Margin Gate Three-Row Scan - Electronic Circuits IX & X: Feedback Control and Sampled Conversion Step by Step

A margin-gate scan turns the correction factor into a strict stability decision, showing why the boundary values fail while the interior passes. The pass/fail rows are exact only for the declared correction fraction and ideal linear recurrence; real feedback systems have nonlinear gain, delay, saturation, sensor noise, actuator limits, component tolerance, temperature drift, and stability-margin estimation uncertainty.

The strict stability gate is visible at zero, one, and two correction. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Zero correction fails the strict lower gate

The strict gate is 0 less than c less than 2. Correction 0 fails because it does not move.

0<c<2,\quad c=0\Rightarrow \text{fail}

One correction passes inside the gate

Correction 1 is inside the gate, so the model label is pass.

0<1<2\Rightarrow \text{pass}

Two correction fails the strict upper gate

Correction 2 reaches the upper boundary, so the strict gate fails.

0<c<2,\quad c=2\Rightarrow \text{fail}