Understanding the effect of duty cycle on the brightness of LEDs

[JC2000]

TL;DR Summary

If I have understood correctly, the duty cycle of a pulse signal can be used to control the brightness of an LED. I am unsure as to why this happens.

The brightness of an LED is a result of the current passing through it. The current is a function of the voltage across the LED.

The duty cycle represents the percentage of the time period that the signal is in the ON state ( which means that the voltage is at max value as compared to 0 V for the rest of the time period).

If I have understood correctly, it seems that the duty cycle can be increased to make the LED brighter?!
I don't see why this should happen given that at the end of the day the voltage across the LED is constant irrespective of the duty cycle.

The explanation seems to be that the effective voltage is what causes the LED to change brightness (Effective/ Average Voltage = Duty Cycle * Maximum Voltage). However I am unable to see why this should be so given that actually the max voltage is always being applied in reality.

 

[Averagesupernova]

Why do you think max voltage is always applied? Duty cycle implies there is a percentage of time there is NO voltage across the LED. BTW, the current through and the voltage across an LED do NOT have a linear relationship as you seem to imply.

 

[Borek]

Two ways of dimming the LED. One is to lower the voltage, then the current goes down and LED gets dimmer (it is in no way related to the duty cycle, and as @Averagesupernova mentioned, this won't be linear). Second is to always use the same voltage (current will follow) but to flicker the LED (duty cycle, as far as I am aware typically implemented with PWM) on/off so fast you can't see it. Net effect is the light gets dimmer.

 

[DaveE]

First, current as a function of applied voltage is not a very stable function in diodes (because of temperature). Also the light emitted is really related to the charge carriers that cross the junction (i.e. current) more than the voltage. So, it's not really your question, but it is much better, IMO, to think of the current applied through the diode than the voltage. In fact this is how good circuit designers will power an LED. In practice, it is incredibly common for the LED manufacturer to include a series resistor in the package to help do this for you. If you ever see an LED that is advertised with a voltage like 5V, 12V, etc. then you can be sure that they have done this.

The "brightness" you speak of is integrated by the response of your visual system; i.e. total photons collected over some time period (maybe 20msec, or so). The PWM method of controlling brightness relies on this, it will operate at frequencies high enough that you don't notice the on/off flicker. So, you are correct, the instantaneous brightness of the LED is the same when its on. But when averaged with the on/off duty cycle, it will appear to change in brightness.

The PWM approach is easier to implement because it only involves switching, instead of analog control of the LED current. Varying the LED voltage is an even worse method of brightness control, since the I-V relationship is very non-linear and varies with temperature.

 

[JC2000]

Why do you think max voltage is always applied? Duty cycle implies there is a percentage of time there is NO voltage across the LED.

I think only max voltage can be applied since the voltage source can only produce that voltage. The rest of the time there should be no voltage. The only way I can come to terms with the average voltage being produced is to think in terms of power wherein the power is the same if you consider the max voltage for a percentage of the time period or the average for the entire time period (?).

Just realized that a diode won't have linear characteristics!

 

[Averagesupernova]

Average voltage is peak * duty cycle. Forget power for this.

 

[JC2000]

Two ways of dimming the LED. One is to lower the voltage, then the current goes down and LED gets dimmer (it is in no way related to the duty cycle, and as @Averagesupernova mentioned, this won't be linear). Second is to always use the same voltage (current will follow) but to flicker the LED (duty cycle, as far as I am aware typically implemented with PWM) on/off so fast you can't see it. Net effect is the light gets dimmer.

Yes I remember now that the voltage current relationship is not linear for diodes!

Regarding the second method of dimming the LED ...
Why does flickering affect the brightness?

 

[JC2000]

Average voltage is peak * duty cycle. Forget power for this.

I know that if the LED flickers fast enough then it seems like it's on all the time. I am not able to use this information to explain why the brightness seems to change due to this.

 

[Averagesupernova]

I know that if the LED flickers fast enough then it seems like it's on all the time. I am not able to use this information to explain why the brightness seems to change due to this.

I cannot see why. Average current is usually what we are worried about with LEDs as @DaveE has eluded to. But, if you can understand one, why not the other? When you alternately dump cold and hot water into a bucket can you see how the average forms a warm temp? I know people on here hate analogies, flame away. Lol.

 

[JC2000]

The "brightness" you speak of is integrated by the response of your visual system; i.e. total photons collected over some time period (maybe 20msec, or so). The PWM method of controlling brightness relies on this, it will operate at frequencies high enough that you don't notice the on/off flicker. So, you are correct, the instantaneous brightness of the LED is the same when its on. But when averaged with the on/off duty cycle, it will appear to change in brightness.

Since intensity is the number of photons per unit area at a given time.
Would it be correct to conclude that in reality the voltage applied across the LED is always the max voltage. However the "dimness" is due to the fact that a smaller duty cycle would mean fewer photons emitted for the same time period and hence the lack of intensity?!

 

[JC2000]

I cannot see why. Average current is usually what we are worried about with LEDs as @DaveE has eluded to. But, if you can understand one, why not the other? When you alternately dump cold and hot water into a bucket can you see how the average forms a warm temp? I know people on here hate analogies, flame away. Lol.

I think I get it now. I think I needed to revisit the definition of intensity. My understanding now is that fewer photons are emitted for a shorter duty cycle and hence the dimness (?)

 

[Averagesupernova]

I think the actual intensity as you see it is more about perception.
-
The same way we see motion pictures as smooth rather than the choppy still images they actually are. It's about perception.

 

[Averagesupernova]

The off period of the cycle results in an LED that is actually emitting NO photons. A phototransistor hooked to a scope will show it. I've built PWM circuits that carry audio over a light beam. I've seen this.

 

[JC2000]

I think the actual intensity as you see it is more about perception.

But for the same time period, if one duty cycle (the dimmer one) is lesser than another, then doesn't the dimmer one actually emit fewer photons for that time? I get that the flickering is seen as a continuous glow due to persistence of vision.

 

[Averagesupernova]

But for the same time period, if one duty cycle (the dimmer one) is lesser than another, then doesn't the dimmer one actually emit fewer photons for that time? I get that the flickering is seen as a continuous glow due to persistence of vision.

Yes for the period of the signal there are less photons.

 

[Borek]

Why does flickering affect the brightness?

Because the eye integrates and averages over time.

 

[DaveE]

Since intensity is the number of photons per unit area at a given time.
Would it be correct to conclude that in reality the voltage applied across the LED is always the max voltage. However the "dimness" is due to the fact that a smaller duty cycle would mean fewer photons emitted for the same time period and hence the lack of intensity?!

Yes, exactly.

Your question is really more about the response of your visual system, than about LEDs.

 

[russ_watters]

The same way we see motion pictures as smooth rather than the choppy still images they actually are. It's about perception.

er, also dimmer than they actually are --- this example is exactly the issue of the OP.

[for older style projectors]

 

[scottyyyyyyyy]

Why do you think max voltage is always applied? Duty cycle implies there is a percentage of time there is NO voltage across the LED. BTW, the current through and the voltage across an LED do NOT have a linear relationship as you seem to imply.

From what I understood in college electronics is that diodes have a fixed voltage drop across them, meaning regardless of the voltage applied if it’s over the threshold (0.7V or whatever) then it cross in on state and otherwise is off.

 

[Baluncore]

Welcome to PF.
You are correct. PN junctions and LEDs have an activation voltage or energy.
LEDs typically need a voltage of between 1.5 and 4 volts, depending on colour.

The wavelength, λ, of a photon determines the colour of the light emitted.
The energy of a photon is proportional to its frequency, ν.
ν = c / λ ; where c is the speed of light.
Photon energy is, E = h·ν ; where h is the Planck constant.
For energy in electron volts, eV, and wavelength, λ in nm;
E eV = 1239.84 / λ nm .
Which is the band gap voltage step needed, for the electrons to emit that wavelength photon.

So, knowing the colour of a simple LED, you can work out the wavelength.
From that, you can work out the band gap voltage required for the LED to operate.

There will be some thermal broadening, so it will start to emit photons at a slightly lower voltage, and take a slightly higher voltage to emit the maximum number of photons. For higher currents, the internal resistance of the LED will increase the voltage required to drive the current, and it will generate more heat due to; W = I²·R .

 

[DaveE]

From what I understood in college electronics is that diodes have a fixed voltage drop across them, meaning regardless of the voltage applied if it’s over the threshold (0.7V or whatever) then it cross in on state and otherwise is off.

Umm... OK, sort of, mostly. That depends on how closely you look (or care).

PS: I just noticed they screwed up the formatting in the forward biased equation. They meant
$$ I_D~=~I_S(e^{\frac{qV_D}{nkT}}-1) $$

 

[Merlin3189]

As DaveE and AverageSupernova seem to be saying, you've come to the wrong forum here. The physics IMO is relatively simple, but it is the physiology and psychology which you need to understand.

When any light is on it emits light and when it is off it doesn't! Talking of duty cycle just means it is switched on and off cyclicly. The average amount of light emitted is proportional to the time it is on in each cycle. When a light is on continuously, it emits twice as much light as when it is on only half the time. If it is on only one thousandth of the time, it emits one thousandth of the light it would emit if always on, etc.
There are some practical considerations around switching not being instantaneous, and a continuously on light maybe having a higher temperature than one which is not continuously on, etc, but I think these are negligible in the sort of situation you are probably talking about (switching time much shorter than pulse time, operating at low powers and at only slightly above ambient temps.)

The interesting bit comes when that light enters your eye - a very old-fashioned and very slow response detector. How does the brain perceive a flashing light compared with a constant one?
With slow enough flashes - say up to about 10 Hz - it sees a light with the "on" brightness being switched on and off (flashing). So at very low frequencies, varying the duty cycle would not change the perceived brightness, only the duration of the flashes.
By the time you get up to 50 Hz it sees it as a continuously "on" light, with the brightness of a light emitting the same average amount of light continuously. Now duty cycle does change the brightness according to the duty cycle and average light flux. (If the flashes are extremely short and intense, it appears to cause other effects.)
Another caveats is that the light is fixated, not moving across your visual field. As others have mentioned, there is an apparent motion effect that might (I don't know) interact with this integration. My own observation is that I often see a pulsed LED as a row of separate lights, if it moves across my visual field (even when I estimate it at over 100 Hz .)

Since Fechner's law says that perceived brightness has a logarithmic relationship with physical intensity, there is some ambiguity in the term "brightness". I mean physical brightness of the source and leave, what it is seen as, to those who like to deal in nits, Trolands and the myriad other "units" people use for light. (eg. "Trolands are a widely used measure of retinal illuminance in vision science and visual optics, but disagreements exist for the definition and interpretation of this photometric unit." para 1 of the abstract to
Journal of the Optical Society of America A, Vol. 35, Issue 5, pp. 813-816 (2018) )

 

[Tom.G]

By the time you get up to 50 Hz it sees it as a continuously "on" light, with the brightness of a light emitting the same average amount of light continuously.

A minor quibble on this. I have been in and observed buildings with incandescent lamps driven by a 25Hz power source.

Direct line-of-sight indeed appears continuous; however flicker is definitely visible using averted or peripheral vision. It takes a bit of getting used to when the area you are looking at is directly lit and the rest of the room is flickering!

This was observed in an old building in Buffalo, New York that was still using 25Hz power from Niagara Falls for some lighting.

 

[anorlunda]

I love those vestigial applications of 25 Hz from Niagara Falls.

Flicker perception is very individual. I noticed flicker on at CRT at 50 Hz but I can't detect it at 60 Hz. I believe the perception threshold varies considerably.