Re: NEC-LIST: small loop inductance

On Thursday, January 16, 2003 12:36 AM, Grant Bingeman wrote:

>
> can anybody give me an accurate formula for an electrically small
> single turn loop? I have a feeling that the formula for a
> single-layer solenoidal coil falls apart when the number of turns
> is one. MoM antenna analysis also has a problem with small loops.
>

Grant,
    The reactance of an electrically small loop aerial can be determined by
way of:

    X = jZ0*tan(k0*L/2)

where L is the perimeter length of the loop and

    Z0 = 276*log(4*A/(L*r))

where A is the area of the loop, r is the radius of the conductor, and

    k0 = w*SQRT(u0*e0)

where w is the frequency in radians/sec, u0 is the permeabiliuty of free
space, and e0 is the permittivity of free space.

    These equations are from:

    Awadalla, K.H. and A.A. Sharshar, "A Simple Method to Determine
    the Impedance of a Loop Antenna," IEEE Transactions on Antennas
    and Propagation, Vol. 32, No. 11, Nov 1984, pp. 1248-1251.

where they are compared favourably with results from NEC simulations. These
equations provide a reasonable approximation for the reactance of loop
aerials of a variety of geometries through the first antiresonance and
slightly beyond. The method of using an inductance formula for the
inductance of a loop is generally useful only for A<lamda^2/100 (Krauss,
"Antennas").

Chris

     ,----------------------. High Performance Mixers and
    / What's all this \ Amplifiers for RF Communications
   / extinct stuff, anyhow? /
   \ _______,--------------' Chris Trask / N7ZWY
  _ |/ Principal Engineer
 oo\ Sonoran Radio Research
(__)\ _ P.O. Box 25240
  \ \ .' `. Tempe, Arizona 85285-5240
   \ \ / \
    \ '" \ IEEE Member #40274515
     . ( ) \
      '-| )__| :. \ Email: christrask_at_earthlink.net
        | | | | \ '. http://www.home.earthlink.net/~christrask
       c__; c__; '-..'>.__

                       Graphics by Loek Frederiks

-- 
The NEC-List mailing list <nec-list_at_gweep.ca>
http://www.gweep.ca/mailman/listinfo.cgi/nec-list