Tips: Voltage Divider
I have been bugged by quite a few people on how accurately divide voltages. I have seen designs using 0.1% tolerance resistors cost more than the rest of the components and box put together. Below is a description of a very cheap method to get close to lab accurate results.
As soon as you start getting serious about analog electronics (and sometimes even for digital circuits) you run into voltage divider problems. Most of the time you can tweak the voltage with a potentiometer. These are available in various versions ranging from cheap 270 degree turn trim pots to multi-turn trip pots. You might even be tempted to use a large potentiometer, like for volume controls, but you can be sure someone will turn the knob.
Many times you need a fixed division, e.g. 5V / 2. So your first instincts are to take 2 resistors and tap the voltage in the middle. And it will work, ...but not without problems. If you are not seriously worried about accuracy and temperature drift you can use this and in fact many designers are.
Problem with the diagram above is that the resistance is not guaranteed. When you buy those normal carbon resistors one of the colour bands indicates tolerance. The normal resistors out there are 5% but with SMDs these days 1% is becoming popular. Lets look at a worse case scenario. Assume the use of 2x 10kohm resistors. The one deviates by the maximum of 1% in the top range and the other 1% maximum in the bottom range. On 10 000ohm the 1% is 100ohm.
If R1 is the 9900 ohm resistor and R2 the 10100ohm resistor then Vout will be 2.525V. The other way around Vout is 2.475. By having these extremes your tapped voltage will be 25mV off from where you wanted it. 25mV is a lot when you are building voltage references for an A to D system.
Lets say you want a different voltage division ratio, e.g. 1/8Vin. Not too difficult. R1 must be large and R2 small. R1 must be 7 times larger than R2 ( Vout = V1 x (R2/R1+R2)), so you could choose R2 = 10k and R1 = 70k. The 10k is easy to find but the 70k not. You could approximate it by using standard values, but you will need more than one resistor. If you do another 1% extreme test then a 10V input signal will be off by 22mV from the expected 1.25V output. That is not all. Temperature plays a roll. Each type of resistor has a certain temperature coefficient. This means that the two resistors will start behaving differently at different temperatures. Also the two components are at different parts on the circuit board seeing slightly different temperatures. Now, for the amateur only building one circuit this won't be a problem as you can just buy a trim pot (which also drifts with time and temperature), but when you build thousands of boards you cannot sit there and tune each board.
You find these little devices everywhere, and they are relatively cheap. Resistor packs/arrays are used where space is critical or typically in bus applications where there are many parallel lines to pull up/down/terminate. So what makes them so special? They are manufactured (1) on the same substrate (2) using the same process and material.
If you measure a single resistor (e.g. 10k) you would be shocked to see the horrible tolerance. You could easily find that a 10k resistor gives a reading of something like 9700 ohm or worse. In fact I don't think I have ever measured one that was spot on. So why use a resistor that is so far from even a 1% discrete? Simple, they are all the same. Go and measure the rest. If one measures 9700 ohm then the others in the same pack will also be the 9700 ohm. They will all share the same temperature coefficient and be very close in tolerance relative to each other.
4 in 1 resistor pack
Take a resistor pack and wire it as below. Assume the nominal resistance is something obscure like 9764 ohm per resistor. Vout = 5 x 9764/(9764 +9764) = 2.5V. The resistance won't be perfectly matched in all cases but it should be better than the 1% option.
Ra and Rb part of same package.
So how do you do the 1/8V divider? Get a resistor pack with 8 resistors in and wire them like below. The top 7 resistors (Rb to Rh) will add up to 70 000 ohm in series. The bottom one (Ra) is 10 000 ohm. Vout = 10 x (10 000/ (10 000 + 70 000)) = 1.25V. The 70k side behaves like 7 x 10k sections.
Well, there are always problems. The first is impedance. If the resistance is too low your source might not be able to drive it. You might be putting in 5V from a sensor but the series resistance, to ground, it pulls the source down thus causing an error in reading. There are two common options (and the combination of them). Firstly you can raise the resistance. With the circuit above the 10V sees a 80k ohm load (excluding the circuit that is reading the voltage). The resistor network is thus drawing 0.125mA. This might not seem much to certain sensors (e.g. strain gauges) it will spell disaster. By increasing the resistor values to 100k each the load will be lessened, but (always a but as well) the noise levels will go up. Second option is to insert an op-amp in the circuit. The simplest is a voltage follower (gain = 1).
With the op-amp you will have a very high input impedance and a driver circuit that will put some effort into the divider. Note that you can use this same resistor-pack concept when designing the feedback resistor values for an op-amp for precise gain.
The 2nd big problem is high voltage. When you start measuring higher voltages the small resistors tend to break down and all this exact magic goes out the window. This will happen at voltages exceeding the manufacturer's specification. So don't go and try to measure 500V DC without understanding the mechanics behind this.
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