This is a typical filter capacitor inside a measurement setup
In real life any capacitor comes with an additional parasitic inductance and a real resistance in series,
labeled Lc1 and Rc1 ( = ESL and ESR inside the data sheet)
what results in this characteristic frequency response
For low frequencies, the reactance of the capacitor is dominant – but above resonance, the parasitic inductance
is extremly disturbing :
There is nearly no more effect from a standard capacitor at high frequencies (> 100 MHz)
If we could create a negative inductance, equal to the parasitic inductance and in series, both inductances
would cancel each other (Lc1 – Lx = O ) independent of frequency
The filtering effect wouldn’t decay above resonance, but instead would remain constant
despite the rising frequency – as indicated with the dotted orange line
So – how do we get a negative inductance ?
Initially – this seems to be impossible:
passive, absolute, negative devices cannot be built in real life just like that, because they do not
comply with the conservation-of-energy-principle. Negative devices do not spend energy – instead
they would generate energy.
In other words – with such a negative device, you could drive a perpetual motion machine.
So – the question is:
How do we solve a problem that cannot be solved ?
The answer is – by means of shifting the problem !
We use a simple ordinary inductance
and place it inside a local field of negative time
The induced voltage across the inductance L is proportional to the change of current di/dt flowing through
To generate a reversed voltage across the inductor, we would either need an inductor with negative L,
or a current change with negative time : di/-dt
This would result in a voltage reversed to normal polarity.
But – how do we generate this field of negative time ?
Right – we use a time machine !
During a time travel into the past the time lapse is negative – the clock is proceeding backwards –
inside the effective area of the time machine, exactly the necessary local field of negative time is being formed.
Well – mission accomplished – minus the time maschine !
Let’s have a look to known time machines :
One of the first versions can be seen in the movie “The Time Machine”
Quite nice – but definitely too much mechanism for our purposes
Still – too complex !
And this ?
That’s it !
The Flux-Capacitor ! (= Flux-Kompensator)
Capacitor in this context is less referring to a capacitor device
but to its capacity of handling flux
If 2 of the flux elements are being excited by positive flux energy…
… there will come out a negative flux field across the 3rd element – generating the negative time !
So far the idea from the movie !
Now – the practical, electrical realization !
We supply current (i) to one of the connections of the flux capacitor
thus causing flux inside the element – Flux / i
The ratio of generated flux per current i we define as L
For each element of the flux capacitor – L1, L2, L3 accordingly …
… and suddenly realize, absolutely perplex – the flux capacitor is identical to a transformer !
The conversion of L1 and L2 follows the above given formulas …
… and – this is the point ! – L3 becomes in fact negative !
We built a passive, frequency-independent, negative inductance – using a time machine !
You don’t believe it ? Everything is correct !
For the experts – all the necessary conversions and formulas as overview
This is how a handmade negative inductance looks like in reality :
The capacitor is soldered to the center tap of the coil.
The area of the turn (inductance) and the distance between turns (coupling coefficient k) is such
as to generate a negative inductance at the connection to the capacitor, which is exactly of the
amount of parasitic inductance of the capacitor.
You can easily imagine the difficulty to accomplish this by hand (taking into account the tiny
dimensions) – so, normally you will have a deviation of about ±10%.
But even so – the result is impressing and amazing.
The method of building a negative inductance, was widely unknown until recently – though the physics
(transformer) and the corresponding formulas had been taught and applied since over 100 years.
However -asking what to do with negative results from calculating equivalent networks , students regularly
heard the reply, they could not use this – because there were no negative devices in reality !
And many people still believe so !(classic interpretation of negative inductance)
In fact – it is the other way round ! If the equivalent network results in a negative device – the real
network behaves as if there was such a device really present – though being invisible.
For additional information see to Filter using Negative Inductance
Just for fun – google for negative inductance and look what you get !
Or even worse – google for negative Induktivität and see what you get then !