Measuring Photoresistor Voltage vs Resistance

Cadmium sulfide photoresistor
Cadmium sulfide photoresistor

A friend wants a digital clock that’s dim when the house lights are low; standard clocks aren’t nearly dim enough. I know how she feels, having added a primary-red filter in front of a blue vacuum-fluorescent clock display to get rid of those garish digits in the middle of the night.

This job calls for a photosensor of some kind, as you can’t figure it out by time alone.

After a brief struggle, the parts heap disgorged a 1-inch diameter CdS (cadmium sulfide) photoresistor with a dark resistance over 500 kΩ and a full-sunlight resistance around 50 Ω. Ordinary room light, at least around here, is in the 1-10 kΩ range, more or less, kinda sorta. Down the Basement Laboratory, it’s tens of kΩ.

Photoresistor circuit and equation
Photoresistor circuit and equation

The canonical sensing circuit is a simple voltage divider, with the photoresistor either on the top or the bottom. Putting it on the top means the voltage increases as the light gets brighter, which has a lot to recommend it.

The resistance varies more or less linearly with the light intensity, to the extent that you can make a very nice linearly variable isolated resistor by bottling up an LED (which has linear intensity with current) with a CdS photoresistor in a light-tight enclosure.

Anyhow, although the resistance R varies linearly, having the R in the denominator means that the voltage V varies inversely. Worse, because the value of R spans about four decades, there’s a serious range & resolution problem.

This graph of V against log R shows the situation.

Output voltage vs log resistance
Output voltage vs log resistance

The dots between R=10 Ω and R=1 kΩ are what the circuit spits out, with the “decade resistor” DR = 100 Ω and R values chosen for nice dot spacing. The long tail beyond 1 kΩ shows that for R greater than 1 kΩ, V doesn’t change by very much at all. Ditto for R less than 20 Ω or so, which is beyond the limit for this photocell.

The straight line through those points is an eyeballometric curve fit to the range from about 20 to 700 and (most crucially) passing through (10 Ω,5 V) and (1000 Ω,0 V). The equation for that line is the usual y = mx + b, albeit with (log R) where you’d expect x. The equation in the lower-left corner is pretty  close to what you want, with D = log DR

V = (5/2) * ((1+D) – log R)

Running the photosensor circuit with DR = 1 kΩ would produce an identical series of dots snuggled up along the second line as R varies from 100 Ω to 10 kΩ. Each factor-of-10 change in DR handles another chunk of R’s range, with identical output voltages: when the voltage gets above about 4.5 or below 0.5, just switch to the next value of DR and continue merrily along.

So that’s a low-budget (if you have cheap relays, like MOSFET analog switches), high-dynamic-range (if you have a good buffer amplifier) light sensor.

More on how to turn this into a brightness control tomorrow…

Memo to Self: Can we correlate a digital camera’s exposure at a known ISO with the cell resistance, so I can get some remote light level values?

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