Basic Electronics, Chapter 9: Challenge 2 solution (drivers, servos, steppers and relays)

Formulas: driver loss P = V(drop) x I;   motor share = (V - V(drop)) / V
          servo: pulse = 1.0 ms + angle / 180 x 1.0 ms;  duty = pulse / 20 ms;  angle = (pulse - 1.0 ms) x 180 deg / 1.0 ms
          A4988: Vref = I x 8 x Rs;  DRV8825: Vref = I x 5 x Rs;  steps per rev = full steps x microsteps;  step frequency = rev/s x steps per rev
          relay coil: I = V / R, P = V^2 / R;  switch loss: I^2 R (contacts), V x I (SSR)

(a) Drivers at 1 A on a 6 V supply
    L298N:     motor voltage = 6 - 2.2 = 3.8 V;     driver heat = 2.2 V x 1 A = 2.2 W;      share = 3.8 / 6 = 63 %
    TB6612FNG: motor voltage = 6 - 0.5 = 5.5 V;     driver heat = 0.5 W;                   share = 5.5 / 6 = 92 %
    DRV8833:   motor voltage = 6 - 0.36 = 5.64 V;   driver heat = 0.36 W;                  share = 5.64 / 6 = 94 %
    For a battery robot below about 12 V use a MOSFET driver (TB6612 or DRV8833): the L298N wastes 37 % of the energy as heat and leaves the motor with 3.8 V.
    (The TB6612 is rated 1.2 A continuous: fine at 1 A, but stalling the motor would exceed it; the DRV8833 is 1.5 A RMS.)

(b) Servo
    30 deg:    pulse = 1.0 + 30 / 180 = 1.167 ms           duty = 1.167 / 20 = 5.83 %
    120 deg:   pulse = 1.0 + 120 / 180 = 1.667 ms          duty = 1.667 / 20 = 8.33 %
    1.72 ms:   angle = (1.72 - 1.0) x 180 = 129.6 deg
    Three servos moving: 3 x 0.25 = 0.75 A.       Three servos stalled: 3 x 0.65 = 1.95 A.
    The supply must be separate because 0.75 A to 1.95 A (with sharp spikes) is more than a board's 5 V pin or a USB port can give (about 500 mA), and the spikes
    and the dip in the supply voltage would reset the microcontroller. Use a 5 to 6 V supply (four NiMH cells or a buck converter) with 470 to 1000 uF
    next to the servos, and join only the grounds.

(c) Stepper NEMA 17, 1.2 A per phase
    A4988, Rs = 0.068 ohm:    Vref = 1.2 x 8 x 0.068 = 0.653 V     (check: 0.653 / (8 x 0.068) = 1.20 A)
    DRV8825, Rs = 0.100 ohm:  Vref = 1.2 x 5 x 0.100 = 0.600 V
    1/8 microstepping of a 200-step motor:  200 x 8 = 1600 steps per revolution
    Step frequency at 120 rpm = 2 rev/s x 1600 = 3200 steps per second (a 3.2 kHz pulse train)
    0.9 deg motor at 1/16:  400 full steps per revolution;  0.9 / 16 = 0.05625 deg per microstep (6400 microsteps per revolution)
    (the 1/16 figure for a 1.8 deg motor would be 0.1125 deg)

(d) Relay and SSR
    12 V relay, 400 ohm coil:   I = 12 / 400 = 30 mA       P = 144 / 400 = 0.36 W    (too much for a microcontroller pin: use a transistor and a flyback diode)
    8 A load:  mechanical relay, contacts 0.05 ohm:  P = 8^2 x 0.05 = 3.2 W   (voltage drop 0.4 V)
               triac SSR, 1.2 V drop:                P = 1.2 x 8 = 9.6 W      (needs a heatsink; three times the loss)
    The SSR wins on life, silence and switching speed; the relay wins on heat and on the perfect off state.

Checklist
  - A "continuous" current rating is for the running current: check the stall current too.
  - Servos: separate supply, common ground, a bulk capacitor, signal 50 Hz.
  - Stepper: set Vref with the motor disconnected or at rest, never connect a motor while the supply is on, 100 uF at VMOT.
  - Relays and SSRs: flyback diode on the coil, derate DC inductive contacts, never mains on a breadboard.