Series-Parallel LEDs

This common arrangement of LEDs in circuits has definite advantages, but there are pitfalls, too, of which the designer must be aware.

Ever notice how people will take an escalator, if available, to avoid the steps on the way to the step machine in the gym? Or circle the parking lot in their cars to get a spot close to the front door of the fitness center?

(Source: www.LaughToTears.com)

Electrons seem to behave a lot like people in this regard. Given a choice between two paths, the majority of electrons will chose the path with least resistance. Only the braver souls will elect the more strenuous route. (Although from the point of view of quantum mechanics, all the electrons could be said to traverse every available path.)

I've noticed a growing prevalence to connect LEDs in combination series and parallel strings, such as the example illustrated in Figure 1. This happens to depict a cluster of three parallel chains of four series LEDs, but it could be virtually any series parallel combination. The basic concept is that if the chains are exactly equal, in terms of impedance, the electrons will elect the various paths with equal probability.

Figure 2: Series-parallel LED chain

There's a big benefit to connecting LEDs in this fashion. For any given number of LEDs, the series-parallel configuration will be easier and less expensive to drive. It operates at lower voltages and requires just one current source. The alternative configurations, either using one long chain of LEDs, or independent chains of LEDs each driven by their very own power supply, have the corresponding drawbacks. They will require higher voltages (with its associated higher risk of shock hazards and short circuits), or the expense of multiple current sources. So, that's why the series-parallel concept is finding favor. But, like most things in life, it has a downside.

Now, it's not like this idea hasn't been around for a while. In fact, a similar concept is used very successfully in an application commonly known as a "current mirror." In this circuit, the current flowing in one of its two chains is mirrored in the other. There are many applications for the current mirror, the most widespread being the input stage of an operation amplifier. But there is a key requirement for this concept to work. It relies on a precise matching of the drive transistors. To accomplish this goal, they are normally built on the same die and mounted in close proximity, usually within micrometers.

The relationship between the voltage across a diode and the current through the diode is exponential. Slight differences in the LED's construction or the temperature between parallel LED paths could result in significant differences in their respective currents. Since the LED's light output is a linear function of its current, this difference will result in variations in light output. This is the risk when using the series-parallel approach.

When diodes or LEDs are not manufactured on the same die, the chances of a mismatch between them increase significantly. In a mismatch, a particular voltage across the LEDs could result in significantly different forward currents. Mathematically, the equation of a non-ideal diode has a factor n as shown in Equation 1 that indicates this concept. The factor n varies between 1 and 2 and is a fundamental characteristic of the LED. Figure 3 contains two curves, illustrating the potential difference in forward current for an LED with n=1 versus one with n=2. Granted, this is the maximum possible spread, but it shows that there can be a significant current mismatch between two LEDs operating at the same voltage.

Equation 1: Non-ideal LED current to voltage transfer function

Figure 3: LED Current as a function of forward voltage and n

Where:

q = the charge on an electron

k = Boltzmann's Constant

T = Temperature in degrees K

I_rs = Diode's saturation current (varies with LED)

n = a factor between 1 and 2 that varies from LED to LED

Manufacturers bin the LEDs in flux, color, and voltage bins. By selecting LEDs from a particular voltage bin, the effects can be mitigated, but there are no guarantees. Caveat emptor.