Math 'N Resistors

[T.Jackson]

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With the help of some relatively simple maths, using resistors for purposes other than just limiting current can be quite easy. Sometimes, resistors can form the heart of many circuits. Most often enough resistors play key-critical roles throughout many circuits, and normally their value needs to be spot on, which is not usually the case with simple current limiting applications, such as for a LED. I wouldn’t be too surprised if most people just pluck a figure out of the air for this, because I know I certainly do. But unfortunately it’s a near impossible ask to come up with accurate approximation values for much else. This is where a calculator and some relatively basic math come into play.

A very common application for resistors is voltage references. Bet your audio amplifier has a ton of them, if not two. This even includes your all very expensive, state-of-the-art microprocessor controlled one as well. And while we’re on the topic of audio, another application that springs to mind is speaker crossovers; passive types use resistors in collaboration with inductors and or capacitors to form high-pass & low-pass filters. Active crossover systems on the other hand use countless arrays of resistors in conjunction with their solid-state operational amplifiers. But more on the basics – how do we go about working out the values for resistors in a voltage divider network?
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<u><b>Here's The Steps</b></u>
<ul>
<li> Decide on a sensible value for RT (resistance total)</li>
<li> Calculate the total current</li>
<li> Kirchhoff's law says that, in a closed loop circuit the sum of all voltage drops must equal the total supply. Decide on sensible voltage drops for each resistor</li>
<li> R = (The voltage we want "VR1" / the supply voltage) x RT </li>
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Pretty easy huh?, no excuse for guess work anymore! So for argument sake, lets say we decided on RT to be (100K) This is a sensible power conservative figure to settle on if all we need the Vref's for is say, a voltage comparator! Next we proceed to calculate the total amount of current that will be consumed in our network.

<ul>
<li> RT (total resistance) = 100K</li>
<li> IT (total current) = RT / VDD
= (10 / 100,000)
= 100uA</li>
<li> R1 = (VR1 / VDD) x RT
= (5 / 10) * 100K
= 50K
</li>
<li> R2 = (VR2 / VDD) x RT
= (3 / 10) * 100K
= 30K
</li>
<li> R3 = (VR3 / VDD) x RT
= (2 / 10) * 100K
= 20K
</li>
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*You could keep going, going & going with as many resistors as you like with this - Happy resistor'N