How to build a negative inductance ?

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• zur ==> deutschen Version

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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:

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How do we solve a problem that cannot be solved ?

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The answer is – by means of shifting the problem !

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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.

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But – how do we generate this field of negative time ?

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Right – we use a time machine !

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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 !

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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 !

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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

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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.

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Ordinary capacitor

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Capacitor connected to a negative inductance (as in the pictures above)

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Addendum

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

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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 !