-UnixWebMath-

# Log Periodic Monopole Array (LPMA)

The field patterns, input impedance for each dipole, overall input impedance and VSWR are computed.
The array is fed at the high frequency end and loaded at the low frequency end.
The LPMA specified by the tau and sigma provided is displayed to ensure a realistic design was specified.
The LPMA is oriented such that the smallest element is at the top and largest element is at the bottom with respect to the E and H field pattern plots.

The picture below depicts a LPMA over a ground plane:

This schematic view of the LPMA (below) shows how the image generated by the ground plane causes the LPMA to appear much like a Log Periodic Dipole Array (LPDA) with the exception of its feed structure. Tau and sigma are the standard defining parameters for log periodic antennas and are defined by the equations given in the figure. These are the same tau and sigma that are given in the LPDA simulation for convenience (they are based on Lamba/4 lengths as opposed to Lambda/2 lengths).

The primary difference between a LPDA and a LPMA is in the feed network. Unlike the LPDA, there is not a single standard feed that is used. Our experimental work has been done with high-frequency (K-band) array and microstrip feeds. A convenient feed for this application is the modulated feed line structure. It consists of cells that have two different impedances separated by a step-discontinuity. The characteristic impedance (Zo) section is generally the same as the source and load (Zs and Zl). The modulated impedance (Zm) is normally higher and is connected to the elements. By varying:

1. The percentage of each feed cell that is modulated (k)
2. The modulated impedance (Zm)
3. The length of the total feed (lfeed1)

we can attempt to match the LPMA and the source for a given LPMA physical structure. After matching, the characteristic impedance sections can be varied in length by the phase factor to change the pattern itself with little impact on the VSWR. The feed network is illustrated below:

To simulate a LPMA you need to specify the following:

• frequency (in MHz) at which the antenna will operate
can be a single number or a list: 3000.0 or {3000.0,3100.0,3200.0}
• number of Elements
must be between 3 and 20 elements
• tau (shortening factor)
• sigma (separation factor)
• length of monopole 1 (largest element in meters)
• element radius Type (1 means fixed; 2 means fixed radius/length ratio)
• Zs (real source impedance)
• Zo (real characteristic impedance of the feed line)
• Zm (real modulated impedance of the feed line)
• length of feed between dipole 1 and 2 (meters)
• k (percentage of the feed which is modulated)
• phase factor (deviation from standard endfire in terms of %of length)
• dynamic range to be diplayed (dB range of interest)
• If you want to have the admittance matrix plot for the array suppressed
then set Yplot to 0. The admittace matrix varies with frequency and shows the
coupling between elements as well as the self admittance. It is only for the
radiating structure and is independent of the feed.

Input Block:

#### Adjacent images can be compiled into a movie and 3D graphics can be converted to a VRML format:Note:VRML images require a VRML viewer and Movies require a MPEG viewer.

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 This script was developed at the Center for Computational Electromagnetics (CCEM) in the University of Illinois at Urbana with funding from the Sloan Center for Asynchronous Learning Environments(SCALE).

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