you just need to combine the serial and parallel forms of
Vbatt - nVled
R = mIled
It's important that there are n LEDs (connected in
series) in each of the m parallel branches of the circuit and
that the LEDs all have the same Vled and Iled. Otherwise, all
bets are off. Figure 2(a) shows four LEDs connected in
such a way that the previous equation does not apply.
Figure 2(b) shows one of several "proper" ways to connect
Brightness control is useful for gadgets that might
be used under different ambient lighting conditions
(outside/inside, night/day, etc.). This feature requires
two resistors — one fixed (Rf) and one variable (Rv).
Rf limits the current when Rv is at its minimum setting —
usually 0 Ω — which allows maximum current to
flow through the LED. The value of Rf is calculated
when Rv = 0:
Vbatt - nVled
Rf = mIled(max)
where Iled(max) is the maximum current you want
through the LED.
Increasing the Rv setting adds resistance to the circuit,
decreasing the current through the LED. When Rv is at its
maximum setting, the minimum amount of current flows
through the LED. The value of Rv is given by:
Figure 2. LED arrays.
"ideal" resistor values.
• Select appropriate "real" resistor values. If the calculations specify a 132.27 Ω resistor, the nearest "real" resistor
values are 130 Ω and 150 Ω (5% tolerance). Of course,
you could select other values based on what you have
• Plug the values of the resistors you selected back
into the calculations to see if they will satisfy the desired
• Run through the calculations using the selected resistor
values at the extremes of tolerance. A 150 Ω resistor with
5% tolerance can range from 142.5 Ω to 157.5 Ω and will
seldom be precisely 150 Ω. Also, calculate the current
draw of the circuit and the necessary power dissipation of
Some folks don't go through any of these steps and
just guess at a value. Most go through the first two steps,
which is usually fine — as long as you don't operate too
close to the LED’s limits, where tolerances can push
you over the edge. By following all four steps, you can
guarantee that your LEDs, at least, are operating safely
and should last a good long time.
Vbatt - nVled
Rv = mI - R led(min) f
where Iled(min) is the minimum current you want through
Multiple Iterations Are a Drag
Calculating the proper resistors for LED circuits is
pretty simple. It takes just a few moments, even when
going through all four design steps. That's no big deal, if
There are four steps to
selecting the proper
current limiting resistor
• Using the desired
operating characteristics and LED specs,
solve the appropriate
equations for the
Figure 3. Brightness control.
Figure 4. Ways to connect six LEDs.