Negative feedback

Negative feedback is feeding part of an amplifier’s output back to its input in the opposing sense, so the fed-back signal subtracts from the input. You give up raw gain and get back predictability, linearity, bandwidth, and insensitivity to device parameters — almost always a winning trade. It is one of the recurring structural patterns of the whole course (the book calls it Pattern 3), and it culminates in the Operational amplifier.

The core idea

A bare transistor amplifier has enormous but untrustworthy gain — it depends on $g_m$, $V_t$, $k_n$, $\beta$, temperature, and the manufacturing process, all of which spread widely. Negative feedback samples the output, scales it, and subtracts it from the input. The amplifier now works to cancel its own error: anything that would make the output drift (a hot day, a high-$\beta$ part) produces a counteracting change at the input. The closed-loop behaviour ends up governed mostly by the stable feedback network (resistors) rather than by the wobbly device.

Concretely, if the raw (“open-loop”) gain is $A$ and a fraction ${\beta }_{fb}$ of the output is subtracted from the input, the closed-loop gain is

$A_{cl}=\frac{A}{1+A{\beta }_{fb}}\underset{A{\beta }_{fb}\gg 1}{\to }\frac{1}{{\beta }_{fb}}$

[Background from general knowledge, not the source PDF: the explicit closed-loop formula $A/(1+A{\beta }_{fb})$; the PDF presents negative feedback qualitatively and through specific circuit examples.] The key feature: when the loop gain $A{\beta }_{fb}$ is large, $A_{cl}\to 1/{\beta }_{fb}$ — set by the feedback network alone, independent of $A$. Trade away the excess (and unreliable) gain to get a precise, robust one.

Where it shows up in this course

Negative feedback is not one circuit — it is a principle that reappears everywhere:

• Source degeneration: an un-bypassed source resistor in a Common-source amplifier feeds drain-current changes back to oppose $v_{gs}$; gain drops to the resistor-ratio value $-R_D/R_S$.
• Emitter degeneration: the BJT counterpart, an un-bypassed emitter resistor.
• Drain-to-gate feedback bias and the BJT collector-to-base scheme: feedback used purely to stabilise the DC operating point (see MOSFET biasing).
• Closed-loop gain: the op-amp result, where the gain is set entirely by a resistor ratio and the amplifier’s own enormous open-loop gain is deliberately swamped.

Every one of these is the same move: sacrifice excess gain to make the circuit depend on stable passives instead of unreliable active-device parameters. Recognising the pattern lets you analyse all of them the same way.