mA, beta 150)" subject: "Electronics Devices and Circuit" chapter: 2 key: "semester_3/electronics_devices_and_circuit:ce-divider-design-12v-2ma" source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/ce-divider-design-12v-2ma site: BCT Engineering --- # Design CE divider bias (12 V, 2 mA, beta 150) Electronics Devices and Circuit · Chapter 2: The Bipolar Junction Transistor - Asked in: 2078 Kartik, 7 marks; 2070 Ashad, 6+2 marks (asked 2 times) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/ce-divider-design-12v-2ma - Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-2 ## Question Design a voltage divider type dc biased CE amplifier to obtain β independent biasing. Use appropriate guidelines to support your design. Given VCC = 12 V DC, IC = 2mA and β =150. ## Short answer Voltage divider bias: VE = VCC/10 = 1.2 V, VCE = 6 V, I2 = 10 IB. RE = VE/IE ≈ 596 Ω, RC = (12 – 1.2 – 6)/2 mA = 2.4 kΩ. VB = 1.9 V gives R2 ≈ 14.2 kΩ, R1 ≈ 68.9 kΩ. With RE bypassed, Av ≈ –192. ## Answer Design of a voltage divider biased CE amplifier (VCC = 12 V, IC = 2 mA, β = 150). #### Why divider bias is β independent Voltage divider bias is called **β independent** because the divider holds the base voltage almost fixed, so the collector current is set only by the resistors and VBE, not by β. With the divider current I2 ≫ IB (I2 = 10 IB), the base voltage is VB ≈ VCC R2/(R1 + R2), which does not depend on β. Then ```text IE = (VB - VBE)/RE , IC = α IE ≈ IE ``` Neither equation contains β. If β changes (a different transistor or a change in temperature), IB changes but VB stays constant, so IC and the Q-point remain stable. (Exact Thevenin form: IC = β(VTH - 0.7)/(RTH + (β+1)RE); with RTH ≪ (β+1)RE, β cancels.) #### Design guidelines used 1. **Emitter voltage** VE ≈ VCC/10 (large enough for thermal and bias stability, small enough to leave room for the output swing). 2. **Collector-emitter voltage** VCE ≈ VCC/2, so the output can swing equally up and down (Q-point at the centre of the load line). 3. **Divider current** I2 = 10 IB, much greater than IB, so the base voltage is fixed and the bias is independent of β. 4. VB = VE + 0.7 V. #### Design ```text IC = 2 mA IB = IC/β = 2 mA/150 = 13.3 µA IE = IC + IB = 2.013 mA VE = VCC/10 = 1.2 V RE = VE/IE = 1.2/2.013 mA = 596 Ω VCE = VCC/2 = 6 V RC = (VCC - VE - VCE)/IC = (12 - 1.2 - 6)/2 mA = 2.4 kΩ VB = VE + 0.7 = 1.9 V I2 = 10 IB = 133.3 µA R2 = VB/I2 = 1.9/133.3 µA = 14.2 kΩ R1 = (VCC - VB)/(I2 + IB) = 10.1/146.7 µA = 68.9 kΩ ``` Calculated values: R1 ≈ 68.9 kΩ, R2 ≈ 14.2 kΩ, RE ≈ 596 Ω, RC ≈ 2.4 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) ```text re = VT/IE = 25 mV/2.013 mA = 12.4 Ω rπ = β re = 1863 Ω gm = IC/VT = 80 mA/V R1 || R2 = 11.8 kΩ Rin = R1 || R2 || rπ = 1.61 kΩ Av = -gm RC = -80 mA/V × 2.4 kΩ = -192 ``` Ro ≈ RC = 2.4 kΩ. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the bias beta independent? A. IB is large B. RE is zero C. VB is held fixed by the stiff divider so IE = (VB - VBE)/RE D. VCC is large Answer: C. Beta does not appear in IE. (Key point: Beta independence) 2. What is I2? A. 10 IB = 133 uA B. 0 C. IB = 13.3 uA D. IC = 2 mA Answer: A. I2 = 10 x 13.3 uA. (Key point: Divider current) 3. What is RE? A. About 596 ohm B. About 5.96 kohm C. About 2.4 kohm D. About 60 ohm Answer: A. RE = 1.2 V/2.013 mA. (Key point: RE) 4. What is RC? A. 1.2 kohm B. 4.8 kohm C. 2.4 kohm D. 600 ohm Answer: C. RC = (12 - 1.2 - 6)/2 mA = 2.4 kohm. (Key point: RC) ## Close variants set in other exams - [Why divider bias is beta independent; design (24 V)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-divider-design-24v-1p5ma) — Electronics Devices and Circuit, chapter 2, asked 4× ## Related in Electronics Devices and Circuit - [Design divider-bias CE amplifier (24 V, 2 mA, beta 90)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-design-24v-2ma-beta90) — Electronics Devices and Circuit, chapter 2 - [Design beta independent CE amplifier (20 V, 2 mA)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-design-beta-independent-20v-2ma) — Electronics Devices and Circuit, chapter 2, asked 6× - [Design CE amplifier with divider bias (20 V, 10 mA)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-design-divider-20v-10ma) — Electronics Devices and Circuit, chapter 2 - [Design CE voltage divider bias, beta 200](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-divider-bias-design-beta200) — Electronics Devices and Circuit, chapter 2 - [Why divider bias is beta independent; design (IBQ 10 μA)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-divider-design-24v-ib10ua) — Electronics Devices and Circuit, chapter 2 - [Design common base amplifier (24 V, 1 mA, beta 200)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Acb-amplifier-design-24v) — Electronics Devices and Circuit, chapter 2 ## Related in other subjects - [Voltage divider bias, DC load line, Q point (20 V)](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Avoltage-divider-bias-20v) — Basic Electronics Engineering, chapter 3, asked 2× - [Voltage divider bias, DC load line, Q point (15 V)](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Avoltage-divider-bias-15v) — Basic Electronics Engineering, chapter 3, asked 2× - [Voltage-divider bias load line and Q point](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Avoltage-divider-bias-q-point) — Fundamental of Electrical and Electronics Engineering, chapter 5