Basic Electronics 11, Chapter 11: Challenge 3 solution (plan a bench toolkit with a budget)

Formulas: meter error = (a / 100) x reading + b x (resolution of the range)          t(r, scope) = 0.35 / BW          t(displayed) = sqrt( t(signal)^2 + t(scope)^2 )

(a) Essentials and extras (budget 120 pounds; prices approximate)
    Essentials:   multimeter 20 + soldering station 28 + solder 8 + braid and flux pen 6 + cutters and strippers 10 + safety glasses 3 + breadboards and jumpers 12 + component assortment 12
                  = 99 pounds       left over: 120 - 99 = 21 pounds
    Best extras for health and safety, within 21:
        Fume extractor fan 14 (smoke is the main health risk of soldering)   -> 99 + 14 = 113
        Tweezers 5 (handling small parts, holding hot leads)                  -> 113 + 5 = 118
    New total: 118 pounds, 2 pounds left over.
    Not bought now: helping hands (10), logic analyser (10), silicone mat (8): useful but they do not fit with the fan, and the fan comes first for safety.
    (Alternatives that also total under 21: helping hands 10 + logic analyser 10 = 20, but that skips the extractor; the safety item wins.)

(b) The next two purchases
    Bench supply 55 + 20 MHz scope 60 = 115 pounds
    At 15 pounds a month:   115 / 15 = 7.67, so 8 months (8 x 15 = 120)
    Buy the supply first: a current limit protects every later experiment, while the scope only measures them; with batteries and a fuse in the meantime
    (Basic Electronics 9), or the 10-pound logic analyser to look at digital signals while saving.

(c) Meter, 2 V range (0.001 V steps), +/-(0.8 % + 3 digits)
    Reading 1.000 V:   error = 0.008 x 1.000 + 3 x 0.001 = 0.008 + 0.003 = 0.011 V      range 0.989 to 1.011 V      1.1 % of the reading
    Reading 0.100 V:   error = 0.008 x 0.100 + 0.003 = 0.0008 + 0.003 = 0.0038 V        range 0.0962 to 0.1038 V    3.8 % of the reading
    The digits dominate small readings, so use the lowest range that does not overflow.

(d) Meter, 20 kohm range (0.01 kohm steps), +/-(1.0 % + 2 digits), reading 4.70 kohm
    error = 0.010 x 4.70 + 2 x 0.01 = 0.047 + 0.020 = 0.067 kohm       so the true value is between 4.633 and 4.767 kohm
    A 5 % resistor labelled 4.7 kohm lies between 4.7 x 0.95 = 4.465 and 4.7 x 1.05 = 4.935 kohm.
    The measured range (4.633 to 4.767 kohm) sits fully inside the tolerance band: the resistor is within tolerance. (It does not prove the value is 4.70: the meter's own uncertainty is
    about 1.4 %, much smaller than the 5 % tolerance, so the meter checks the band, not the third digit.)

(e) 20 MHz oscilloscope
    Scope rise time:   0.35 / 20e6 = 17.5 ns
    Displayed rise time of a 10 ns edge:   sqrt(10^2 + 17.5^2) = sqrt(100 + 306.25) = sqrt(406.25) = 20.2 ns      (the scope, not the circuit, sets what you see)
    Highest square-wave fundamental by the 5-times rule:   20 MHz / 5 = 4 MHz
    So the scope shows a 20 kHz motor PWM or a 1 MHz I2C clock well, and shows a 20 MHz clock only as a rounded wave.

Figures for prices are approximate; check current prices and the specifications on the meter's and scope's own datasheets.