Calculating odd Resistor values (Beginner)

Thread Starter

I0sens

Joined Jul 9, 2019
8
There are plenty of resistor calculators on the in internet, but all I found stop short at 2 resistors.

While large resistor values can be assembled to a good tolerance relatively easy by adding values, small resistor values need to be designed by paralleling existing values.
And there is some pesky math there. (Yes, math and physics run the world).

It might be logical to many of the users in this forum, but for beginners it is sometimes hard to grasp how to get to a 10.02 Ω resistor for instance.

(All of this is of course based on the formula Rres= 1/(1/R1 + 1/R2 + 1/R3….), basically we are adding
smaller and smaller 1/R3, 1/R4 … until we get close enough to 1/Rres.)

Here is the procedure:

Start with the closest value you can get, in this case you might choose a 12 Ω resistor or
10 Ω + 1 Ω. (You can use one if the above mentioned internet calculators to get the best starting value).
Remember: You always need to start with a higher value than the desired value as paralleling resistor will always lower
the resulting value.

OK, here we go…

Let’s say we start with 11 Ω, we are almost 10% off the goal.

Take the inverse of the desired resistor 1/10.02 Ω = 0.099800…

{
Subtract the inverse of the currently used resistor (11 Ω) = 0.090909

0.099800 - 0.090909 = 0.008891308 invert it -> 112 Ω (omit the minus)
choose the next higher available value -> 120 Ω

Invert and add to the inverted first chosen resistor 1/120 + 0.090909 = 0.099242

Invert and we are at 10.07 Ω a 0.5% error.
{

Not good enough? Repeat:

Take the inverse of the desired resistor 1/10.02 = 0.099800
{
Subtract the inverse of the currently resistor (now 10.07 Ω) = 0.092242 from the
desired resistor again.

Result: - 0.0005579 invert it -> 1792 Ω choose the next higher value -> 1800 Ω

Invert add to the inverted first chosen resistor 1/1800 + 0.092242 = 0.099798

Invert and we are at 10.0202 Ω a 0.002% error.
}

Repeat until you are satisfied. BTW, when you are at the last step, you might want to try also the next LOWER available value. Sometimes instead of an error of + 0.002, you might get to – 0.001 for instance.



In this example we now have 4 resistors 10+1 in series, with 120 and 1800 in parallel,
not too bad for a mathematical 0.002% difference to the desired value.
Of course you still will have the tolerance of the resistors themselves, like 1%,
but that is he max – if you are lucky, some of the tolerances will cancel each other.

Last not least, if you do have a really good Ohm meter, you can measure the actual result after each step
and can use that as the input to the next iteration.


I am attaching an Excel sheet with the calculation in formulas, you only need to add values to column D.
For those who don’t trust Excel sheets, there is also a screenshot with the formulas used.

I hope this is useful for some.
 

Attachments

SamR

Joined Mar 19, 2019
3,413
The question begs why do you need a 10.02Ω resistor? What tolerance are the resistors you are using? Did you measure the resistors first?
 

Tonyr1084

Joined Sep 24, 2015
5,993
If I want a 12Ω resistor I'll just use a 10 and a 2. The tolerance on both may be anywhere from 1% to 20%, depending on what I use. Assuming 1%, a 10Ω resistor might be 9.9Ω or 10.1Ω. Or it could be really close to 10.08Ω. I would have to dig through my stock of 10's just to find one that is satisfactory. THEN I put it into circuit where it warms - or even gets hot - and its value changes. Even if I found an exact match resistor to what I want I would still have to expect some variation in the real world applications.

Timing circuits use crystals to oscillate at a given frequency. Capacitors are added to assist in accuracy. Resistors are not used to tune the frequency because they vary too much over time and heat. Especially heat.
 
Last edited:

MrChips

Joined Oct 2, 2009
23,559
Read over each response carefully. None of them are meant to be snarky or tongue-in-cheek.
Collectively you are looking at over 200 years of professional experience in electronics and they ought to know what they are talking about.
 

Papabravo

Joined Feb 24, 2006
16,180
Read over each response carefully. None of them are meant to be snarky or tongue-in-cheek.
Collectively you are looking at over 200 years of professional experience in electronics and they ought to know what they are talking about.
This is an excellent point and well worth mentioning. Most of the pesky math problems have been automated in one way or another so even that no longer represents much of an impediment. We sent men to the moon with paper, pencils, slide rules, and Katherine Johnson.

https://crgis.ndc.nasa.gov/historic/Human_Computers
 

SamR

Joined Mar 19, 2019
3,413
Last not least, if you do have a really good Ohm meter, you can measure the actual result after each step
and can use that as the input to the next iteration.
Actually, I do, and if I attach it to a resistor the measured value will drift. Why? Because as Tony pointed out current through resistors generates heat and that will cause the value to change.
 

jpanhalt

Joined Jan 18, 2008
11,088
I appreciate that old cartoon. You are at best rude to ridicule a new poster in such a way, more likely you and others of the same kin are sick.
 

Thread Starter

I0sens

Joined Jul 9, 2019
8
Wow.. this IS a very active forum.... I am not offended by any answer telling me
the obvious uselessness of my post. (Most of my garage work is pretty useless
(according to my wife))...So is collecting stamps or glass animals.
Or trying to design a nice discrete transistor amplifier, when you can buy an OP-Amp
for cheap, that is better than anything you can do.

But it's still fun to figure out stuff.
Most of the math I learned in university I have not used ever since.


But:

Unfortunately I do not have a E48 series of resistors in my drawer.

And yes, I don't know, why I would need a 10.02 Ohm resistor.
But obviously some people have a use for a 9.31 resistor... (E96 series :))

I was just annoyed why all the calculators online are only doing 2 resistor calculations.
(including the http://jansson.us/resistors.html site.).
 

MrChips

Joined Oct 2, 2009
23,559
And yes, I don't know, why I would need a 10.02 Ohm resistor.
But obviously some people have a use for a 9.31 resistor... (E96 series :)

I was just annoyed why all the calculators online are only doing 2 resistor calculations.
(including the http://jansson.us/resistors.html site.).
You are a lost soul that needs some direction.
No. There is no one in this electronics world that needs a 9.31 resistor and yet you can buy one.

1607300596944.png

I started out in electronics when all that can be had were 20% tolerance resistors, even before 10% resistors became widely available.

E3 values = 10, 22, 47

E6 values = 10, 15, 22, 33, 47, 68

I don't need a 39 value resistor. However when something between 25 and 50 may work well for me, I can choose 27, 33, 39, 47, or whatever is in my parts bin.

1607300735824.png

The values of manufactured resistors are what they are based on the mathematical value as they fall in the progression of the series. It is like the tonal frequencies of musical notes. Musicians know what 440Hz sounds like. Not many people can tell the difference between 440 and 441Hz.

What you need to pay attention to is the tolerance of your calculated value versus the tolerance of what is available. I have little use for 1% values. Therefore I don't lose sweat trying to find a 35.67 resistor value that my calculator has determined that I need in any given circuit.
 

MrChips

Joined Oct 2, 2009
23,559
In order to make my point clear, let us look at an example.

Suppose that I want to build a passive 1st order high pass filter with a capacitor and resistor.
I would like to attenuate frequencies at 60Hz and lower.

1607303033552.png

I have a 1μF capacitor. What value resistor do I need?

Suppose I select a roll-off frequency at 150Hz.
Calculation determines the value of R to be 1062Ω.
What would be the consequences of using a 1kΩ 5% resistor?

The actual value of 1kΩ 5% could lie between 950 and 1050Ω (not exactly but close enough for this discussion).
This would put the cut-off frequency to between 152 and 168Hz.

But wait a minute. The 1μF capacitor comes with a 10% tolerance.
This puts the cut-off frequency to between 138 and 185Hz.

The point is I am not going to look for a 1062Ω resistor knowing the fact that any cut-off frequency between 138 and 185Hz will not jeopardize the proper functioning of my circuit.
 
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