Steven S. Holland

Came across a link for some free math texts.

Link!

So today, shortly after getting home from work, I heard some singing, some bells, and all sorts of banging on drums and whistles outside my building.  Due to the porch roof, I couldn’t see anything from my window, so I went downstairs to investigate more closely.  What I found was a group of men dressed in white, with bells, drums, and towels (or so they appeared) dancing right outside.   One of them spotted me, and came over and told me about their background.  Apparently, my building, The Perry, was once The Drake (which clarifies the graffiti down the block that says “save the drake”), which was apparently once a bar/brothel/hotel that was a pretty wild place to be back 30 years ago.  The guy told me all about the respectable first floor, which regularly rejected them, and the “rat hole” basement, which readily let them in, including – according to one of the dudes dancing – beer served in metal buckets.  These guys used to hang out at the Drake in the 60s/70s and have been doing the dancing ever since, which is a good 30 years, as one specified.  Specifically, every 7th Tuesday after Easter is “Drake Tuesday”, which they come and dance out in front of the building, on the porch, and in front of the “save the drake” graffiti.

One of the guys also mentioned that, in viewing this dance, I was granted 1 year and 1 day of good luck.  I’ll take it.

The dancing?  According to their website:

The Morris is a living tradition of ritual dance and music, whose origins are shrouded in mystery, not to mention antiquity. The dance comes from England where it has been danced for hundreds, perhaps thousands, of years. John of Gaunt is said by some to have brought the dance back from Saracen Spain where he had been crusading. Others believe its origins are pre-Christian, possibly Druidic, perhaps even pagan. Similar dances are found throughout Europe and the Near East. Believe what you will. Many theories exist and, for now, no one can prove you wrong.

Morris dancing was almost lost in England during the nineteenth century. The tradition nearly died along with many other old, community based customs during the Industrial Revolution. The most recent revival began in England in the early twentieth century with the work of collectors like Cecil Sharp. There are hundreds of Morris teams in England now and at least 100 in the U.S. and Canada as well as other parts of the world.

Here are some pictures I took:

The videos were way over the upload limits for this site, so I threw them up on youtube:

Here is what I first saw when I walked outside.

Then they headed up onto the porch!

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 only have one course this semester, focusing on my Probability and Random Processes course and doing research.  This is by design, since I knew probability is a course I haven’t taken in 6+ years now…and I am super rusty.  But I have our text for the class, the schaum’s outline, and 3 other probability and random processes texts, and have been reading like crazy this semester, and doing sample problems out of the 4 texts and schaum’s.  Daily.  It’s good because I am having a much better time with this material than I expected, although the homeworks have been taking a long time to complete.

All this being said, here’s a sign it’s really starting to mess with my life: when I woke up this morning I asked myself what the probability of me getting out of bed when my snooze alarm went off for a third time (it’s set for 10 min intervals).  So I told myself, given how freezing it was in my apartment, and that I didn’t feel particularly awake, that I’d rate the likelihood of me getting out of bed on a given snooze alarm as 2/5, assuming I feel the same way independant of which snooze alarm is going off.

SO to get out of bed at the third snooze would be the probability of 2 failures to get out of bed, again assuming independence to make my just woken life easier, and one success:

P(I get out of bed on third snooze) =  (1-P(I get out of bed on first snooze))*(1-P(I get out of bed on second snooze))*P(I get out of bed on third snooze) = (1-2/5)(1-2/5)(2/5) = 18/125 ~ 20/120 = 1/6 ~slightly below 0.2, I’d say around 0.18 = => 18%

Then I went to sleep again and got out of bed on the 4th snooze alarm.

btw: The probability of me ever getting out of bed on my snooze alarm, found by summing over all probabilities from 1 alarm going off to infinitely many snooze alarm events, is 1, as you’d expect.  So it was bound to happen, eventually…

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.

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…

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…