3 resistor voltage divider

[Christopher]

I have 3 resistors in series, tapping off two voltages to the inputs of a high-impedance comparator.

If I know the output voltages, input voltage, how is best to calculate the three resistors needed in Excel or similar?

This is probably more a question for a Maths forum..

Here are my equations:

[JacquesBBB]

You cannot deduce the values of the resistors. You can only find their relative values

A solution is

R2/R3 = (V2-V1)/V1
R1/R3 = (Vin-V2)/V1

Any value  of R3  will work.

(edit :  to get the absolute values you need the   intensity of the current in the circuit).

[Zero999]

Yes, find the relative values and search for the combination which gives the best results.

[Christopher]

You cannot deduce the values of the resistors. You can only find their relative values

A solution is

R2/R3 = (V2-V1)/V1
R1/R3 = (Vin-V2)/V1

Any value  of R3  will work.

(edit :  to get the absolute values you need the   intensity of the current in the circuit).

Lovely clear formulas. This now makes more sense to me.

[German_EE]

1) Start by considering this as a single voltage divider with Vin, V2 as output, R1 and (R2+R3)

2) Assign R1 a nominal value (say 1K ohm) and work out (R2+R3) for the voltage you need.

3) Do the calculation again but this time for the second voltage divider. Input is V2, output is V1 and make a best guess for R2 before you work out R3

So, let's suppose you have an input of 10V and you want your output voltages to be 7,5V and 2,5V

R1 is 1K ohms
(R2+R3) needs to be 3K ohms for 7,5V out

Vin for stage 2 is 7,5V
R1 is 2K ohms and R2 is 1K ohms (sum 3K ohms)

Edit: JacquesBBB got there before me by expressing this as formulae rather than practical examples, c'est la vie

[Christopher]

Great. Thanks.  I was getting mixed up in various sim equations earlier which wasn't helping .


Now, just say I have two comparators drawing bias current from both V1 and V2. What's the best way to stop the voltage drop across the two resistors? Or will it be so negligible that it doesn't matter?

[PSR B1257]

just say I have two comparators drawing bias current from both V1 and V2.

Sure they do 

Or will it be so negligible that it doesn't matter?

Most likely. Unless you choose resistors in the terra-ohm region, you should be fine 

[Christopher]

just say I have two comparators drawing bias current from both V1 and V2.

Sure they do 

Or will it be so negligible that it doesn't matter?

Most likely. Unless you choose resistors in the terra-ohm region, you should be fine 

I have a series feed resistor of 27k on my input. With 200nA bias current, that will drop 6mV.

Kinda insignificant knowing my input offset maximum is about 6mV, too..

[PSR B1257]

With 200nA bias current

Holy crap, what type of comparator do you use?

input offset maximum is about 6mV, too..

Rather tight. In this case you also need a stable refevenre voltage. And you should use trimmers in between the resistors, in order to fine tune the voltage.

[Christopher]

With 200nA bias current

Holy crap, what type of comparator do you use?

LM2903, which has a max bias current of 200nA over temp range & 15mV offset.

Rather tight. In this case you also need a stable refevenre voltage. And you should use trimmers in between the resistors, in order to fine tune the voltage.

I think i will just use trimmers to set the comparator limit & shut them closed with some red Loctite. Works out easier than trying to fit a load of resistors in series, and trimming becomes a whole load easier.

[PSR B1257]

LM2903

Why did you use this one, if it is supposed to be a precision application 

Works out easier than trying to fit a load of resistors in series, and trimming becomes a whole load easier.

Yes, but with the resistor-trimmer-assembly you have a smaler range to adjust the voltage, and therefore you can use more of the trimmer-range.

[Christopher]

LM2903

Why did you use this one, if it is supposed to be a precision application 

I can use any I like, this just happens to be the first I have chose for these basic calculations! In my final project I will use a better specced comparator (the only real specs I need to look at are offset voltage, bias current and response time, right?).

Any advice on a decent part to use?

Works out easier than trying to fit a load of resistors in series, and trimming becomes a whole load easier.

Yes, but with the resistor-trimmer-assembly you have a smaler range to adjust the voltage, and therefore you can use more of the trimmer-range.

Good point. I plan on using 10-turn pots and a 5V reference. I can put some series resistance below the pot to decrease the pot range!

[PSR B1257]

this just happens to be the first I have chose for these basic calculations!

You should not use this one for any calculations, if you know, that it is not suited.

the only real specs I need to look at are offset voltage, bias current

Yes, these values should be low.

and response time, right?

Who knows? We still don't know, what your application looks like.

[abit]

If I know the output voltages, input voltage, how is best to calculate the three resistors needed in Excel or similar?

Excel has a function for permutations, so if you care to run all of E variations (not to mention power ratings and tolerances of 0.1% to 5%) you are going to end up with a DATABASE larger than Earth.. There is a reason why the E-standard was designed as such, and to save your sanity - do not ever think about going parallel more than 2 resistors. Even then, the effort is not going to justify the cost.

I have nothing to back this up but I have gone insane before along these lines, and the first approximation of the math in bash script was as expected, it ran for days and gobbled up gigabytes of disk space for a loose result.

Do not go beyond two resistors paralleled - and go there only when in dire straights for an odd value. Even then, you are going to loose some precision, since the approximation is a logarithm, and when there IS a PERFECT match you SHOULD have a discrete value of E192 of the same.

Now, the question is if you need it in:
0.125W, 0.250W, 0.500W, 1W, 2W or higher.
0.01%, 0.2%, 0.5%, 1% precision or lower.
... You got the idea

Do not think about it, do not go there. The variations of all these man-made objects is larger than Earth itself.

[JacquesBBB]

@abit

I am sorry, but I do not understand the purpose of your post.

The initial question of this thread is on voltage divider, and it is solved (see above).
Then  discussion  followed on proper resistance values compared to the impedance of 
the opamp that is in the circuit.

You seem to answer to a question, but as the answer is confuse, it would at least be nice to
state again which is the question to which your answer corresponds.

Apart from that,  despite the uncertainty of  the question,  let me remind you that to solve a
simple circuit problem, the best method is not  to try all possible values for the components.

A   simple circuit can be modelized by mathematical formulae  that can often be solved,
thus providing answer without filling a Earth sized database. 

[Zero999]

It's possible to minimise the effect of the bias current by making the impedances connected to each input as close as possible, that way the offset due to the bias on each input will be the same.