# BosonQuest

## Inception for geeks

There are times when a geek should do their best to fit into normal society; to rein in the inner nerd, and resist the urge to commit atrocities against traditional sensibilities. But this isn’t one of them, and so I present the (99% spoiler-free) programmer’s guide to Inception.

class Inception implements ChrisNolanFilm {
void plot() {
try {
Idea.write();
} catch (RuntimeInception ri) {
ri.printStackTrace();
}
}
}

Sorry. First tweeted here.

July 17, 2010

## iPhone 4 versus duct tape

There has been an awful lot of talk lately about the iPhone 4’s antenna troubles. And indeed, from having used one for a few weeks, it does indeed behave badly if held in a particular manner in a weak signal area. But one rumour has been following this story around like a bad smell—the legendary Duct Tape “Solution”.

It seems obvious enough—two antennae next to each other, separated by an insulated gap; fine until you “bridge” the gap by having your hand in contact with both sides, causing a short-circuit. Hey presto: no signal. So a small square of insulating tape over the gap, and problem solved! Alas, no.

Most people have heard of a capacitor, though perhaps don’t know what one is or does. Quite simply, it is two conductive “plates” separated by a thin dielectric, or insulating, layer. So an antenna with a layer of tape being held by a person such that an area of skin is in contact with the tape is basically a large capacitor. When a voltage is applied across a capacitor, charge builds up on the two conducting plates over time. As the charge builds up, the capacitor starts to resist more and more current from flowing, eventually stopping the flow altogether. The amount of charge that can accumulate is called the capacitance, and this varies directly with the area of the conducting plates (area of hand covering antenna), and inversely with the thickness of the dielectric layer (tape).

In an alternating, or oscillating, current, both the voltage across a component and the current flowing through it resemble a sine-wave. If you divide the amplitude (height) of the voltage wave by the amplitude of the current wave across a component, you get a number that is called the impedance of the component. Note the similarity with the resistance of a component in a DC circuit, which you might recall from school is equal to the (constant) voltage divided by the (also constant) current. The impedance of a component in an alternating current is essentially how much it… well… impedes the flow of current.

What this is leading up to is the fact that, across a capacitor in an alternating current, the impedance varies inversely with both the capacitance and the alternating frequency of the signal, which for mobile phone radio waves is pretty high—around 400-1800 Mhz. So the impedance of a piece of tape separating a radio antenna and your hand is negligible. You may as well be touching the antenna directly.

Roughly speaking, in an alternating current, rather than charge flowing round a circuit, it oscillates back and forth. With a capacitor in the way, charge builds up on the plates just as in a DC circuit, but at high frequencies, it turns round and goes the other way too fast for enough charge to build up on the plates to impact the current.

The good news for people whose phones work with a bit of duct tape on the antenna is that your phone works without it too. Trust me. The bad news is that if you have gone around saying your phone is unusable without tape, then you are fooling yourself. And the really bad news for people who have published damning reviews of the iPhone 4 while suggesting that duct tape will fix it, is that you are lying to your readers. Plain as. This is not to say that the phone doesn’t have an antenna problem—it does—but if you say your tests showed improvement with duct tape, you cast serious doubt on the validity of your tests.

As for solutions, well, with a bumper, or other case, you are increasing the thickness of the dielectric layer in the “capacitor” between your hand and the antenna, dropping the capacitance way down, and to the point that its impedance is too great to cause the antenna detuning issue, even at radio frequencies. You can also minimise the capacitance by altering your grasp of the phone—lower the contact area and you lower the capacitance. So Apple’s well-published suggestions “not to hold it that way” or “use a case” are scientifically the best ways to reduce the problem. But as many have pointed out, a phone for which the natural grip is the wrong one (all phones have bad areas, most aren’t right where you want to put your hand), or for which you need to spend additional cash to get a decent performance is a poorly designed phone. Apple should really address this somehow; right now it seems that the best course would be the free case, and iPhone users putting up with the fact that our phones are awesome at pretty much everything… except being phones. Or return it, of couse.

If you read the rest of my blog here you will see that I am but an amateur physicist, so it’s fair to say I could have this wrong. But the level of physics in this material is not particularly high, and since there’s no real way that I can be setting up experiments in the areas I’m currently studying, I jumped at the chance to test this theory out for myself. And while the results were more qualitative than quantitative (since I lack the means), I have tested duct tape, electrical tape, Sellotape and the plastic overlays that came off the phone when I unboxed it. No difference was noticeable with any of these materials entirely covering the parts of the antenna that were in contact with my hand. If you want a more credible source for these findings, there are a number of posts worth reading at www.antennasys.com/antennasys-blog.

Ain’t science a bitch?

Update: thanks to the nice folk at Anandtech, it seems I’m right and wrong. High impedance tape does exist, and can be applied to the phone. Even with such tape, the impedance is not enough to completely isolate you from the antenna, though perhaps it could do so enough to bring the phone into line with others. I would guess the tape must be made from a material with an impressively low dielectric constant; I still believe that the DIY fixes involving bog-standard tape are spurious, and if you want the best performance in a weak signal, a case would be a good idea. But it’s nice to think that there is a potential solution out there—also nice to know I was on the right tracks.

July 14, 2010

## My brain hurts.

Currently reading some results regarding complex numbers, the proof of which involves a radius term $R$, euler’s notation $Re^{i\theta}$, and the splitting of a complex number $z=\mathop{\mathrm{Re}} z + i\mathop{\mathrm{Im}} z$. So finding terms like $\mathrm{Re}^{i\theta}$ and even $\mathop{R\mathrm{e}} z$ is doing my nut. This is in a printed book too, so it’s not a bad e-book translation error.

On the other hand, posting this did teach me how to define roman-style functions in $\LaTeX$ without \operatorname (which WordPress doesn’t support on their hosted blogs). If anyone cares, it’s \mathop{\mathrm{Op}}.