Category: Software

The general idea is a simple light sensor that can cope with typical indoor illumination, brightening and dimming the digits on a clock so that it’s both visible in the daylight and doesn’t light up the room at night.

This circuit produces a voltage that varies more-or-less inversely with the photoresistance R. The “decade resistor” DR acts as a range selector: the output voltage will be 2.5 V when DR = R.

Yesterday I doodled about the voltage-vs-resistance curves and how DR works, showing the equations that spit out V when you know R, which is handy from a circuit-analysis standpoint (if you can say that with a straight face for a two-resistor circuit).

What you want is the equation that spits out R when you know V, because you can actually measure V. Rearranging the equation in the doodle above produces that equation

R = DR * (5 – V) / V

Actually, what you really want is log R, because your sensation of brightness varies logarithmically with the illumination intensity: each doubling of intensity makes the scenery twice as bright. So you could find R, apply a floating-point math package to it, and come up with log R.

There’s a better way.

Stand yesterday’s graph on its ear and flip it side-to-side to get this view of the same data points. It’s plotted with a log scale on the Y axis, because the resistance varies over such a huge range.

The dots represent the values of R produced by the equation above with DR = 1 kΩ. Those are the actual resistance values, at least according to the circuit model.

The midsection of those dots is pretty straight, so the diagonal line second from the bottom is a straight line “curve fit” with intercepts at

(0 V, log 10000)

and

(5 V, log 100)

The y = mx + b equation fitting that line is

log R = (-2/5) * V + 4

where the (-2/5) comes from the slope of the line:

(log 10000 – log 100) / (0 – 5)

and the (+ 4) comes from the intercept at (log 10000), as set by the value of DR. In fact, the intercept is 1+ (log DR), because it’s always a factor of 10 higher than the value of DR.

Now, what’s nice about that is the equation spits out log R directly, with just some multiply-divide-add action.

Changing DR by factors of 10 produces the other lines, so (as before) switching DR gives you a low-budget, wide-dynamic-range output.

DR need not be a power of 10, of course. The dashed line near the middle is DR = 3 kΩ, which puts the more-or-less linear region between about 20 kΩ (fairly dim) and 500 Ω (rather bright). That’s a useful range in my house and it might be close enough for my friend.

The dashed line approximating those points has an intercept at 1 + log 3000 = 4.5, so the overall equation is

log R = (-2/5) * V + 4.5

The approximation gets progressively worse below, say, V = 0.5 and above V = 4.5, so the outline of the algorithm is:

• V < 0.5 = pretty dark: lowest digit intensity
• V between 0.5 and 4.5: puzzle over log R
• V > 4.5 = lots o’ light: max digit intensity

The Arduino ADC produces a 10-bit integer: 0 through 1023. Call that Vb (“V binary”), which you can scale to V like this

V = (5/1024) * Vb

Plugging that into the equation produces

log R = (-2/5) * (5/1024) * Vb + 4.5

log R = (-2/1024) * Vb + 4.5

The useful limits on Vb for the linear approximation are

• V = 0.5 -> Vb = 1024 * 0.5/5 = 102
• V = 4.5 -> Vb = 1024 * 4.5/5 = 922

Checking those limits against the actual formula for R

• Vb = 102 -> log R = 4.3 (instead of 4.43)
• Vb = 922 -> log R = 2.7 (instead of 2.52)

That’s about what you’d expect from the graph: the line is lower than the dots on the dim end (left) and higher on the bright end (right). On the other paw, getting log R without the floating-point math package makes up for that.

Now, given that you’re going to use a table lookup anyway, you don’t need any arithmetic on Vb at all. Shove all the stuff surrounding Vb to the other side of the equation

(log R – 4.5) * (-1024 / 2) = Vb

(4.5 – log R) * 512 = Vb

Precompute the left side for useful values of R, fill in the corresponding bit pattern to get the desired brightness, then index into the table with the measured Vb: shazam, log R -> brightness bits in one step!

If you’re exceedingly lucky, the brightness bits will be more-or-less in a binary sequence, in which case you can just right-shift Vb to get that number of bits and send ’em directly to the LED drivers. No table needed: one shift and you’re done!

So, for example, suppose you want eight brightness levels controlled by three Brightness Bits BB

BB = Vb >> 7

What’s not to like?

Maybe you already knew that and were wondering why it took me so long to get there…

The first bit in an Arduino bit field is the lowest-order bit.

Set up a bit field to hold, oh, say, the data bits from the WWVB radio time code:

struct WWVB_bits_ {
 unsigned char Minute_10:3;
 unsigned char Minute_1:4;
 unsigned char Hour_10:2;
 unsigned char Hour_1:4;
 unsigned char DOY_100:2;
 unsigned char DOY_10:4;
 unsigned char DOY_1:4;
// unsigned char UT1_SIGN:3;
// unsigned char UT1_CORR:4;
// unsigned char Year_10:4;
// unsigned char Year_1:4;
 unsigned char LY:1;
 unsigned char LS:1;
 unsigned char DST57:1;
 unsigned char DST58:1;
};

[Update: Remember, that struct is bass-ackwards. You want the most-significant fields on the bottom, rather than the top, so the bits fill them in properly. This is how I found out that’s true…]

Coerce the bits into an unnatural union with an unsigned long int and create a variable:

union WWVB_code_ {
 uint32_t WWVB_ul;
 struct WWVB_bits_ WWVB_bits;
};

union WWVB_code_ ReceivedBits;

Then set a few bits to find out how the compiler arranges things:

 ReceivedBits.WWVB_bits.DST57 = 1;
 ReceivedBits.WWVB_bits.DST58 = 1;
 ReceivedBits.WWVB_bits.Hour_1 = 9;
 ReceivedBits.WWVB_bits.Minute_1 = 4;

 sprintf(PrintBuffer,"Bit field: %08lX",ReceivedBits.WWVB_ul);
 Serial.println(PrintBuffer);

Which produces this informative line:

Bit field: 03001220

Soooo, rats, the DST bits are on the left and the Minute bits are on the right. That doesn’t tell you how they’re actually laid out in memory, but if you’re doing the interrupt handler in C, then you just stuff the incoming MSB-first bits from the radio directly into the right side of the int and let them slide leftward.

If you count ’em up, you’ll find that the commented-out bits allow the remainder to fit into an unsigned long int, which is all of 32 bits on the Arduino. You can actually use an unsigned long long int to get 64 bits, but it seems Arduino bit fields can’t extend beyond 32 bits.

There are ways around that, particularly seeing as how I’m using a simpleminded interpreter to parse the incoming bits, but I’ll doodle about that later.

Insert the usual caveats about portability and interoperability and maintainability and … well, you know why bits fields are such a bad idea.