Steven S. Holland

There is a program in California to replace 8th grade algebra textbooks with ipads.  It will be interesting to see how this turns out.  While I am all for trying new ways to teach a subject, singling out math as the test subject for this program seems like a bad choice.  While I can understand that perhaps they feel math is a key to technology, and that math is a natural link to technology that will make this transition seamless, I also feel that, of all subjects taken in 8th grade, the one class you are not reading a textbook page by page, like a novel, is math.  Math texts typically aren’t page-turners, at least when it comes to actual textbooks (OK, so that’s not true for all…and many non-textbooks, especially at advanced levels can be if written well…), and this is because studying a math book requires lots of flipping around to various pages, which might be in different sections, or even different chapters of the book.  How do you do this efficiently on something like an ipod?  Even if there are links that let you jump to other pages, who knows exactly what pages would be appropriate to provide links to?  History, or English, for example, typically have lots of linear reading – page after page.  Yes, of course even in these books you may need to flip to a different section or page to reference something, or compare…but that occurs rarely compared to a math book.

What makes math such an appealing hoice for this pilot program?

Although this ipad app puts graphing calculators to shame (source: http://thehill.com/blogs/hillicon-valley/technology/117625-california-testing-ipads-as-algebra-textbooks).

Came across a link for some free math texts.

Link!

The other day at work my monitors suddenly shut off.  The computer was still running, which is a good sign, and connecting one of the monitors to the motherboard’s video card (and seeing an image!) quickly showed this to be a failure of my primary video card.

So I harvested a video card from another computer and when I took the video card out of my computer I saw, to my surprise, this:

Four of the 1500uF caps have popped!

A web search showed that this was not an isolated failure – many of these cards have had caps exploding on them.

So Discovery Channel is finally doing the show they should have a long time ago: a show dedicated to high speed camera footage, called “Time Warp”.  I did mention a while back how amazing I find high speed camera footage.  Maybe they owe me royalties for the show idea?…(or rather that video I saw in grammar school where they showed ordinary things, like sneezes, a fly flapping it’s wing, etc, at high speed).  I definitely look forward to seeing this show.

EDIT:  turns out their site is full of videos already.  Take a look!

There is a joke, or saying, when it comes to designing an oscillator or amplifier:

“amplifiers oscillate, and oscillators amplify”

The statement describes the fact that, when attempting to design one, there are many pitfalls that cause you to have the other happen.  Usually when designing an amplifier oscillations are your enemy, and you tune them out with bypass capacitors and work to ensure the stability criteria is met.  When designing an oscillator, on the other hand, the circuit can readily swing into a stable state if you don’t have a very good design, and end up as just an amplifier.  Granted, with proper design and construction this is avoidable, but when you are building one for the first time or just quickly building one, this can happen.

I propose a similar saying for antenna design, although to make this work, i am going to use “radiator” instead of “antenna”:

“Radiators couple, and couplers radiate”

This only applies, really, to antennas with more than one port, and really can apply to any microwave circuit.  But this way the phrasing works out much better.  But basically says that usually when designing an antenna, you are battling this coupling between ports, trying to get efficient radiation.  Yet on the other hand, when designing a microwave circuit, one of your enemies becomes radiation, and you work to keep that to an absolute minimum, because unwanted radiation is unwanted loss.

One of my favorite things to point out to friends of mine is this fact:

Remember in Back to the Future (I, II, and III) Doc Brown used a “flux capacitor” to travel through time?  Well, what if I told you that every capacitor is a flux capacitor?

Well that’s true.   As a simple example, say I took a capacitor and hooked it up to a battery, as below.  Then I show the capacitor as two metal plates with electric field between them, and a surface “S” parallel to the two plates.

As this crude analysis points out, the flux is nonzero so long as the voltage across the capacitor – any capacitor  – is nonzero.

Movie fans will point out that this isn’t magnetic flux, to which I have two rebuttals:

1.) the movie never states whether Doc Brown means electric or magnetic flux

2.) fine, you want a magnetic flux capacitor?  I give you, the mystical LC network – the transmission line stub, the antenna, the cavity resonator…etc.

Sorry Robert Zemeckis.

I need to take some time to find a good plugin and get this site setup so that spam comments are reduced — I am getting upwards of 10 spam comments a day at this point — but until then I am shutting them all off.  Currently I don’t even look through the comments in the moderation queue so I don’t want someone to post a comment and then it get buried in the spam noise.  So, if you have commented in the last few months, and it never showed up…this is likely why.

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 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.