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Two main sections here with a few interesting points:
Close the switch to turn both LEDs on.....they both come on almost instantly.
Open the switch to turn them both off.
See how the blue trace LED shuts off quickly, but the orange trace curve shows the delay for its LED to fade off.
Do that again and see the kink in the orange curve at 12v .....that is where the Pmos gate bar shuts off.
Both Mosfets are identical, with their VTO set at -3v .......hence the gate bars shut off in both at 15v-3v=12v above zero.
Now look at the gate voltage on the orange Pmos .....approx zero ..... ie 19mV when the switch is closed.
That gate voltage is adjustable by using those two gate resistors as a divider.
See the different resistor settings on the blue Pmos ...they can be set as you wish to achieve delay or current.
Mosfets are better suited for fast gate operation, and if you wish to avoid delays then review your resistors.
Delays in CMOS setup can result in conducting current at the wrong time during crossover....shootthrough.
Notice that instead of putting an initial direct gate voltage of greater than 12v to shut the gate off, I have chosen 5v so as to use the transistor to drive these mosfets as shown (as for control by arduino output etc).
Finally...Note that I have set the blue resistors so that the gate v only drops to a few volts below the VTO threshold point of 12v above zero rather than sending it on a longer journey down to zero as in the orange section when the switch is first closed.
When the gate voltage swings across its threshold (as it normally would rather than being fixed for these demonstrations), then you might want to consider just how you want the swing range to be applied, with delay in mind.
Hopefully those two described sections can help towards making the gate operate as we require.
Suggestion..... Try altering the blue section top gate resistor to get the swing down to about 9v instead of its present 10.8v seen there....that could help in selecting an appropriate initial 5v pulse duration.
(The two sections stem from the same switch here for these demonstrations, but they may interact if you alter a resistor too enthusiastically here....it is a demo for the stated purpose not a proposed design).
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