Basic Electronics 10, Chapter 10: Challenge 1 solution (pins, pull-ups and the ADC)

Formulas: R = (V(pin) - V(LED)) / I          I = Vcc / Rp when a pull-up is pressed          rise time = 2.2 Rp C
          LSB = Vref / 2^N          code = floor(Vin / Vref x 2^N)          divider k = R2 / (R1 + R2)          V(bat) = code x LSB / k

(a) Red LED, V(LED) = 2.1 V, Uno pin at 5 V, target 12 mA
    R = (5 - 2.1) / 0.012 = 2.9 / 0.012 = 241.7 ohm
    Nearest of 220, 270, 330, 390: 220 ohm (21.7 ohm away; 270 is 28.3 away).
    Actual current with 220 ohm:  I = 2.9 / 220 = 13.18 mA     (under the 20 mA recommended per pin)
        (with 270 ohm it would be 10.74 mA, a little dimmer and more conservative: both are acceptable)
    Total current for N LEDs at 13.18 mA each:
        6 LEDs:   6 x 13.18  =  79.1 mA     under 200 mA: OK
        12 LEDs:  12 x 13.18 = 158.2 mA     under 200 mA: OK (and every pin is within its own limit)
        20 LEDs:  20 x 13.18 = 263.6 mA     OVER the 200 mA chip total: not allowed, even though each pin is fine
    So 12 LEDs at once is the largest of the three; use 270 ohm and they total 128.9 mA, or add a driver chip beyond that.

(b) Button on a 3.3 V board, external pull-up 4.7 k
    Current when pressed:    I = 3.3 / 4700 = 0.702 mA
    Rise time with 150 pF:   2.2 x 4700 x 150e-12 = 1.55 us
    Internal pull-up 50 k:   I = 3.3 / 50000 = 66 uA            rise time = 2.2 x 50000 x 150e-12 = 16.5 us
    The internal resistor takes a tenth of the current and is ten times slower; both are fast enough for a button on a short wire, and the
    external 4.7 k is the better choice for a long cable or a noisy place.

(c) LSB of each board and a TMP36 reading
    Uno:   LSB = 5 / 1024 = 4.883 mV
    Pico:  LSB = 3.3 / 4096 = 0.806 mV
    Uno reading 300:   V = 300 x 4.883 mV = 1464.8 mV = 1.465 V       (adding half an LSB for the centre of the step: 1.467 V)
    TMP36:             T = (1.465 - 0.5) x 100 = 96.5 degrees C        (a hot reading: a hand-held soldering iron tip would do it)
    Pico reading for 1.65 V:   code = floor(1.65 / 3.3 x 4096) = 2048

(d) Divider for a 3-cell LiPo with a Pico, R1 = 33 k, R2 = 10 k
    k = 10 / (33 + 10) = 0.2326
    12.6 V:   V(pin) = 12.6 x 0.2326 = 2.930 V       code = floor(2.930 / 3.3 x 4096) = 3637
    11.1 V:   V(pin) = 11.1 x 0.2326 = 2.581 V       code = floor(2.581 / 3.3 x 4096) = 3204
    Source impedance seen by the ADC:  33 k || 10 k = 33 x 10 / 43 = 7.67 k   (under 10 k: acceptable; add the 100 nF at the pin)
    One LSB at the battery:  0.806 mV / 0.2326 = 3.46 mV
    Divider current at 12.6 V:  12.6 / 43 k = 0.29 mA

Expected readings (check by simulation or on the board)
    (a) 220 ohm: LED current 13.2 mA, 2.9 V across the resistor, 2.1 V across the LED
    (b) pressed: pin at 0 V, 0.70 mA drawn from the 3.3 V supply
    (c) Uno at 1.465 V reads 300; Pico at 1.65 V reads 2048
    (d) pin 2.930 V at 12.6 V (meter), code 3637 (Pico read_u16 shows about 58 200 = 3637 x 16)

Wiring checklist
  - Check the LED's polarity (long leg to the resistor side) and the resistor value with the colour code or a meter.
  - For (d), measure the divider output with a meter BEFORE connecting it to the Pico pin: it must be under 3.3 V at the full pack voltage.
  - Add 100 nF from the divider output to ground; use a fuse in the pack lead; connect the pack's negative to the Pico's GND.
  - Never put the full pack voltage on a Pico pin: it is not 5 V tolerant, let alone 12 V tolerant.