Basic Electronics, Chapter 6: Challenge 2 solution (MOSFET losses and the gate)

Formulas: VDS = ID x RDS(on)      P = ID^2 x RDS(on)      temperature rise = P x thermal resistance
          peak gate current = V / Rg      tau = Rg x Ciss      10-90 % rise time = 2.2 x tau
          gate voltage with pull-down = V x Rp / (Rp + Rg)

(a) 12 V motor, 1 A running, 3 A stalled, IRLZ44N, 5 V gate.  RDS(on) hot = 2 x 25 = 50 mohm.
    Running: VDS = 1 x 0.05 = 0.05 V      P = 1^2 x 0.05 = 0.05 W (50 mW)
    Stalled: VDS = 3 x 0.05 = 0.15 V      P = 3^2 x 0.05 = 0.45 W
    Temperature rise when stalled in free air = 0.45 x 62 = 27.9 degrees C   (fine; use a heatsink if the stall lasts long)
    A BJT-style VCE(sat) of 0.9 V at 3 A: P = 0.9 x 3 = 2.7 W, which is 6 times the MOSFET and would need a heatsink.
    (Cold, the MOSFET would be about half of the numbers above.)

(b) Gate drive, 5 V pin, Ciss = 3.3 nF
    Rg = 220 ohm:   peak current = 5 / 220 = 22.7 mA     tau = 220 x 3.3e-9 = 0.726 us     10-90 % = 2.2 x 0.726 = 1.6 us
    Rg = 1 kohm:    peak current = 5 / 1000 = 5.0 mA     tau = 1000 x 3.3e-9 = 3.3 us      10-90 % = 2.2 x 3.3 = 7.3 us
    At 20 kHz the period is 50 us. A 7.3 us edge is about 15 % of the period on EACH edge, so the MOSFET spends a large part of
    every cycle half-on, where it dissipates the most heat, and the effective duty cycle is blurred. With 220 ohm the edge is
    only 3 % of the period. The pin current is the price of speed: 22.7 mA is the limit of what a pin should see.
    (The real edge is a little longer than the RC value because the gate charge also includes the Miller charge.)

(c) Pull-down values
    5 V pin, Rg = 220 ohm, Rp = 10 kohm:
       gate = 5 x 10000 / (10000 + 220) = 4.89 V        wasted current = 5 / 10220 = 0.49 mA
    3.3 V pin, Rg = 220 ohm, Rp = 100 kohm:
       gate = 3.3 x 100000 / (100000 + 220) = 3.29 V    wasted current = 3.3 / 100220 = 0.033 mA = 33 uA
    Which is better? Both keep the gate within 0.1 V of the pin. 10 kohm holds a floating gate more firmly against noise
    and a hand nearby, so it is the usual choice; 100 kohm saves 0.46 mA, which matters on a battery-powered build. Either
    is fine: avoid values below about 2 kohm (they waste current and pull the gate voltage down).

(d) 24 W LED strip on 12 V, AO3400A (RDS(on) about 50 mohm at 2.5 V gate), 3.3 V pin
    Current = P / V = 24 / 12 = 2.0 A
    VDS = 2.0 x 0.05 = 0.10 V (the strip gets 11.9 V)
    P(MOSFET) = 2.0^2 x 0.05 = 0.20 W   (a small SOT-23 part handles this on a few square centimetres of copper;
                                          check the datasheet's thermal figure)

Checklist
  - Read RDS(on) at the gate voltage you really have (3.3 V or 5 V), and allow for it doubling when hot.
  - Size for the stalled or peak current, not just the running current.
  - Rg 100 to 470 ohm; Rp 10 kohm gate to source.
  - Rg sets switching speed: tau = Rg x Ciss.