Design common base amplifier (24 V, 1 mA, beta 200)

This is a common base amplifier with voltage-divider (β-independent) bias. The base is grounded for ac through CB.

Given: VCC = 24 V, IC = 1 mA, β = 200.

Guidelines

1. VE ≈ VCC/10 for bias stability.
2. VCE ≈ VCC/2 for maximum symmetrical swing.
3. Divider current I2 = 10 IB (≫ IB), so VB is fixed and the bias is independent of β.
4. VB = VE + 0.7 V; a large capacitor CB from the base to ground makes the base an ac ground.

Design

IE = 1.005 mA     IC = α IE = 1 mA     IB = IE/(β+1) = 5 µA
VE = VCC/10 = 2.4 V      RE = VE/IE = 2.39 kΩ
VCE = VCC/2 = 12 V     RC = (VCC - VE - VCE)/IC = (24 - 2.4 - 12)/1 mA = 9.6 kΩ
VB = 3.1 V
I2 = 10 IB = 50 µA
R2 = VB/I2 = 62 kΩ
R1 = (VCC - VB)/(I2 + IB) = 20.9/55 µA = 380 kΩ

Choose R1 ≈ 380 kΩ, R2 ≈ 62 kΩ, RE ≈ 2.39 kΩ, RC ≈ 9.6 kΩ, and a large bypass capacitor CB; C1 and C2 are coupling capacitors.

Small-signal check (ac equivalent: input at the emitter, output at the collector)

re  = VT/IE = 25 mV/1.005 mA = 24.9 Ω
Rin = RE || re = 24.6 Ω      (low, as expected for CB)
Rout ≈ RC = 9.6 kΩ
Av  = RC/re = 9.6 kΩ/24.9 Ω = 386   (no load, non-inverting)

Voltage gain from the ac equivalent circuit

In the T-model, the emitter (input) is driven through the resistance re, and the collector current α ie flows in RC:

vi = -ie re ,    vo = -α ie RC  (output across RC; unloaded)
Av = vo/vi = α RC / re ≈ RC/re = 9.6 kΩ / 24.9 Ω ≈ +386

Answer: R1 ≈ 380 kΩ, R2 ≈ 62 kΩ, RE ≈ 2.39 kΩ, RC = 9.6 kΩ; Av ≈ +386 (in phase), Rin ≈ 25 Ω.