Switching Boundary Depth Scans

Ramp Current Limit Boundary Three-Row Scan

An inductor current ramp is voltage times time divided by inductance, so changing the on-time can pass, touch, or exceed the current-rise limit. With 9 V across 3 H, the 1/2, 1, and 3/2 s intervals give rises of 3/2, 3, and 9/2 A against a 3 A limit exactly for the ideal ramp model; real switching adds saturation, winding resistance, switch drops, delay, ripple, heating, current-sense tolerance, and voltage/current/time measurement uncertainty.

The same voltage and inductance can pass, touch, or fail a current-rise limit. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

1/2 s ramp row

Voltage stays 9 V and inductance stays 3 H. Interval 1/2 s gives current rise 3/2 A against a 3 A limit, so margin is 3/2 A.

ΔI=32 A,m=32 A⇒pass\Delta I=\tfrac{3}{2}\ \text{A},\quad m=\tfrac{3}{2}\ \text{A}\Rightarrow\text{pass}
Ramp current-limit boundaryThe interval alone moves the current-limit margin.L 3 HV 9 Vdt 1/2 sIi 0 AdI 3/2 AIf 3/2 A

1 s ramp row

Voltage stays 9 V and inductance stays 3 H. Interval 1 s gives current rise 3 A against a 3 A limit, so margin is 0 A.

ΔI=3 A,m=0 A⇒pass\Delta I=3\ \text{A},\quad m=0\ \text{A}\Rightarrow\text{pass}
Ramp current-limit boundaryThe interval alone moves the current-limit margin.L 3 HV 9 Vdt 1 sIi 0 AdI 3 AIf 3 A

3/2 s ramp row

Voltage stays 9 V and inductance stays 3 H. Interval 3/2 s gives current rise 9/2 A against a 3 A limit, so margin is negative 3/2 A.

ΔI=92 A,m=−32 A⇒fail\Delta I=\tfrac{9}{2}\ \text{A},\quad m=\tfrac{-3}{2}\ \text{A}\Rightarrow\text{fail}
Ramp current-limit boundaryThe interval alone moves the current-limit margin.L 3 HV 9 Vdt 3/2 sIi 0 AdI 9/2 AIf 9/2 A