This is a handy technique when designing circuits. Sometimes you don't have the voltage access you need for a circuit. Whether you're using a Bench-top supply that doesn't have enough output options, or you only have batteries on hand, this is an easy way to get multiple voltages from one source with just resistors. The theory is all based off of voltage division, done over and over again in a large branch.
If you have a DC voltage source, lets say 10 volts for an example, you can create a tree out of resistors using voltage division to make several "tap" points for your circuit.
Say you want to be able to get 2 volts, 4 volts, 6 volts, 8 volts, and 10 volts for some circuit design, and all you have available is 10 volts and ground.
The only component we need is resistors.
Your first reaction may be that this is going to waste a lot of power, but you will see in the end that if you use high resistor values, it will not. The higher your resistor values go, the lower power usage the tree has.
The design works off of voltage division, the equation is
Vout = (Vin)*((R2)/(R1+R2))
Where R1 will be the resistors on the top of each tap point, and R2 will be the resistors below each tap point.
By using the same resistor values we can create evenly separated voltage points, if we wanted an irregular pattern we could use different resistor values to do that.
Here is our example from above:
We have 10 volts and Ground
We want 2 volts, 4 volts, 6 volts, 8 volts, and 10 volts for out circuit
We will use resistor values of 100 kOhms (for this example only, you can use any values you would like for your application)
You can see in the image the Voltage reading at each of the tap points along the tree. Also, because I am using 100 kOhm resistors, my current draw is 20 uA, so power usage is only 0.2 milliwatts. Not bad for such a simple design.
This technique can be very useful for creating different voltage points in circuits. It is used a lot with comparator circuits when compared to output levels.
See my example of a comparator circuit here : http://www.instructables.com/id/LED-Comparator-Display-Audio-Volume-Level/
And that's it, the Voltage Tree Very easy to use and understand, can be configured to not draw too much power, and can be very useful.
If using this in a circuit, you cannot connect the branches directly to loads. You need to include a buffer at each end of the branches. I typically use an op-amp buffer or comparator, but there are different options. The second image shows the buffer configuration for an op-amp. Using this connection, the source (branch) sees the load as infinite resistance, and same with the load looking at the source. The op-amp may have leakage current (no component is perfect) but for the most part this is negligible.