LED Current Sharing Parallel Puzzle

[sleemanj]

This is doing my head in, every time I think I'm just starting to grasp the reasons, it slips through my fingers.

Right, so this video from BigClive about some cool led filament.  You can see, and it's mentioned, that the ends are brighter than the middle.



The diagram that Clive made is this, I've changed the colours and removed the double connections for clarity, the blue in this image is the leds, the yellow is the copper (and the green is the PCB)



Ok, so each LED has one leg on the bottom "bus" and one on the top "bus", progressing from left to right the first led has a short bottom trace and a long top trace, and the last led has a short top trace and a long bottom trace.  The knee-jerk is "yeah, they balance out so all the leds have the same total resistance in series, should be equal brightness assuming matched leds right".  But the  big brightness drop off towards the middle says otherwise.

So we introduce here a simulation Falstad Link




And so far so good, each diode equal current, but this is treating wires as ideal, so let's fix that with a sledgehammer...



and there we go, reducing LED current towards the middle, high current at the ends.

So looking at this for a while and musing, I came to the partial realisations
 
  * The resistor current of course is not the same for all resistors, that's obvious from the get go, the bottom left and top right resistors each carry "4 leds worth" of current, while the top right and bottom left resistors each carry "1 leds worth" of current, and the midde two are between that.
  * So let us attribute "an led worth" as a unit of current
  * The resistors in the rightmost led's current path carry, from left to right, 4 units, 3 units, 2 units and 1 unit of current
  * The resistors in 2nd from the right (next to the rightmost) path carry 4 units, 3 units, 2 units and another 4 units for the top most resistor
  * Since the resistors here are 1 ohm, we can say then that the voltage dropped by each resistor equal it's units of current, so we can total those units to get the total voltage dropped by the resistors in the current path
  * The resistors in the rightmost led therefore drop 10 units of voltage, and the resistors in the led next to it drop 13 units of voltage

And this is about the point where I introduce the forward voltages of diodes and my brain short-circuits.  I feel like I'm so close to an intuitive understanding of this effect, but not quite there, maybe I'm looking at it in the wrong way.

NB: I know it can be "fixed" with this and it, very nearly clicks for me, the higher current paths need more conductivity, the lower current paths need less.

[drola]

You made a mistake at assuming there is such thing as "1 led worth of current". There isn't. If you look at an I-V curve of an LED, you'll see this current can vary wildly for a small change in voltage.

Take a look at Dan Wentworth's site to learn about I-V curves for different diodes: https://sites.google.com/site/dancaulfieldwentworth/services

[Benta]

There are still over two months to April 1st.
Dunno who this BigClive bloke is, but on electronics he's a dud.
Electrics, no idea.

[mcz]

And this is about the point where I introduce the forward voltages of diodes and my brain short-circuits.  I feel like I'm so close to an intuitive understanding of this effect, but not quite there, maybe I'm looking at it in the wrong way.

What exactly seems to be the problem?
Lets just assume the forward voltage is ideal and all LEDs are equal.. and we just ignore the LEDs nonlinearity. That means we subtract the forward voltage from the supply voltage aka just get rid of it in the circuit diagram. And because we don't care about actual values we don't need to subtract really anything here. Now making the LEDs linear means just replacing them with a resistor.
Also we can further simplify the circuit in a way where we mirror it and only look at it from one end to the middle. This gives us the following example:

Simplified version of your circuit

I also didn't bother to change anything from standard values but the effect should be quite clear. Nothing special going on here... or is there?

[tooki]

There are still over two months to April 1st.
Dunno who this BigClive bloke is, but on electronics he's a dud.
Electrics, no idea.

No, no he’s not a dud on either. What makes you think that?

[drola]

Simplified version of your circuit

An edited version of your simplified circuit, such that the ground connects to the bus from the left side to more closely match OP's PCB photo and make left- and right-most LEDs (resistors) have symetric current.

[sleemanj]

Thanks all, yes I guess I see it now and those two other explanations help show how it is analagous to a resistor ladder.

I suppose I was just looking for a "more simply intuitive" way to view the problem.

As for Benta's comment about BigClive, well you are one of today's 10000, allow me to introduce you to BigClive

[Zero999]

There are still over two months to April 1st.
Dunno who this BigClive bloke is, but on electronics he's a dud.
Electrics, no idea.

No, no he’s not a dud on either. What makes you think that?

He should have known why the LEDs at either end are brighter, than those in the middle. It was pretty obvious to me. I don't think Big Clive is an electronics dud. He probably had a brain fade.

I was hoping the OP would recognise it's a resistor ladder network, which is why I withheld fire on this thread.

[Microdoser]

There are still over two months to April 1st.
Dunno who this BigClive bloke is, but on electronics he's a dud.
Electrics, no idea.

No, no he’s not a dud on either. What makes you think that?

He should have known why the LEDs at either end are brighter, than those in the middle. It was pretty obvious to me. I don't think Big Clive is an electronics dud. He probably had a brain fade.

I was hoping the OP would recognise it's a resistor ladder network, which is why I withheld fire on this thread.

Clive has recently been talking about how he has been ill since before Christmas, first with Covid, then with the reaction to a booster jab he had too soon after having Covid. He says he has had a brain fog, and has only just within the last few days reverted to the normal perky Clive.

[Renate]

It was pretty obvious to me.

Well, it wasn't immediately obvious to me that there was a problem. So the first thing I did was cut it down to 3 LEDs and draw it out. Hmm, that's an amusing little puzzle. 3 IR drops vs. 4.