Where To Find This Example
Select Help > Open Examples... from the menus and type either the example name listed above or one of the keywords at the bottom of this page.
You can also open the project directly from this page using this button. Make sure to select the Help > Enable Guided Help from the menus before clicking this button.
Design Notes
Radiation Pattern Studies of Small Loop Antennas
This project shows how AXIEM can be used in the simulation of loop antennas. In particular, radiation patterns and current annotations are used to better understand real versus theoretical antennas.
Overview
Small loop antennas are practical because they can be printed on the PCB at no extra cost. Ideal small loop antenna can be viewed as a magnetic dipole with a zero along z-axis. This project compares a sample loop (with fixed dimensions) with the theory. The finite size of the loop is causing "filling" the zero at zenith. The reason is that the theoretical zero is a result of symmetrical cancellation of the field due to opposite current filaments along the loop. For a finite frequency there is a finite phase shift along the loop, causing imperfect cancellation. This project can easily be modified to quantify the imperfection for any given size/frequency.
To underline the importance of the relative phase difference of the current along the loop antenna, a high frequency fc representing a whole 360 degree phase shift is also considered. The result is that the roles of zeros and maxima are toggled. Thus, from radiation pattern point of view, going from DC to fc means a smooth transition between these extremes, and this project demonstrates the transition by viewing the pattern at selected frequencies.
Furthermore, two EM documents are defined to consider some practical implementation aspects.
Drawing a loop
The loops in all EM documents "small loop small gap X" (where "X" refers to the frequency (in MHz) at which the particular document is simulated) are drawn following the procedure described here.
It is easiest to start by drawing a circle in a blank EM document. Either Draw > Circle or find the Ellipse tool in the drawing toolbar, usually located below the workspace. Then apply Draw > Modify Shapes > Make Ring or find the Make Ring tool in the drawing toolbar. Give the width of the trace forming the loop, e.g. "1" (mm; pay attention to your length units). Note that the center line of the ring is the perimeter of the original circle.
The internal port is an excellent port choice here to model a narrow gap excitation. Notice the internal edge on the south of the loop. Select the shape and Draw > Add Internal Port (or find the Internal Port button in the toolbar, usually located above the workspace) and point the edge such that it is highlighted, and click to add the port.
Specifying the frequency
For radiation pattern studies it is often a good practise to specify the frequency locally per document. It is set right-clicking the EM document and selecting Options > Frequencies.
An EM document is easily copied by dragging it on top of EM Structures node in the Project Tree. This way one can quickly make variants, and e.g. set different frequencies for the same structure.
For frequency response simulation, one can specify the frequency range under Project Options > Frequencies and apply them to one copy of the structure. It is indeed typical that one EM document is used for the frequency response, and a few documents for radiation pattern and current animation studies. In this project, the EM document "small_loop_small_gap_frequency_response" and graph "Frequency response" are used for that purpose. It is typical for small antennas that they are very poorly matched to a 50 ohm source, i.e. their radiation resistance is very low. It is not evidence of a malfunction or poor design.
Radiation pattern measurements
The total power far field radiation pattern measurement is found under Electromagnetic > Antenna > Sweep Theta > PPC_TPwr. Phi=0 gives the XZ plane cut, and Phi=90 gives the YZ plane cut. The horizontal cut is found under Electromagnetic > Antenna > Sweep Phi > PPC_TPwr and setting Theta=90 degrees.
Far field results
Graph "Far field" shows the XZ and YZ plane patterns for a loop of 20mm diameter at 434MHz. The zero at zenith is not perfect but is 14.7dB below the maximum. At 434MHz (a common frequency range for short-range wireless appliances) the length of the loop is about 30 degrees, and so the field cancellation at opposite points along the loop is not perfect.
Graph "Far field vs frequency" shows XZ plane pattern at 4MHz, 40MHz, 434MHz, 2.4GHz (loop length ~ 180 degrees) and 4.8GHz (loop length ~ 360 degrees). At 40MHz the zero is 35.5dB deep with respect to maximum, so the cancellation principle is almost perfectly valid as long as the total loop length is at most a few degrees.
Interestingly, the radiation zero and maximum invert roles when the opposite current filaments have opposite phase (@4.8GHz): the antenna is essentially at "even" mode then which can neatly be seen from the current animation. To see the mode, open the 3D view of EM document "small_loop_small_gap_4800" and make sure the EM_CURRENT annotation is toggled on. Use the VCR style buttons on the toolbar to animate the current.
Real loop implementation
AXIEM can easily be used to study more practical loop antennas on PCB. In particular, the ground planes play significant role. Sometimes ground edge can even be part of the antenna, but anyway we need to pay attention to the induced currents.
EM document "real_loop_434_v1" shows a candidate design, but its radiation pattern is very different from a similar standalone loop's pattern - see graph "Far field real loop". The maximum is at zenith, contrary to the ideal loop. Looking at the 3D view of "real_loop_434_v1" and animating the current, we see that there is a circulating ground current on the opposite direction of the loop current - disturbing the cancellation principle.
If we reshape the loop a little and prevent the ground plane current making complete loops, we get a result that is much closer to the isolated loop pattern. This has been accomplished in EM document "real_loop_434_v2" and shown in the magenta curve in graph "Far field real loop". See also the Rules in this document's Enclosure for a way to represent the ground vias as square vias for EM geometry simplification.
A final note: the symmetry of the loop is also disturbed if we introduce a finite gap to the excitation. See EM document "small_loop_finite_gap_434" and graph "Far field small vs finite gap". We can see that introducing a 0.5mm gap on a 20mm diameter loop makes the zero depth at zenith being only 9dB (infinitesimal gap: 14.7dB).
In summary, AXIEM is a powerful EM tool to study all kinds of printed loop antenna characteristics, including effect of phase delay, geometrical asymmetry and local ground plane.