Here is the proper way to select a resistor to match your decoders function output voltage and the lamps selected or supplied by the locomotive Mfg.
Before You Start
Find a nice clean area to work on, one with good lighting. One that you can lay out parts as you remove them and not get lost. You will also need a few basic tools and items. Small flat and phillips blade screwdrivers. Tweezers and and a hobby knife are handy. A small pair of wire cutters and a good pair of wire stripper. Read good as in a quality pair that is sized for the small wires. A good soldering iron around 25-35 watts, a temperature controlled one is nice. Good quality rosin core solder of about 1/16 inch diameter or smaller. Heat shrink tubing of assorted sizes around 1/16 inch diameter. Some tape both electrical and double sided foam tape come in handy. A magnifier or pair of loops really helps. And all the paper work that came with both the decoder and the loco. If you did not get any, talk with your dealer and/or manufacturer and ask where it is at. These are the normal basics of any decoder install you might do. But to properly figure the function voltage and lamp ratings you will also need to add a typical Multi-Meter and some basic understanding of Ohm's law. The Multi-Meter does not have to be a expensive one, a very simple basic meter will do, as long as it can measure voltage, ohms, and current. The basics of Ohm's Law, I hope to supply you with here.
Ohm's Law is actually very simple to understand and use. And is based on the fact in a DC circuit, 1 volt across a 1 Ohm resistor will cause 1 amp of current to pass through the resistor, at 1 Watt of power. Based on this Law, any given Voltage, Resistance, Current, or Wattage can be found by knowing any 2 of the 4 factors. These factors are known as: E = Volts I = Current R = Resistance P = Watts.
To the right is what is known as a Ohm's Law Wheel. This should help you understand the above statements and come in handy to help figure out how to use Ohm's Law. Just right click on it and download to print out your own copy.
What we are going to be concerned with here is only finding the value in Ohms and Watts to use so that with the lamps used on the decoders function outputs will receive the proper voltage for the amount of current they are designed to draw. But once you learn a little about Ohm's Law, you will find other ways to apply it to your model railroad.
Ready to start
Now we get to put the Multi-Meter and the Ohm's Law wheel to some practical use. As stated above, we need to know a couple things to find the answer of how many Ohm's does the resistor need to be, and how many Watts will the resistor have to handle. Both form the common rating of a typical resistor. We will need to know what the output voltage of our decoders functions is. And what is the rating of the lamp we are going to use, voltage and current draw. You may find these in your manuals, or you may have to find them yourself. Typical voltages found on decoder function outputs will be something like Nscale track voltage will equal a function output voltage of approx. 10.91 volts, HO track voltage will be something like 12.60 volts on the function outputs. Bulbs will be rated something like 12-14 volts at 50 mA. 3 volt at 50 mA, 1.5 volts at 30 mA, 1.5 volts at 15 mA. LED's will be in the range of 2 volts at 15 mA, etc. We could easily use these factors/rating as a guide to guess what value of resistor to use. But it is not hard at all to find the actual factors and apply Ohm's Law to get the proper values the first time around.
Finding the Required Values
The first thing we will find is the output voltage of the decoders function. This very easy, just measure the voltage with you Multi-Meter between the function output wire, and the decoders Blue function common. Note: The Blue function common is a + Common. And the decoders function outputs are actually current sinks. In other words the function Blue common is the voltage source, and the functions output are the actual ground to complete the circuit.
All this means is you will set your Multi-Meter to read DC volts, put the Red or + probe on the Blue Common wire, and the Black or - probe on the function output wire, and read the voltage with the function turned on. This is easiest to do with just the decoders Red and Black leads connected to the rails or booster output. But can be done with it already installed, just remove the shell. Be careful of the wires that nothing gets shorted, and watch where the probe tips touch. This voltage will very depending on the actual digital voltage across your rails. And will very from one decoder Mfg. to another. But as a rule will usually be the same from decoder Mfg. between different decoder models. You should find that the actual function output voltage will be from 1.4 to 2.5 volts lower then the actual digital voltage across the rails.
If you followed the above correctly, you will now know one of the required factors, the actual function voltage output in DC volts. Make a note of this voltage.
As Ex: on my layout using a Digitrax Chief with the DCS100 output set to Nscale track voltage. The actual digital track voltage is 12.41 volts, and the function output on a Digitrax decoder is 10.36 volts DC. With the DCS100 set to HO track voltage the Digital voltage is 14.64 volts and the function output is 12.69 volts DC.
Now we need to find out a little about the bulbs we are going to use.
Here we need to know the voltage and current draw of the bulb. If you purchased
the bulbs just for this install, you more then likely know what these are
from the Mfg.. specs. But if these were already installed in the
locomotive, you might not be sure on this. Also note, the actual current
draw of any bulb will very some from specs and Mfg. So it is always a good
idea to find out what you really have. If you are going to use a bulb with
a voltage rating of less then 12-14 volts, then we should check the current
draw at it's rated voltage. This is another simple thing to do. All we
need is a voltage source to power the bulb at it's rated voltage. As Ex:
If the bulb is rated at 1.5 volts, all you need is a good flashlight battery
such as a typical D cell or C cell. These are rated at 1.5 volts. If the
bulbs are 3 volts, then two of the cell type batteries in series will give
us the required 3 volts.
Now you have the voltage and the proper source, just set your Multi-Meter to read current. And place in series with the bulb. That is connect one lead of the bulb to the battery/s - end, the other lead of the bulb to the Red or + meter probe, and the Black or - meter probe to the battery/s + end, now read the current the bulb is drawing.
If you followed the above correctly, you will now know the second factor, the actual current the bulb draws at it's rated voltage. Make a note of the bulbs voltage and actual current draw.
Putting It All To Use
Now we know the actual function voltage, the bulbs rated voltage, and the bulbs actual current draw at it's rated voltage. What we want to do next is use part of Ohm's Law, remember that from above, to find the value and wattage need for a resistor. We know the function voltage and bulb voltage, so we know how many volts need to be across the resistor. This is because the resistor and the bulb will be in series. And the voltage across the resistor will be that of the function voltage minus the bulbs voltage. Thus using the factor of E [voltage across a resistor] this would be written as E = Function voltage - Bulb voltage. And using the factor of I [current through the resistor] this would be written as I = bulbs current draw. You might ask why is this. Because in a series circuit, current will always be the same between the bulb and the resistor. But the voltage will have to be shared with the bulbs voltage, or the voltage across the resistor will have to equal the source voltage minus the bulb voltage.
So lets use what we have to figure it out. The Ohm's Law formula we are going to use is R=E/I. Or the resistance required will equal the function voltage minus the bulbs voltage, then divided the answer by the current draw of the bulb. Written as R = Resistor value in Ohms. E = Function Voltage - Bulb Voltage. I = Current drawn by Bulb.
Using the 12.69 voltage on the function output of my Digirax decoders with the track voltage set for HO. If I want to use a 1.5 volt bulb with a current draw of 25 mA. This would be R=E/I, or 12.69-1.5=11.19 volts. Thus E = 11.19 volts DC, and I = 0.025 amps[25 mA.]. 11.19 / 0.025 = 447 Ohms. We will use the next largest common resistor value which will be 470 Ohms.
If the bulb happened to be a 3 volt 50 mA, then we just say 12.69 - 3 = 9.69 volts. thus E = 9.69 volts DC and I = 0.050 amps[50 mA]. 9.69 / 0.050 = 194 Ohms. We use the next largest common resistor value which will be 200 Ohms.
Ok we are almost there, we only need to know one more thing, how much power or wattage does the resistor need to handle. We already know how much voltage will be across the resistor, and how much current will be flowing through it. So we use the Ohm's Law formula of P=ExI. Or the Power in Watts will equal the voltage across the resistor multiplied by the current through it
Using the above Ex. 11.19 volts DC times 0.025 equal 0.279 watts. Next common resistor would be a 470 Ohm 1/2 watt resistor. 9.69 volts DC times 0.050 equal 0.485 watts. Next common resistor would be a 200 Ohm 1/2 watt resistor.
I am sure by now you have noticed that I have not said much about 12-16 volt lamps. With lamps that match or exceed the function output voltage, we could say there is no need for a current limiting resistor. But we would be wrong if we did. Bulbs are funny things when it come to current draw. When the filament is cold, such as a bulb that is not lit. When it lights the cold filament can exceed 10 times the rated or actual current of a hot bulb, this is called the cold filament current surge. This only lasts for a very short time till the bulb get fully lit, and hot. Lets look at this a second. A 12 volt bulb rated at 35 mA. If the cold filament current surge was 10 times this, that would mean when the bulb is first turned on the current draw would be 35 mA. time 10, or 350 mA. Remember most decoder function outputs are rated somewhere between 100 and 200 mA. This means that the 350 mA. surge is from 50% to 300% over the rated current capacity of the function output. This is for a very short time period, and may or may not take out a function output of a decoder, but every time it turns on the bulb, it will be working on doing it. This is why it is always a good idea to put a 20-40 Ohm resistor in series with a full voltage bulb. It will not dim the bulb by much, and limit the cold filament current surge to a value that will make the function output much happier.
Series and Parallel modes of operation. It is always best that each and every bulb has it's own current limiting resistor. But this is not always possible. When it is not, then do we put the bulbs in series or parallel.
If we put them in series, we know voltage adds and current stays the same. So we can look at two bulbs the same as one bulb at twice the voltage and the same current. Or two 1.5 volt at 25 mA. bulbs in series will be the same as a 3 volt at 50 mA. bulb, and we would use this as the rating to figure out our resistor using Ohm's Law. If one bulb should burn out the other will go dark, you will have to find the one that burned out.
If we put them in parallel, we know voltage stays the same and the current adds. So we can look at two bulbs the same as on bulb at the same voltage and twice the current draw. Or two 1.5 volt at 25 mA. in parallel will be the same as a 1.5 volt at 50 mA. bulb. And again we would use this as the rating to figure out our resistor using Ohm's Law. If one bulb should burn out, the other will burnout quickly. It will receive twice the voltage/current as it's rated for.
Project Page has some drawings that will show how to wire the bulbs up and also some different forms of voltage regulation for decoder function outputs.