Associate CET Components 3.5 · Amplifiers 11.x

🔌 Transistor & Amplifier Calculator

Work through the transistor and amplifier math the Associate CET exam tests. Calculate BJT bias currents and voltages, current and voltage gain, and op-amp circuits — each with the formula shown and the answer worked out.

BJT Voltage-Divider Bias

The most common and stable way to bias a transistor. R1/R2 set the base voltage, and the calculator finds the resulting currents and the collector-emitter voltage (the Q-point). Assumes an NPN in active region with VBE ≈ 0.7 V.

VB = VCC·R2/(R1+R2)   VE = VB−VBE   IE = VE/RE   VCE = VCC − ICRC − IERE
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Reading the Q-point: For a good amplifier, VCE should sit near the middle of its range (roughly VCC/2) so the signal can swing both ways without clipping. If VCE is near 0, the transistor is saturated; near VCC, it's cut off.

BJT Current Gain

A bipolar transistor is current-controlled: a small base current produces a much larger collector current. Beta (β) is the ratio; alpha (α) relates collector to emitter current.

β = IC/IB    IE = IC + IB    α = β/(β+1) = IC/IE
µA
mA

Common-Emitter Voltage Gain

An approximate voltage gain for a common-emitter stage. With the emitter resistor fully bypassed by a capacitor, gain is set by RC and the internal emitter resistance r′e. Unbypassed, RE dominates and lowers the gain (but improves stability).

r′e = 26 mV / IE    Av (bypassed) = −RC/r′e    Av (unbypassed) = −RC/RE
mA

Op-Amp Gain

Operational amplifiers set their gain with two external resistors. Pick the configuration; the inverting amp flips signal polarity (negative gain), the non-inverting amp keeps it (gain is always at least 1).

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Exam tip: The inverting amp's gain is −Rf/Rin (note the minus — output is 180° out of phase). The non-inverting amp is 1 + Rf/Rin, so it can never have a gain below 1. A voltage follower (buffer) is just a non-inverting amp with Rf = 0, giving a gain of exactly 1.