.

.

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)**

**.**

.

**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**

.

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 !

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 |

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 |

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 |

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

http://4gang.wordpress.com/gibt-es-zeitmaschinen/#english

and more insight into the technical background you will find here

http://4gang.wordpress.com/simulation/#english

Heinz

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

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 |

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 |

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

Glenn

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

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

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