Once had to assist in curing the murder of MOSFET GateDriver ICs on a 10,000 horsepower speed controller PCB.
The older version had no failures at all. This new PCB had numerous failures, in the field. Were 6+ ICs, but only a few locations had failures.
I "What was changed?" of the programmer/consultant who was asked by management "Can you also make the PCB smaller." (Notice management was involved with engineering.)
One change was to move the PCB somewhat closer to the power buss, that handled 2,000 amps to a number of IGBTs, that switched the 2,000 amps in a PulseWidthModulation behavior.
OK So 2,000 amps is being switched. They would not tell me the switching speed.
But I knew SLOW SWITCHING would linger in the VDD/2 * IDD/2 = 5,000volts/2 * 2,000 amps/2 = 2,500 * 1,000 = 2,500,000 watts dissipation, and no semiconductor device can handle that much power for very long.
So I decided "1 uS switching time" and the customer said "About right."
I already knew there was a problem, because the dI/dT would be huge. So I introduced the concept of
Vinduce (between a long straight wire, and a co-planar wire loop) modeled as
- Vinduce = [MUo * MUr * Area / (2 * pi * Distance)] * dI/dT
and with Area = 10cm * 10cm (4" square region on the PCB ground traces),
Distance = 2cm (between the power buss and the PCB), and 2,000 amps switching
in 1 uSec === 2 Billion amps/second, we have
Vinduce = 2e-7 * (0.1 * 0.1)/0.02 * 2Billion
Vinduce = 2e-7 * 0.01/0.02 * 2e+9
Vinduce = 1e-7 * 2e+9 = 200 volts induced into the Ground.
I suggested they interpose a metal_plate shield, with complaints immediately rising "That is too close to the 5,000 volt power buss"
and I offered "That is why gutta percha is useful."
What does a 10,000 HP PCB look like?
This was the controller for the IGBT gate drives, which has FiberOptic_isolation to various MOSFETs that drove the IGBTs.
The GateDrive ICs for the MOSFET gate were failing because Ground_here was not the same as Ground_there.
The PCB was 6" by 12" (or 15cm by 30cm, if in France).
Notice the weakness of the 3_D (2_D?) model: the current thru a wide copper bus is modeled as a single wire.