Impedance on thin wire dipole using method of moments

In summary, the conversation discusses the task of calculating the input impedance on a thin wire antenna using Pocklington's integral equation and the method of moments. The equation is broken down and fit into a matrix expression, with the source point on the outside of the wire and the field/observation point on the axis of the wire. The conversation also mentions using a pulse as the basis function and a point matching and delta-gap generator as the 'source'. The attempt at a solution involves numerically integrating the Green's function over each segment using quadgk() in Matlab. However, the resulting impedance does not match the expected value, potentially due to issues with the integration of the Green's function. Assistance with the general approach is requested.
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Homework Statement


Write code to calculate the input impedance on a thin wire antenna using the below form of Pocklington's integral equation. Use Method of moments.
Use a pulse as the basis function, point matching and delta-gap generator as the 'source'.
Assume the wire is broken up into 7 segments (N=7), the wire is 0.47λ long with radius 0.005λ.

Homework Equations


Pocklington's integral equation was given as
[itex]E^{i}_{z}=\frac{j}{ωε}∫^{L/2}_{-L/2}I_{z}(z')\frac{e^{-jkR}}{4 \pi R^{5}}[(1+jkR)(2R^{2}-3a^{2})+(kaR)^{2}]dz'[/itex] where [itex] R=\sqrt{a^{2}+(z-z')^{2}}[/itex]

Note that the source point (vertical z) is on the outside of the wire and the field/observation point (z') is on the axis of the wire.

The Attempt at a Solution


I have broken down pocklington's equation to try and fit it into the matrix expression [itex] = [Z]^{-1}[E] [/itex]. I ignored the pulse function as it was a constant 1 over the integral for each segment. [itex][/itex] is the set of weights representing the current on each segment which ends up out the front of the integral since they don't have dependence on z'.

For the E column, I used all zeroes except for the 'gap' (relating to middle segment N=4) where it is V/Δz.
In this case V=1. I multipiled [E] by constant -j4∏ωε as I moved them from the RHS to the LHS in the above equation.

For the Z matrix, I am using the integral of the Green's function, which is the everything under the integral to the right of [itex]I_{z}(z')[/itex]. I am numerically integrating it over each segment using quadgk() in Matlab.

To get , multiply inverse of [Z] by [E].
Then finally to get the input impedance, I divide V (=1) by the centre segment current N=4.

The result I am getting (1.5541e+01 + 4.8658e+02j) doesn't match up with what I am expecting (closer to 100 + j100).

The gist of my program is shown by pseudocode:
N=7; freq=3e8; omega=2*pi*freq; c=3e8; lambda=c/freq; k=2*pi/lambda; a=0.005*lambda
epsilon=8.85e-12; dz=L/N;
<<
for(m=1:N) {
zm=m*dz-(dz/2);

for(n=1:N) {​

zn=n*dz-(dz/2);

//This integrates over nth segment length
Z(m,n)=quadgk(greens,zn-dz/2, zn+dz/2);
};​
};

E=zeros(N,1);
E(4,1) = -j*4*pi*omega*epsilon/dz;

I=inv(Z)*E;

Zin=1/I(4,1);
>>

Any assistance on the general approach would be greatly appreciated. I have tried different integrators which has yielded different but silly results.
I believe the integration of the Green's function is the problem.

Thanks,
Cram
 
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Bumping as thread has changed categories.
 

1. What is the method of moments?

The method of moments is a numerical technique used to solve electromagnetic problems, particularly those involving wire antennas. It involves dividing the antenna into small segments and using mathematical equations to calculate the current and voltage at each segment.

2. How is impedance calculated using the method of moments?

The impedance of a thin wire dipole can be calculated by first determining the current distribution along the length of the antenna using the method of moments. The total current at each segment is then multiplied by the segment length and the characteristic impedance of free space. The sum of these values is the total impedance of the antenna.

3. What factors affect impedance on a thin wire dipole?

The impedance of a thin wire dipole is affected by several factors, including the length of the antenna, the diameter of the wire, the proximity of nearby objects, and the operating frequency. These factors can alter the current distribution along the antenna and therefore affect the overall impedance.

4. How does impedance affect the performance of a thin wire dipole antenna?

The impedance of a thin wire dipole is directly related to its radiation efficiency and bandwidth. A mismatch between the impedance of the antenna and the impedance of the transmission line can result in signal reflections and reduced performance. It is important to match the impedance of the antenna to the transmission line for optimal performance.

5. Are there any limitations to using the method of moments for calculating impedance on a thin wire dipole?

While the method of moments is a useful tool for calculating impedance on thin wire dipoles, it does have limitations. It assumes a perfectly straight and infinitely thin wire, which may not accurately represent real-world antennas. Additionally, the accuracy of the results may be affected by the size and number of segments used in the calculation.

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