microchip an-710
时间：04-10
整理：3721RD
点击：
RE: Possible bug in Microchip AN710 ?Antenna Design for RFID Applications? (?)
Collegues, please take a look:
http://ww1.microchip.com/downloads/e...tes/00710c.pdf
?Inductance of various antenna coils? chapter (page 9). Eq. 26 gives the inductance of a square coil. Eq. 27 gives the inductance of a rectangular coil. One would think that if the rectangle with x=y is plugged into eq. 27, the resulting inductance should be the same as calculated by eq.26. But it isn?t.
I thought that some assumptions have been made during the derivation of these formulae (eqs. 26 & 27). I have tried a set of different antenna sizes from 1cm to 1000cm with the following MATLAB code:
I thought that as the size of the antenna increases, the difference between the formulae would vanish. But as the size increases, the inductance values diverge (see plot).
I would rather trust the formula for a rectangle, because it resembles the formula for a circular loop (eq.23), which I was able to cross-check successfully.
What do you think?
Cheers,
Nick
Collegues, please take a look:
http://ww1.microchip.com/downloads/e...tes/00710c.pdf
?Inductance of various antenna coils? chapter (page 9). Eq. 26 gives the inductance of a square coil. Eq. 27 gives the inductance of a rectangular coil. One would think that if the rectangle with x=y is plugged into eq. 27, the resulting inductance should be the same as calculated by eq.26. But it isn?t.
I thought that some assumptions have been made during the derivation of these formulae (eqs. 26 & 27). I have tried a set of different antenna sizes from 1cm to 1000cm with the following MATLAB code:
Code:
% Filename: eq26_vs_eq27.m
% purpose: Demonstrate the difference between the eq.26 and eq.27 in [1]
% version:
% 0.1; Mar 20, 2007; Nick Alexeev; Beginning. Calculation
% for the wire-wound antenna on the air core
% references:
% [1] Microchip AN710
clear all;
% system parameters
f0 = 125e3; % [Hz] RFID frequency
% transponder parameters
NS = 0.0185; % [m^2] Cumulative catch area of the antenna.
l_out = 0.050; % [m] outer size of the spiral antenna
S = l_out^2; % [m^2] Area of _one_ POC antenna turn
N = NS / S; % Number of wire turns in the POC antenna turns
% temp code below. [1] eq.
x = [1:1000]; y = x; % square
b = 0.0001; % [m] diameter of a 34awg mag wire
h = b * N;
C = x + y + 2*h;
L_rect = 0.0276 * (C.*N).^2 ./ (1.908*C + 9*b + 10*h); % formula for a rectangle
L_sq = 0.008*0.5 * (x*N^2) .* (2.303*log10( 0.5*x ./(b+h) ) + 0.2235*2*(b+h)./x + 0.726); % formula for a square
plot(x, L_rect, x, L_sq);
legend('Formula for rectangle', 'Formula for square');
I would rather trust the formula for a rectangle, because it resembles the formula for a circular loop (eq.23), which I was able to cross-check successfully.
What do you think?
Cheers,
Nick
well,
i am not sure but i can focus on something that i found.....
there are some differences that could be make the two equations not equal even for the the same x=y value.
1) in the square loop equation the side a is defined as the "side of square measured to the center of rectengular cross section of winding" where in the rectangle it is rather straight forward ..side og a loop/turn
2)c is directly the depth of the winding but in the rectengle it is not that simple formula
so i think its not really like that x=y type relationship between a square and rectengular antenna coil...