# Determining which resistors to use in a common-base amplifier

The assignment is to design a common-base amplifier from a supplied schematic, and quite frankly amplifiers are a significant weakness of mine.

Given:

• Small-signal voltage gain A_V≥50 V⁄V
• Input resistance R_in=75Ω
• Peak output voltage swing without distortion ≥2V
• β_F=90
• V_A=800V

Based on my hand calculations I've got:

• g_m=1/75 S
• I_C=346.666 uA
• r_o=2.308 MΩ
• I_B=3.852 uA
• I_E=350.5 uA

But I still have no idea what to pick for R1 and R2. I want to see what the underlying math is.

Good job so far. Going off your calculations, you already have the emitter current. All of this current has to flow through R1 (there's no other DC path) so R1=[V(emitter)-VEE]\I_E. Assuming a 0.7V base-emitter voltage (depends on doping as well as current), you'd have -0.7V at the emitter; 9.3V/351uA=26.5kOhm.

To bias the collector for max output swing, you'd want it at about VCC/2, so it can swing +-VCC/2 without clipping. That gives you 5V, and since you know your collector current, R2=(VCC-5V)/IC =5V/347uA = 14.4kOhm.

As a quick check, A=gm*(R2//R3)=(1/75)S*12.6kOhm=178, which is well over 50.

Hope this helps!

Edit: I missed the series resistance with the input. This is 75 Ohms, and the input resistance to the emitter is also 1/gm= 75 Ohms, meaning you get a 0.5x voltage divider from your source to the emitter voltage. This cuts your total gain in half, so you'd get a gain of 89 or so instead of 178.

• R2 / R3 is NOT 12.6kO. What is going on with that line? Dec 14, 2023 at 22:01
• Also according to equations for common-base amplifiers (electronics-tutorials.ws/amplifier/common-base-amplifier.html), A_V = alpha(R_C/R_E), so the ratio from collector to emitter theoretically ought to be about 51:1. Dec 14, 2023 at 22:30
• @StarSword thanks for bringing the input resistance to my attention; the voltage gain from emitter to collector is actually RC/r'e in the source you described, which is the number I got. RC/RE is true for a different set of assumptions Dec 15, 2023 at 5:54