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 peaktopeak 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 "SKYROCKET/INFINITE" output voltage? This is only 12V???
