Given the above circuit and the value of either A, B, or C, and given f and g, we want to find the values of the other two resistors. f and g are defined as follows:

You will notice that if we multiply Eq.1 and Eq.2 by source voltage V

_{S}on either side of the equation we get the voltage divider equations. But we don't need V

_{S }to find the resistor values.

We first solve for A in both equations.

For Eq.1

For Eq.2

Equating Eq.3 and Eq.4 we have

We then solve for either B or C. Let's do B first.

Thus,

Using Eq.3 and substituting Eq.6 for C we have

Thus,

Using Eq.3 and substituting Eq.5 for B we have

Thus,

Eq.3 and Eq.4 gave us A in terms of B and C. Using these sames equations we can also find B in terms of A and C, and C in terms of A and B. The derivation is trivial so only the results are provided below.

So there you have it--all the equations necessary to find the resistor values given any of them. In my case I still needed the spreadsheet to help me find values that are commercially available. I plugged in a couple of the equations in the spreadsheet, and then by choosing different values for B given f = 2 and g = 10, I eventually got A = 15K, C = 3K, given B = 12K. Those are values readily available for 5% resistors.

---

Note: I used Codecogs' LaTeX Equation Editor to produce the images for the equations above. Am a newbie to Latex and have no idea how to pad spaces to move "Eq." towards the right. With a bit of trial and error I found that placing x number of "\ ", that's forward slash and then a blank space, will force x number of blank spaces.

## No comments:

## Post a Comment