LED Arrays: One Resistor or Many?

When you have multiple LEDs with a common anode or common cathode, can you use just one current-limiting resistor? Let’s take a look.

One of the most common, if less than thrilling, aspects of electronics design is choosing the right amount of resistance for limiting the current through the ubiquitous little indicators known as LEDs. The procedure is not particularly complicated—we assume a constant voltage drop across the LED and then do a little math to determine the resistance that will give us the desired forward current.
The constant-voltage assumption is completely inconsistent with reality, but we get away with it because generally we don’t mind if the LED current is a little higher or lower than expected.
But the constant-voltage assumption fails us when we are dealing with an array of LEDs integrated into a single package—for example, a seven-segment display. It fails us because it leads to a conundrum: If we assume a constant (and equal) voltage drop for all the LEDs in the device, we can drive the entire display with only one current-limiting resistor. And yet, it seems that everyone decides to use separate resistors for each LED.
Consider the following circuit, which represents a device that has three common-cathode LEDs in one package.



Let’s assume that the forward voltage (V_F) for each LED is 1.6 V. If we apply a 5 V drive signal to each pin, the common-cathode voltage is 3.4 V, and then the current through the resistor is 10.3 mA. Because each LED has the same voltage drop, we assume that they have the same current, so the forward current (I_F) for each LED is 3.4 mA. Done deal—why bother with three resistors?
There are two issues here: First, the voltage drop is not constant. Second, we cannot assume that the three LEDs have exactly the same current–voltage characteristics.
The actual current through the LED is governed by an exponential relationship, such as the following:



Note two things:

• V_F can be considered approximately constant once the LED is in full conduction because even large increases in I_F correspond to small changes in V_F.
• In the region where the slope of the exponential curve is rapidly increasing, small changes in V_F correspond to large changes in I_F.

Now let’s imagine that one of the LEDs has a current–voltage characteristic that is shifted to the left relative to those of the other two.



When voltage is applied, this troublesome LED will enter full conduction at, say, V_F = 1.3 V and, because all the LEDs share a cathode, this one LED will limit the voltage across the other LEDs to 1.3 V. This is a problem because, for the other two LEDs, 1.3 V corresponds to only small amounts of current.
The point here is that you generally don’t want to use only one current-limiting resistor because you can’t ensure that the LEDs will equally share current; furthermore, it is possible that one LED will get much more current than the others.
However, LEDs contained within a single package should exhibit fairly consistent current–voltage characteristics (unless they are intentionally inconsistent, such as with an RGB LED module). Thus, a single current-limiting resistor might provide adequate performance in many applications—but remember to account for the power dissipation! Power is proportional to the square of current, and the current through the single resistor can become quite large if you need, say, eight LEDs all operating at significant brightness.
Apart from the inconveniently high power dissipation with the single-resistor approach, the bottom line is that individual resistors for each LED is the preferred way to drive an LED array.