Simple LocoNet Throttle - The ADC

A closer look on the voltage curve at C1

Let
                   U_a(t) := U_U3,4(t)
                   U_r := +5V
                   R := R₁ + xR₂        where 0<=x<=1
                   C := C₁
then the voltage at C1 follows ([1] equation 2.5a):
(1)              U_a(t) = U_r( 1 - exp(-t/RC) )
where U_a(t=0)=0 has been assumed.

We search
                   Δt := t₂ - t₁ = f (x)
where
(2)               U_a(t₁) = U_r ( R₃ /(R₁+xR₂+R₃) ) = U_r ( R₃ / (R+R₃) )
and
(3)               U_a(t₂) = U_r ( R₇ / (R₆+R₇) )
.

With (1) it follows from (2) and (3):
                   1 - exp(-t₁/RC) = R₃ / (R+R₃)
                   1 - exp(-t₂/RC) = R₇ / (R₆+R₇)
or
                   t₁ = RC ln( (R+R₃) / R )
                   t₂ = RC ln( (R₆+R₇) / R₆ )
or
                   Δt = RC( ln( (R₆+R₇) / R₆) - ln( (R+R₃) / R ) )
                   = RC ln( ((R₆+R₇)R) / ((R+R₃)R₆) )

Measuring the ADC

A sample circuit (where R2 has been replaced by fixed value resistors) build shows the following values:

Tabelle 1
R₂ / kOhms (2%)	ADC_RAW	U_a(t₁) / mV
0	70	140
1.0	81	130
2.2	95	120
3.9	113	110
4.7	122	110
8.2	160	100
10	181	95
15	236	90
22	316	85
39	503	80
47	594	75
56	692	75
68	827	75
82	982	70
100 (1%)	1187	70
100 + 4.7 (both 1%)	1240	70

Plotting gives:
[ slnthr0.gif ]

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© 1997 by Martin Pischky /martin@pischky.de)
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