Steven S. Holland

Every now and then I write or modify a matlab function that I need for my research, and will post them to this blog here and there, with the hopes that they will be useful to someone doing antenna/microwave design.  I know, there is the Matlab File Exchange (which is very useful!) , but hey, this is my blog, I want to post my content here.

Below is a function I used to plot smith chart results in matlab.  I used basic plotting code to generate the chart itself, and added a simply plot function to add the impedance locus and constant VSWR circles.  Hope this is helpeful!  Please let me know if anyone finds a bug.  I will note that there is no safeguard in the function for s-parameters that are greater than 1, which if you are plotting the active S-parameters of a multiport device, are possible.  This isn’t a big deal when the S-parameter goes slightly above 1, but if it swings well above 1 you end up with a tiny smith chart and these erratic line segments…it’s a mess.  For passive applications I haven’t come across a bug yet.

smithchart.m

I got an email informing me that my masters thesis is now accessible through the University of Massachusetts “scholarworks” site, their digital library of thesis and disseratations.

If you are interested in taking a look at what I spent the last two years working on…you can find it  here.

The thesis was on a project aiming to design GPS antennas that fit into a volume of approximately 1.25X1.25X0.2″.

I have been running some Ansoft HFSS simulations of infinite arrays of antennas, recently.  A peculiar thing I noticed is that some of the impedance data, which is calculated from the S-parameter matrices, had sizable spikes (upwards of 300Ohms) inside a frequency band that, from the S-parameters, looked smooth and well matched.  Clearly something was wrong.  A low VSWR and S11 imply impedance levels close to the source impedance, yet these spikes in the impedance were there.

So I decided that, being able to compute all the data I need from S-parameters alone (as HFSS does), I exported the entire S-matrix to MATLAB and took a look at the impedance values I calculated.

HFSS gives the equation for finding the Z matrix as :

Z = sqrt(Zo*I)*inv(I-S)*(I+S)*sqrt(Zo*I)

where I=identity matrix, and S is the full S-parameter matrix

from this I plotted the exact same thing HFSS was giving for the impedances.  So I started plotting different chunks of the equation (e.g. inv(I-s) alone, (I+S) alone…) and found that the inv(I-S) term was spiking at the exact places my impedance was spiking, while the other terms were well-behaved.  Well, looks like that inversion is messing things up…indicating a singular, or more correctly a nearly-singular matrix (singular matrices have NO inverse defined).  Sure enough, using the function:

cond()

in MATLAB revealed huge condition numbers for the matrix (I-S) where the impedance spikes occurred, 2 orders of magnitude larger than the condition numbers calculated over the rest of the frequency sweep.  So I need to invert a matrix that is nearly-singular….now what??  I need single-value-decomposition (SVD) to take out those values that make the matrix singular and do a quasi-inversion, basically approximate the inversion.  MATLAB includes just such a function:

pinv() — where it’s use is  pinv(matrix, tolerance)

The tolerance can be set to an arbitrary value.  For my purposes, I can stand to lose some accuracy, so I chose a relatively large tolerance (around 0.02 or so) to take out those spikes but preserve the overal shape of the impedance waveforms.  Usually you will want to keep this very small to keep the inversion close to the true value.  But this solves my problem.

But it leads to another conclusion — HFSS, apparently, doesn’t test if its S-parameter matrices are nearly-singular (or at least I haven’t seen a way to have it do so).  Certainly it is using all sorts of inversion approximations in the solver the software uses (you can even do iterative matrix solutions in v11 of HFSS…), I don’t think it is likely that they have skimped on such checking on the data output front end.   Please post comments if you konw of any solutions in HFSS for this.

Here is an interesting Java applet that allows good visualization of the fields of some basic antenna elements.

 http://www.falstad.com/antenna/

You can readily see the field pattern distortions that occur from things like making a dipole or loop longer than half a wavelength in size, the multiple lobes that form, and how the current distribution forms on the structure.  You can for from a triangular current distribution on the dipole, to 10 or 20 sine wave variations along the length.  Really easy way to see what happens to the pattern.  There are also some array examples of end-fire arrays and schelkunoff polynomial alrrays.

I passed my oral thesis defense today, so I currently have a masters!

In celebration, watch this:

Today! 10AM. I have put a lot of work over the past few months into putting together my thesis, and I am hoping that will pay off.

I found this xkcd comic strangely appropriate — hopefully I am not subconsciously doing something like this during my presentation:

I guess there aren’t imaginary antennas…

Back in the 1960’s antenna sites started getting a tad crowded, and one solution proposed was to connected many transmitters to a single antenna, using a parallel network of bandpass filters that would allow isolation between transmitters.  After looking for ways to accomplish this at VHF, it was found that resonant cavities could be formed using a readily found, well constructed, tight tolerance, cheap and widely available solution — beer kegs.

It was found that a coaxial resonantor could be formed by making a center conductor that is adjusted to tune the frequency. As the article states, many problems were overcome in order to make them as successful as they were, and the article estimates tens of thousands of radio transmitter sites around the world equipped with these bands of beer kegs transformed into resonators!

A lot of people in RF/Microwaves/Electromagnetics can probably trace back a path of teachers to Maxwell…and here is mine:

Maxwell taught emag to Jeans (at Cambridge),

Jeans taught emag to Smythe (at Princeton)

Smythe taught emag to Rusch (at CalTech)

Rusch taught emag to Strangeway (at University of Southern California)

Strangeway taught emag to me (at Milwaukee School of Engineering) - that’s 5th generation.

Hopefully someday I can add to the list:

Holland taught emag to _________ (at ___________) …

Antennas!  I have spent the last few days learning to use our milling machine, practicing on cheap substrate, fixing the alignment here and there…but I think I have the hang of it now.  I built my first antenna today, which I was pretty happy about.  One problem I ran into was the ceramic substrate I used isn’t very easily cut, but I figured out a way to cutout substrate pieces using a router bit for the mill.

Now I need to find a big ground plane so I can measure it and see how it compares to my HFSS simulations.  Currently it is a 31X31X3mm susbtrate with a single patch on it that resonates at 1.5GHz, to provide a benchmark for my simulations.  I plan on building a number of these to get some experimental verification of some trends, and potentially piece together one of the stacked patch configurations that comes within 4mm of meeting my original design goals.  Assuming this goes well, I will be defending my thesis come early April…

I got a Garmin FM/AM/Shortwave radio for Christmas, and here and there I scan around and see what I can pick up.  For a while I kept catching a channel out of the Netherlands, and a handful of other stations I can’t exactly place because they weren’t in English and I couldn’t listen to hear them say where they were broadcasting from .

The last week or so at night I have been picking up this station, broadcasting from New Zealand!  That is probably one of the furthest places from here I have picked up stations from.  It’s broadcasting on approximately 10MHz according to my little radio, which the site confirms is 9.8MHz.  

Shortwave is really fascinating, both from a sociological and technical standpoint.  On the human side, it allows people to broadcast all over the world, talk to people thousands of miles away, hold conversations, send data (albeit slowly - remember, you’re only at 10MHz, and bandwidth is a tiny fraction of this),  and in emergency situations potentially act as the only form of working, reliable means of communication that can be used to save lives.  I know what you’re thinking — the internet allows people from all over the world to connect already.  Yes and no.  First of all, shortwave has been going for much, much longer than the internet has been open to the public, so historically it was the first means of allowing individual people freedom to connect with people from all over the world.  Besides equipment, it is completely free - you don’t get charged to use the airwaves.  You have to get licensed, but there are no ongoing costs to use the frequency bands.  

From a technical standpoint, one of my favorite aspects is the fact that it is in a special range of frequencies that make “ducting” and groundwaves possible. 

Ducting

Shortwave is at a low enough frequency that it can reflect off the ionosphere, instead of traveling out into space, it bounces back towards the earth.  This is one of the major mechanisms that allows, for example, stations in New Zealand to reach the US — like using a mirror to see around a corner, the reflections off the ionosphere allows signals to reach places beyond line of sight.  This bouncing of the waves can happen multiple times, from the ground, to the sky, back to the ground, to the sky, …, and hence the name “ducting”, since it is like a waveguide. What’s really interesting is that this effect is modulated by the sun cycle and solar weather.  During the daytime, the solar wind pushes the ionosphere down towards the earth, and this can cause the waveguide setup to either be in cutoff or can make it so that the reflections are too shallow to propagate very far beyond line of sight.  But at night, the earth shields the sky from the solar wind, and the ionosphere is higher, allowing this phenomenon to take place.

The other phenomenon that can cause ducting is the change in refractive index in the air.  As altitude increases, the refractive index decreases, and so waves travelling through this medium tend to get bent back towards the earth.  Conversely there are also situations where the refractive index can increase with altitude, and the wave is bent further towards the sky into space.  But both of these allow propagation of radio signal well beyond line of sight, or the horizon.  

Ground Waves

It is possible to have, over a certain frequency range, propagating waves attach themselves to a ground system — in this case the surface of the earth — and propagate following the curvature of the earth instead of going in a straight line off into space as the horizon is reached.  These can also be referred to as surface waves, or Zenneck waves.  
Also, on top of the wave propagation aspect, it also allows people to learn hands on antenna and transmitter design and operation.  It has created a whole Ham radio, or amateur radio culture that build and operate these systems.