Re: Subject: Re: Current Distribution in inductors (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Sun, 07 Oct 2007 13:32:32 -0700
From: Barton B. Anderson <bartb@xxxxxxxxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Subject: Re: Current Distribution in inductors (fwd)

Hi Jared,

Ok, I am a patient man. I try not to react out of emotion (but my 
efforts are not always successful).

I'll wait for your continuation of this. Something I would like addressed:

You defined each region in the 3rd paragraph in terms of the same region 
height, wire length, surface area, volume, and energy storage (of which 
your equations are based). Please explain what occurs at high frequency 
to volume and energy storage and how this affects the numbers.

There are numerous studies regarding changes frequency dependent 
inductance and impedance in every field imaginable. I ran across one the 
other day which I thought was interesting. It is a paper regarding the 
frequency dependence impedance for the TRTS Power Rail system. Within 
this paper, the discussion regarding frequency dependent inductance is 
also shown. It's just one example. Anyway, interesting read.
http://nr.stpi.org.tw/ejournal/ProceedingA/v23n3/419-428.pdf

Take care,
Bart



 


>Hello Bart:
>
>Thank you for the thoughtful response, clarifications are always a good
>thing?..
>
>Inductance is the ratio of magnetic energy storage to current by definition.
>Ldc as some call it would be the inductance at zero frequency.
>
>We can take an inductor and cause; n periodic regions to form by selecting
>an  appropriate frequency. Notice that periodicity means that each region is
>the same in terms of region height, wire length, surface area, volume
>enclosed and energy storage.
>
>Let us define L(region) as the inductance of an individual periodic region.
>Now we can write. Ldc  x Isqrd = n ( Lregion Isqrd). This is a statement of
>the total energy stored in the inductor. Solving this equation shows that
>Ldc = n (Lregion)
>
>Now within the Lregion we find a maximum and a minimum voltage, we can
>conclude that our self capacitance is also found in the same periodic
>region.
>
>The next issue to address is the relationship between frequency and
>partitioning of Ldc. For this we will examine the results of a wire length
>derivation for inductance.
>
>It is already known that for a solenoid: E = u R N/ 2H   di/dt
>
>We also know that V = Ed       so we can write:
>V = uRN/ 2H    di/dt     distance
>
>We also know that V = - L di/dt
>
>Using L = n Nsqrd A / H   we find that the distance in question is (2 pi R
>N) which is simply the wire length.
>
>We also recognize that the E field is also along the entire length of wire
>and write a more complete description for E as: E = u/ 4piH  x  (Wire
>length)  di/dt
>
>We can now see that the expression L = u Nsqrd A / H is equivalent to:
> L = u/ 4pi H  x  (Wire length)sqrd
>
>We can also write this as L = (wire/ C)sqrd  x 1/(4pi e H)
>
>Waves of energy or information travel at a maximum of  C down a wire, this
>becomes important when we talk about the formation of standing waves.
>
>Since we have true periodic regions, a standing wave pattern does exist in
>the inductor. We can use the mathematics of standing waves to describe the
>partitioning.
>
>Standing waves are a function of both position and time, they are composed
>of two opposite traveling waves of equal amplitude and frequency. The
>distance between nodes
>
> ( wavelength /2) is determined by frequency and wave propagation velocity
>along the medium.
>
>Since:  Velocity = Frequency x Wavelength
>
>Now the regions of interest are always wavelength/4 in an inductor because
>the amplitude varies from zero to a maximum in wavelength/4 regions.
>I will continue part II of this discussion sometime between now and next
>Saturday.
>
>Thank you for your patience:
>
>
>
>
>
>Jared Dwarshuis and Lawrence Morris
>
> Oct 07
>
>
>
>
>
>  
>