S4-1.1 BJT Biasing & Amplifiers

What this is and why it exists

Before a transistor can amplify anything it must be held still. Biasing is the art of parking a BJT at a chosen DC operating point and keeping it there while temperature, supply voltage and the part-to-part spread of beta all try to move it. Every amplifier you will ever analyse sits on top of a bias network, and the network you choose decides the gain, the output swing and whether the stage survives a hot afternoon.

The vocabulary

• Operating point (Q-point) — the DC collector current and collector-emitter voltage the circuit rests at with no signal applied.
• Bias stability — how little the Q-point moves when temperature or beta changes; measured by stability factors such as S, the sensitivity of collector current to leakage current.
• Voltage-divider bias — two resistors fix the base voltage, an emitter resistor fixes the emitter current; the standard circuit because it makes the Q-point nearly independent of beta.
• Thermal runaway — heat raises collector current, which makes more heat; without a stabilising emitter resistor the loop can destroy the device.
• h-parameters — the small-signal model of the transistor as a two-port: input resistance, forward current gain, and two terms small enough to drop in the approximate analysis.
• Miller's theorem — a resistor or capacitor connected across an amplifying stage behaves like a much larger one at the input; the tool for handling feedback capacitance.

The mental model

A seesaw with a brick on one side. Fixed bias balances the seesaw by placing the brick precisely once — any change in beta and the balance is gone, because collector current is beta times a fixed base current. Voltage-divider bias instead nails the emitter voltage down with a stiff divider and an emitter resistor: if collector current tries to rise, the emitter voltage rises, the base-emitter voltage falls, and the current is pulled back. That self-correction is negative feedback in DC clothing, and it is the same mechanism that defeats thermal runaway.

With the Q-point held, the amplifier configurations are three ways of using one device. Common emitter gives voltage gain and current gain with a phase inversion — the workhorse. Common collector gives no voltage gain but a very low output resistance — the buffer. Common base gives voltage gain with a very low input resistance — the choice at high frequency. The h-parameter analysis of the CE stage is the pattern; the other two are the same bookkeeping with the terminals relabelled.

Frequency response brackets all of this: coupling and bypass capacitors steal gain at low frequency, device and stray capacitances steal it at high frequency — Miller's theorem tells you the base-collector capacitance appears at the input multiplied by the stage gain, which is why the CE stage's bandwidth is its price for gain.

What you should now be able to explain or do

Draw the four bias circuits and rank their stability. Explain, in feedback terms, why the emitter resistor stabilises both bias and temperature behaviour. Analyse a CE stage with approximate h-parameters and state gain, input resistance and output resistance. Say which configuration you would pick as a buffer, and why.

Check yourself