# IES Square law dimming curve.



## JChenault (Mar 24, 2011)

Does anyone know ( or know where I can find ) some information Re standard the IES square law dimmer curve?

I am trying to ( essentially) build a mapping table from various percentage values on a console to the appropriate DMX output values ( Assuming a linear relationship between the DMX value and the output voltage of my dimmer - probably reasonable as these are old old analog dimmers with a DMX to Analog converter box)

Are there any standards out there as to what is done in the industry? Any ideas how I can get smarter on this subject?

Thanks


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## derekleffew (Mar 24, 2011)

Output=Input^2/100:
00=00
10=01
20=04
30=09
40=16
50=25
60=36
70=49
80=64
90=81
100=100


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## JD (Mar 24, 2011)

It also shows you why low-end trim settings are almost an art form if you want to get the right "feel" on the dimmers! 

Human senses and logarithms go hand-in-hand. Same thing in the sound business. Doubling and halving light or sound levels do not produce the perceived outcome unless you have some second reference. (Ex- stage light vs follow spot.) Alone, they are harder to judge.


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## JChenault (Mar 25, 2011)

Thanks for the reply - but there is still something wierd going on.

If I look at the output of DMX values from an expression (And convert back to percentage values) where the channel is set to IES square law, I get the following values:

00 = 00
05 = 05
10 = 15
15 = 22
20 = 28
25 = 33
30 = 37
35 = 41
40 = 44
45 = 48
50 = 52
55 = 55
60 = 59
65 = 63
70 = 67
75 = 72
80 = 77
85 = 82
90 = 88
95 = 94
100=100

My assumption would be that the number of lumens that a 'standard generic' fixture puts out does not vary porporotionally with the voltage applied. ( Of course - that is assuming that my output voltage from my dimmer matches the percentage DMX value. I guess I have to get out my volt meter.


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## derekleffew (Mar 25, 2011)

JChenault said:


> ...My assumption would be that the number of lumens that a 'standard generic' fixture puts out does not vary porporotionally with the voltage applied. ...


The voltage and output of an incandescent lamp are exponentially proportional, expressed by the formula
lumens/LUMENS = (VOLTS/volts)^3.4

See also this post: http://www.controlbooth.com/forums/...tensity-vs-current-etc-sensor.html#post107828 .


JChenault said:


> ...If I look at the output of DMX values from an expression (And convert back to percentage values) where the channel is set to IES square law, I get the following values: ...


The wiki contains a good explanation (written by STEVETERRY, I believe) of profile, as it applies to the console. Profile is only applicable while a channel is moving during a timed fade. To alter the output voltage based on control input, one needs to alter the dimmer curve on the dimmer rack's control module, or via the trim pot(s) on an analog dimmer.

Try taking your settings again on the Expression, this time with a different profile chosen. The result should be exactly the same, if you are typing [CH] x [@] y and then taking a reading.


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## zmb (Mar 26, 2011)

Maybe this stuff about voltage levels and lumen output could be made into a webpage and have a "Tools" tab next to Home, Forum, etc.


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## WooferHound (Mar 29, 2011)

JChenault said:


> I guess I have to get out my volt meter.



I don't think you will get any accurate readings of voltage if you measure a Dimmer Output since it is not varying the voltage at all, it is varying the Duty Cycle. Also a low priced multimeter is only accurate when measuring Sine Waves. A dimmer set to a level of 50% is a lot like a Square Wave


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## JD (Mar 29, 2011)

Voltage reading would be problematic. Also, what is probably more relevant is % of total wattage output. This gets even trickier as there is a gamma curve to current draw on the lamp. (it is not a straight resistance.) To figure that out, you would need to multiply the equivalent RMS voltage against the current draw biased by the gamma curve of the filament. (and, of course, the filament does not react in a liner fashion either!) 

Anyway, the odd way the load reacts is why the dimmer curve is non-liner to begin with. The wished for result is for the light to *appear* to rise in level in some liner fashion as the control is brought up in the same fashion.


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## STEVETERRY (Mar 29, 2011)

WooferHound said:


> I don't think you will get any accurate readings of voltage if you measure a Dimmer Output since it is not varying the voltage at all, it is varying the Duty Cycle. Also a low priced multimeter is only accurate when measuring Sine Waves. A dimmer set to a level of 50% is a lot like a Square Wave


 
This is easily solved by using a true-RMS-responding meter to measure the voltage at the dimmer output.

ST


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## JChenault (Apr 8, 2011)

I've been doing some additional analysis, and things just are not adding up in my head. I hope someone can clarify.

I made a spreadsheet that shows my confusion. 

```
Level   Lumens   Voltage   Volt%    DMX as %    ETC   
0       0        0         0        0           0 
10      100      31        26       66          39    
20      400      47        39       99          72    
30      900      59        49       125         95    
40      1,600    70        58       149         113    
50      2,500    80        67       170         132    
60      3,600    89        74       189         151    
70      4,900    97        81       206         172    
80      6,400    105       88       223         196    
90      8,100    113       94       240         225    
100    10,000    120       100      255         255
```


Level is the percentage I would expect to see on the console.
Lumens is the light output I would expect to see ( assuming a lamp of 10,000 lumens)
Voltage is the voltage needed for that many lumens ( assuming 120 volts and using the Derek's formula of lumens/LUMENS = (VOLTS/volts)^3.4
Volt% is the percentage of the 120 volt line power we need to get to the desired voltage
DMX as % is the computed DMX value ( volt% on a scale of 0 to 255).
ETC is the measured IES Square Law profile from an ETC console.

I would expect the last two columns to be somewhat similar, but they are not at all congruent. Sure there are a lot of assumptions in the model, but I can't figure out whats going on. Any suggestions?


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## derekleffew (Apr 8, 2011)

It looks to me like the ETC console is outputting an S-curve ("slow bottom, fast top"). 

Actually it seems to be the opposite of an S-curve ("fast bottom, slow top"):

Image from http://upload.wikimedia.org/wikipedia/en/2/2a/Dimmer_curves.jpg .

I think we need to get more knowledgeable people, like STEVETERRY or DavidNorth to help with this.

This Avolites doc describes an S-curve: http://www.avolites.com/products/special/fd-dimmer.htm#Dimmer Law Curve


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## DavidNorth (Apr 9, 2011)

Ok, well you caught us. We do not do a true Square Law in our dimming curves and have not since around 1990. In fact, persons running ETC dimming next to any other manufacturers dimming can sometimes spot a difference in light output from similar lamps.

Why do we not do Square Law? We, to be frank, critical lighting designer eyes don't like it. While theoretically Square Law is supposed to give you the desired performance, in reality it does not. Why is this? There are very many reasons and a few have been identified by JD.

It takes some energy to get a lamp lit and then right after that you then only need to vary voltage small incremental amounts to then make larger changes in light output. Near the top of the curve, again, small changes in voltage can create non-proportional outputs in light. All of this is as seen by the human eye, which ultimately was the deciding factor in our implementation. Oh, and the eye is not a perfect responder as well.

So, by the time you add the lamp physics and eye physiology, you get some difference between math and reality. The important point here is that the curve in our dimmers provide what looks to be a linear light increase as processed by the brain.

In almost all cases, this is why we call it Mod Sq Law, but I don't remember what a console set to IES Sq Law may do as we have rarely even used it. The default output on consoles is linear as we rely on the dimmers to apply a curve.

I guess I missed why the OP is trying to map this all out. Is it because he is wanting to get ideal curve performance from the analog dimmers? Note that analog dimmers are suspect to curves set by electrical design, passive component choices and certainly by the previously mentioned trim settings. JD is right....done correctly, a very nice bottom end is a joy on some old dimmers. With resistors, and expecially capacitors, aging [assuming these are old analog dimmers], there is likely a good variance from dimmer to dimmer. Hence the reason LMI went to digital dimming in an industry leading move in the 80s.

Well, you can call me out on any of this that is confusing or you think is wrong. I may not have this all sorted correctly.

You guys are keeping me up late 

David

oh, well, I guess it's not too much of a secret that we don't do strict Square Law as it's been on our public documentation for well over a decade...


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