How to build a negative inductance ?


• zur ==> deutschen Version



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.

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



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 !


  1. Simulation looks very interesting. Will it work for a circuit down at the VLF frequencies? Up to now only active circuits have been used for the VLF.

    Comment by Dennis Kozakoff — 18/07/2009 @ 20:47 | Reply

  2. This concept of building a negative inductance is per se frequency-independent.
    Normally, there is no big deviation between simulation and reality, as long as
    your components and parameters are linear and set correctly and you don’t have too much
    stray effects.
    This means, that you might get problems if you wanna use magnetic core coils instead of
    air coils and air coupling, because the coil and coupling parameters of magnetic core
    material is not fully linear and may also vary with frequency and temperature.

    Due to stray effects, skin effects etc. the simulation may work for a foil capacitor like
    in the simulation example up to 100 MHz. For the ceramic capacitor in the picture
    the principle did work well up to 1000 MHz.

    Comment by 4gang — 18/07/2009 @ 21:51 | Reply

  3. Oh, i forgot – i like your illustrative approach above, BUT i still cannot see where you got the MINUS (-) sign from in your derivation for L3 = -k…! Can you please show us where it came from?

    Comment by Glenn Roberts — 20/06/2010 @ 16:28 | Reply

    • Glenn – the minus sign for L3 is simply a consequence of the T-equivalent for a transformer.
      I had been inspired by the striking similarity between the T-model and the flux capacitor for this
      funny and stunning derivation (of negative inductance).

      Some more insight into this idea you can find in

      and more insight into the technical background you will find here


      Comment by 4gang — 20/06/2010 @ 17:34 | Reply

    • Glenn,

      I will phrase your question back to you: Where did YOU get the minus sign? Was it because someone taught it to you that way when you were an undergrad?

      The conventional equation for an ideal transformer is wrong and people have been fooled into believing an incorrect solution for over 100 years. I have evidence of this at VLF frequencies and the implications are big. 4gang is correct and a time reversed magnetic field does exist.

      Comment by Jules — 02/07/2010 @ 21:40 | Reply

  4. Hi 4gang,
    Can this negative inductance be scaled up say, to reach the size of a rather big coil with Litz wires and an ultracapacitor? Will the negative parameter be so big as to affect the time-space of the space inmediately adjacent to the negative component??
    What are the direct and practical implications of a modified curve of frequency response of a negative inductive device?

    Comment by aaron5120 — 22/06/2010 @ 12:19 | Reply

  5. hi GUYs
    To help this subject, I have a few scans of a work by Brailsford on such things as negative permeabilty (=> inductance) with graphs etc showing true negative values at certain frequencies and field strengths!!
    If you can provide a way to upload a few pictures here – i will share it with U

    Comment by Glenn Roberts — 01/07/2010 @ 02:36 | Reply

  6. would you provide drawings how did you connect capacitor with soldered coil to the network analyzer?

    Comment by Henryk — 26/07/2010 @ 19:22 | Reply

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    Comment by Tetris — 10/02/2011 @ 03:10 | Reply

  10. Right on!

    Comment by cevon — 21/07/2011 @ 02:48 | Reply

  11. Its wrong to use normal language in electrical terms to maths as negative is the reverse co efficiency of normal current and I do have a powerful free energy negative induction technology .The super flux cap is also a miss conceived math formula as it can not act as a negative field in a co efficient way unless its materials are also chosen to fit that equation ! Its also important not to use the same approach as a point of study as we would in normal electrical engineering as the time variable over resistance does not apply and ohms law is no longer included .

    I can make a simple coil negatively charged by altering the internal position of electrons to one side of that coil ! So we get a 100% compressed to one side of the coil and than super pump the coil with electrons ! The mass electrical charge of the coil becomes super negative by up to 10 000 % … Thats enough to levitate the coil and throw it into space …… Interesting diagrams but its best to
    start from fresh with a new language and formula to express the so called negative term but to be honest its neither negative or positive it more a shift of pressure inside a solid state atomic vacuum ! It make me wonder how such a simple reality is not considered by the likes of NASA ?

    BUT BE WARNED ! there ARE MANY risks in this energy type as all surrounding matter and possible time can be affected including gravity but not atomic nuclei as they are to close to the mass of the earth and there quantum relationship would only change if one was to apply the same amount of energy as to the atomic mass of the earth so forget negative mass ……. its impossible ! But negative co efficiency as an opposite effect to a positive EMF of resistance is a reality and is seen as the reason why galaxies are accelerating away into the inflation of the universe ! But that is another side to this energy and I do mean energy …..

    Comment by michael richardson — 19/11/2015 @ 23:20 | Reply

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