In this article I discuss how to step up voltage using a simple voltage divider circuit.

A voltage divider circuit is nothing but a series circuit made up of a battery and two resistors. It is usually used to step down voltage. Lets say you have 12 V battery but only want 6 V. You will place 2 wires across one of the resistors - let's call it R1. You will then choose your resistors such that V_output = R1/(R1+R2) × 12 V (V_input).
EXAMPLE: Chosing R1 = 1k and R2 = 1k, we can easily see V_output=1k/(1k+1k)×12V = 1000/2000×12V = 6V!

Now - you can actually increase the output voltage instead! - using this same voltage divider! - from say 12 V to 120 V - but we wouldn't do that we will do 4 V to 12 V. How? - here is the trick. When you look at this very equation, notice if the denominator approaches 0, then your output voltage out will skyrocket / go to infinity.
How can we make the denominator go to 0? Well R1 and R2 must be equal in magnitude but one resistor must be negative. That's right one of the resistors must have negative resistance!

Negative resistance? How can resistance be negative? Let's see, V = IR| R = V/I| make V positive and I negative - there we go! negative resistance! Sooooo how do we place this negative resistance in a voltage divider circuit???? Hmmmmm...research such a circuit and replace R1 with it????

Well-thats confusing! That thinking seems to be going no where! And that's because resistance is not defined by ohm's Law (V=IR) but instead as the gradient/slope of a voltage versus current plot of a component. That being the case, V and I can both be positive. As I increase for increasing V - the resistor will be positive, but when I decreases for increasing V, the resistor will be negative.
Now negative resistors we almost never talk about in DC Circuits - but it does exists. Over a certain voltage range in transistors, special metal compounds, tunnel diodes etc. - as voltage increase, current decreases! In AC circuits however, negative resistors are EVERYWHERE! They are produced by capacitors! In fact in AC circuits there are two special types of resistors called not resistors but reactance! Reactances can be formed by capacitors and are called capacitive reactance. Reactances can be formed by inductors and are called inductive reactance.
Capacitive reactance Rc = -1/(2πfC)(Ω).
Inductive reactance Rl = 2πfL (Ω).

Notice the capacitor gives negative resistance!! and the inductor gives positive resistance. Both are also dependent on f, frequency.

So didn't we want to make R1+R2 = 0? By simple math, R1 = -R2. We can use the inductor as our R1 and the capacitor as our R2. Mathematically R1 = -R2 now looks like: 2πfL= 1/(2πfC). We can rearrange this formula and find f. f = 1/(2π) sqrt(1/(LC)). We can now substitute our battery with an AC voltage source with frequency f and we have a voltage divider to step up voltage. So let us make a circuit.

I used a 39 mH inductor, a 560pF ceramic NOT electrolytic!/polarized capacitor, and a 4 V peak-to-peak sine wave generator (via my nice Picoscope). First let's find the frequency at which the denominator of the voltage divider circuit goes to 0! f = (1/2π) sqrt(1/(LC)) Therefore, (1/2π) sqrt(1/(39*10^-3* 560*10^-12)) = 34056hz. We place in series and test.

In the graph below you can see at the input we have 1.6 V????? What? What happened to the 4 V?
Seriously!!! THIS IS WHY I HATE EVERY ELECTRICAL TEXT BOOK, EVERY ELECTRICAL SIMULATOR.....whoa, whoa, whoa - chiiiiilllllll! Ok - this is what we do. I have a fix for this problem! - No not an explanation - like books would give - but a fix that will work for many circuits so you can start liking electrical engineering again :).

It just so turns out that this little incident does not get in the way of demonstrating negative resistance :) So let's continue and after you take a look at the fix. We measure the voltage across capacitor - since it's the component directly connected to ground.

And the result: Huh, will you look at that! The voltage reads 12V! From 4V to 12V!

And if you think this result was impressive - check out the results with the fix! Oh - whatever happened to the "SKY-ROCKET/INFINITE" output voltage? This is only 12V???

Inductor Capacitor Oscillator Caculator Applet

This applet is digitally signed by and works like a charm (Last checked: 24 July, 2015). Simply enter two values and leave blank the quantity you want to find. Enjoy :)

Click Start, then the Load Preset drop down menu and search for LC Resonance Applet. Select the tab at the bottom of the applet labeled 0.

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