I am not sure how to do this analysis but I will give you my thoughts in case they spark input.
115200 baud rate means max switching at 8 micro seconds (maybe not a good assumption). Max gate capacitance is 21.5 pF (I think) resistor used to drain 10k. Assuming this makes a RC circuit my time constant would be 2.15E-07 seconds. I assume that I only need one time constant to reach the Von or Voff. So I am approximately 40 times faster than the period so........ I should be fine????
I am not hooked to the 4.7k or the 10k resistors and can make them smaller if needed.
LarryD:
If you have access to an oscilloscope connect the circuit and look at the waveform.
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I haven't built the circuit just yet but I am going to do that now. I have a logic analyzer.... not as good I know... I can get access to an o-scope. Maybe I will look at that.
If you connect the gate via a small resistor to the arduino switching to 5v, you will have a slew rate....
C* dv/dt = I ie a gate turn-on time of dv/dt = 20mA/22pf => 950v/uS, or about 5nS to 5v - that should be fine. So the gate is fine.
The high/low time of the drain will be very fast - it's got an on resistance of 10 ohms. The worst case quoted is 18nS.
However the output low-high risetime depends on your 10k resistance and the capacitance you're driving. The spec implies a 31nS delay followed by this rc risetime. To obtain 100nS ( safe) you'll need no more than 10pF load - this isn't much. A typical x10 scope probe has about 10pF
I've ignored the gate-drain charge for now .. these sums should be enough.
Conclusion - yes, if you connected the gate directly to the Arduino the gate will be very fast. But the output risetime will be much slower than the fall time with any significant load capacitance.
Suggestion : use a much lower drain resistor - say 1k. Or better still use an active pull-up eg by using a cmos driver and dumping your transistor.
Just to let everyone know how this panned out. I made the circuit and tried it out on my logic analyser and it looked great and then I tried it out on an oscope. The response was slow and never completely reached the voltages I required. I never played around with the resistors as suggested because I decided it would be easier to drop my microcontroller voltage down to the serial voltage.
I think in the future I will be using dedicated shifter ics instead of making my own. There's a reason why they exist.