Hi Bruce,
The outputs of the TCA9539 should be able to drive the gate of the MOSFET. There are limitations to the PWM range that you can utilize for this device. Looking at the datasheet, I estimated about 24bits will be used to interface with I/O expander following I2C protocol. If you operate in fast-mode at max speed >> 400kHz, you can expect to have a data rate of about (400kbits/sec) / 24bits = 16.667kHz. Note that you will have a range for the PWM signal that can support this. I drew out a diagram to help explain this:
Your PWM cycle is roughly 6% < PWM < 94%. Meaning that at the smallest duty cycle, you can reach about 6% minimum, and at the largest duty cycle, 94%. This is because you will need a very fast switching speed to intermittently switch the MOSFET on and off at those times. TO control the MOSFET, you will have to send an I2C packet of data to either drive or turn off the gate of the MOSFET. Please keep in mind that your overall bandwidth on the I2C bus is also effected by the amount of target devices you currently have on the bus. Each target device brings extra bus capacitance with it, effecting the rise times of your SDA line, which is critical when working at such fast data rates.
Regards,
-Tyler
