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Choosing Mosfets and mosfet-driver: Correctly done?

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Rewn

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mosfet driver current calculations

I'm new to mosfets and mosfet-drivers and would just like to check if I correctly determined the correct mosfet + driver to use using the correct calculations.
Any criticism/suggestions are welcome. Thx in advance!

Mosfet: FDS6898A https://www.fairchildsemi.com/ds/FD/FDS6898A.pdf
Mosfet H-bridge Driver: MC33883
**broken link removed**

Motor to Run: 2.4 Amps
V(drain-source) = 12V

Some Symbols used:
V(gs) = gate-source voltage
V(ds) = drain-source voltage
V(th) = threshold voltage
g(fs) = Forward Transconductance
R(on) = on resistance
R(ja) = junction to ambient thermal resistance

Calculations:
V(gs) needed to allow 2.4A of current:
V(gs) = V(th)+2.4/g(fs) = 1.5+2.4/47 = 1.55V
I decided to use 4.5V to reduce the on resistance.

Junction Temperature of non-heatsinked mosfet at 50C ambient temperature at 2.4A motor current:
R(on) = .01 Ω [looked at I(d) vs R(on) graph with I=2.4A, V(gs)=4.5V]
Power Dissipated = I^2*R = (2.4*2.4)*.01 = .0576 W
R(ja) [junction-ambient thermal resistance] = 78 C/W.
T(junction) = 50 [ambient temp] + 78*.0576 = 54.49C
Which is way less than max junction temp, 150, so no heatsink required since
only one mosfet in each 2-mosfet surface mount chip will be on at one time.

Current Drawn when turning on Mosfet;
Gate Charge = 17nC [at V(ds) = 12V, V(gs)=4.5]
Q = I*rise-time, I = Q/rise-time
Let's say rise-time = 20ns
Then, I = 17nC/30nS = .567A

Now, For the Mosfet Driver:
Power Dissipated at 125C junction temperature, no heatsink:
R(ja) = 100C/W
T(ambient) = 50C
(125-50) = 100* power(max)
power(max) = .75W

Now this is where I dont know what to do. I know I must calculate the power dissipated in the mosfet driver given I= .567A and R(source for driver) = 22Ω
However, I don't know how to calculate the average power, since this current
is only present for 20ns. Do i then use this average power with the junction
temperature calculation as above to determine if I need a heatsink?

Thx!

Edit: Oh, I probably also have to calculate the power dissipated in the mosfet while turning on. Hmm... And the schematic I am using is the suggested circuit in the h-bridge ic pdf.
 

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