# Choosing the right voltage divider by load

I'm using an Android IOIO board to detect simple digital pulses from a 12v source.

The input pins are 5V tolerant. Would a simple voltage divider work in this situation? I guess my concern is whether or not the IOIO would have much if any load pull when used as a digital input sensor.

I would say and I don't know this for sure that the max load would be 20mA??

What considerations do I need to make in selecting the correct resistor value ratio to go from 12v to 5v?

I also have these resistors available:

0Ω, 1.5Ω, 4.7Ω, 10Ω, 47Ω 100Ω, 220Ω, 330Ω, 470Ω, 680Ω 1kΩ, 2.2kΩ, 3.3kΩ, 4.7kΩ, 10kΩ 22kΩ, 47kΩ, 100kΩ, 330kΩ, 1MΩ

I've calculated that I can get 3.84V by using a 10k and a 4.7k. Will this be too much resistance?

A digital pin, when used as input, offers a very high input resistance. Note that this holds for DC current.

Since you want to scale $$\12V\$$ to be $$\5V\$$: $$5V=12V\frac{R_1}{R_1+R_2}$$ that leads to $$\R_1=0.417(R_1+R_2)\$$. There still is a degree of freedom, that is the total divider resistance. The factors that can help you to choose it are:

1. Your $$\12V\$$ output resistance
2. Your Android board input resistance
3. The speed of your pulses

Please note that the third factor might be the dominating one. A good cmos circuit has an input impedance composed by the parallel of a resistor and a capacitor, the resistor being some $$\10^{12}\Omega\$$ while the cap being in the $$\10\text{pF}\$$ ballpark. That means that you can forget about factor 2. A good digital circuit can usually deliver $$\1\text{mA}\$$ at least, maybe reaching $$\10\text{mA}\$$ in most cases. Moreover your driver circuit works at $$\12\$$V, that's probably quite stiff. Factor 1 should not be a concern too then, unless you are going to use very low resistors for the divider.

Now to factor three. The cmos input capacitance sees a resistance that is the parallel between the divider resistors$$\^1\$$, i.e. $$R_P=\frac{R_1R_2}{R_1+R_2}$$ As you might know this whole circuit behaves like a low pass filter, its dominant pole being $$\f_p=(R_PC_{in})^{-1}\$$, where $$\C_{in}\$$ is the cmos input capacitance. Now, you wanna keep that pole quite higher than the higher frequency you want to read on the board.

Assuming your highest frequency is $$\1\text{MHz}\$$ you need $$\f_p\gg10^6\text{Hz}\$$ that leads to $$\R_P\ll(10^6\cdot C_{in})^{-1}=100\text{k}\Omega\$$. Let's choose $$\R_P\approx10\text{k}\Omega\$$, and since the two resistors will be of the same order of magnitude $$\R_P\approx0.5(R_1+R_2)\to R_1+R_2 \approx 20\text{k}\Omega\$$.

Finally: $$R_1\approx 8.3\text{k}\Omega$$ $$R_2\approx 12\text{k}\Omega$$

Now you need to choose between your resistors, that are quite limited actually. Depending on your signal bandwidth you can safely increase the values somewhat, just keep the 2:3 ratio. 22k and 33k would be just perfect, if you are ok with the filtering involved. If you want fast signals go with 2k2 and 3k3 and call it a day.

$$\^1\$$ Actually you should sum the $$\12\$$V device output resistance $$\R_o\$$ to $$\R_2\$$ but I am assuming that $$\R_o\ll R_2\to R_2+R_o\approx R_2\$$.

• Re "A digital pin, when used as input, offers very little input resistance.": Don't you mean "...offers very little input current"? Or "...very high input resistance."? Commented Oct 11, 2021 at 1:51
• Thanks @PeterMortensen, fixed. Commented Oct 11, 2021 at 18:07

If the pin is configured as an input, then you should get next to zero load through it. Only if the pin is trying to drive an output voltage will it push or pull any significant current.

The pins are 5V tolerant... but what's the standard IO voltage? 3.3V? I'd select the resistor values to give ~3.3V if that's what the IO port runs at.

One resistor at 3.3K and two others at 1K and 220 in series to give 1.22K would get pretty close to 3.3V (3.239)

How much current can the 12V digital source provide? If it's very low (a high impedance source) then the divider won't quite do what you expect. If it's actually some kind of digital IO pin output then you're probably fine.

There are two competing considerations:

1. Resistor values that are too low can draw too much current from the source and cause its voltage to sag.

2. Resistor values that are too high will no longer behave as an ideal voltage divider. The potentially time-varying load resistance will become part of the resistive divider equation, and at very high values leakage currents due to board contamination can even become an issue.

You should look at the documentation for the max source current from your 12V source to check #1, and look at the documentation for the input pin on your Android IOIO board to check #2. If it's not documented, perhaps you can find a schematic and see what it is connected to; perhaps those components will have datasheets.