Say It With Me: Aliasing

March 23, 2017 by Elliot Williams 28 Comments

Suppose you take a few measurements of a time-varying signal. Let’s say for concreteness that you have a microcontroller that reads some voltage 100 times per second. Collecting a bunch of data points together, you plot them out — this must surely have come from a sine wave at 35 Hz, you say. Just connect up the dots with a sine wave! It’s as plain as the nose on your face.

And then some spoil-sport comes along and draws in a version of your sine wave at -65 Hz, and then another at 135 Hz. And then more at -165 Hz and 235 Hz or -265 Hz and 335 Hz. And then an arbitrary number of potential sine waves that fit the very same data, all spaced apart at positive and negative integer multiples of your 100 Hz sampling frequency. Soon, your very pretty picture is looking a bit more complicated than you’d bargained for, and you have no idea which of these frequencies generated your data. It seems hopeless! You go home in tears.

But then you realize that this phenomenon gives you super powers — the power to resolve frequencies that are significantly higher than your sampling frequency. Just as the 235 Hz wave leaves an apparent 35 Hz waveform in the data when sampled at 100 Hz, a 237 Hz signal will look like 37 Hz. You can tell them apart even though they’re well beyond your ability to sample that fast. You’re pulling in information from beyond the Nyquist limit!

This essential ambiguity in sampling — that all frequencies offset by an integer multiple of the sampling frequency produce the same data — is called “aliasing”. And understanding aliasing is the first step toward really understanding sampling, and that’s the first step into the big wide world of digital signal processing.

Whether aliasing corrupts your pristine data or provides you with super powers hinges on your understanding of the effect, and maybe some judicious pre-sampling filtering, so let’s get some knowledge.

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How Does A Voltage Multiplier Work?

March 22, 2017 by Manuel Rodriguez-Achach 43 Comments

If you need a high voltage, a voltage multiplier is one of the easiest ways to obtain it. A voltage multiplier is a specialized type of rectifier circuit that converts an AC voltage to a higher DC voltage. Invented by Heinrich Greinacher in 1919, they were used in the design of a particle accelerator that performed the first artificial nuclear disintegration, so you know they mean business.

Theoretically the output of the multiplier is an integer times the AC peak input voltage, and while they can work with any input voltage, the principal use for voltage multipliers is when very high voltages, in the order of tens of thousands or even millions of volts, are needed. They have the advantage of being relatively easy to build, and are cheaper than an equivalent high voltage transformer of the same output rating. If you need sparks for your mad science, perhaps a voltage multiplier can provide them for you.

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Negative Resistance: It Shouldn’t Make Sense!

March 21, 2017 by Jenny List 55 Comments

When you leaf through a basic electronics textbook, you’ll find chapters describing in detail the operation of the various components. Resistors, capacitors, inductors, and semiconductors. The latter chapter will talk about P and N type regions, introduce us to the diode, and then deal with the transistor: its basic operation, how to bias it, and the like.

A tunnel diode amplifier circuit. Chetvorno [CC0]

Particularly if your textbook is a little older, you may find a short section talking about the tunnel diode. There will be an odd-looking circuit that seems to make no sense at all, an amplifier formed from just a forward-biased diode and a couple of resistors. This logic-defying circuit you are told works due to the tunnel diode being of a class of devices having a negative resistance, though in the absence of readily available devices for experimentation it can be difficult to wrap your head around.

We’re all used to conventional resistors, devices that follow Ohm’s Law. When you apply a voltage to a resistor, a current flows through it, and when the voltage is increased, so does the current. Thus if you use a positive resistance device, say a normal resistor, in both the top and the bottom halves of a potential divider, varying the voltage fed into the top of the divider results in the resistor behaving as you’d expect, and the voltage across it increases.

In a negative resistance device the opposite is the case: increasing the voltage across it results in decreasing current flowing through it. When a large enough negative resistance device is used in the lower half of a resistive divider, it reduces the overall current flowing through the divider when the input voltage increases. With less current flowing across the top resistor, more voltage is present at the output. This makes the negative resistor divider into an amplifier.

The tunnel diodes we mentioned above are probably the best known devices that exhibit negative resistance, and there was a time in the early 1960s before transistors gained extra performance that they seemed to represent the future in electronics. But they aren’t the only devices with a negative resistance curve, indeed aside from other semiconductors such as Gunn diodes you can find negative resistance in some surprising places. Electrical arcs, for example, or fluorescent lighting tubes.

A typical negative resistance I-V curve. Chetvorno [CC0]

The negative resistance property of electric arcs in particular produced a fascinating device from the early twentieth century. The first radio transmitters used an electric arc to generate their RF, but were extremely inefficient and wideband, causing interference. A refinement treated the spark not as the source of the RF but as the negative resistance element alongside a tuned circuit in an oscillator, These devices could generate single frequencies at extremely high power, and thus became popular as high-powered transmitters alongside those using high-frequency alternators until the advent of higher powered tube-based transmitters around the First World War.

It’s unlikely that you will encounter a tunnel diode or other similar electronic component outside the realm of very specialist surplus parts suppliers. We’ve featured them only rarely, and then they are usually surplus devices from the 1960s. But understanding something of how they operate in a circuit should be part of the general knowledge of anyone with an interest in electronics, and is thus worth taking a moment to look at.

1N3716 tunnel diode header image: Caliston [Public domain].

How To Use A Photo Tachometer

March 17, 2017 by Lewin Day 20 Comments

If you’re into anything even vaguely mechanical on the broad hacking spectrum, you’ve come into contact with things that spin. Sometimes, it’s important to know precisely how fast they are spinning! When you’ve got the need to know angular speed, you need a device to measure it. That device is a tachometer. And the most useful tachometer is the non-contact photo-tachometer.

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Are You Down With MPPT? (Yeah, You Know Me.)

March 17, 2017 by Elliot Williams 41 Comments

Solar cells have gotten cheaper and cheaper, and are becoming an economically viable source of renewable energy in many parts of the world. Capturing the optimal amount of energy from a solar panel is a tricky business, however. First there are a raft of physical prerequisites to operating efficiently: the panel needs to be kept clean so the sun can reach the cells, the panel needs to point at the sun, and it’s best if they’re kept from getting too hot.

Along with these physical demands, solar panels are electrically finicky as well. In particular, the amount of power they produce is strongly dependent on the electrical load that they’re presented, and this optimal load varies depending on how much illumination the panel receives. Maximum power-point trackers (MPPT) ideally keep the panel electrically in the zone even as little fluffy clouds roam the skies or the sun sinks in the west. Using MPPT can pull 20-30% more power out of a given cell, and the techniques are eminently hacker-friendly. If you’ve never played around with solar panels before, you should. Read on to see how!

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Fire Hazard Testing

March 15, 2017 by Anool Mahidharia 28 Comments

How do you know that new appliance you bought won’t burn your house down? Take a look at any electrical appliance, and you’ll find it marked with at least one, and most often, several safety certification marks such as UL, DIN, VDE, CSA or BSI. Practically every electrical product that plugs into utility supply needs to go through a mandatory certification process to ensure it meets these conformity test requirements. Some examples include domestic and industrial electrical appliances, tools, electrical accessories, consumer electronics and medical electronics.

When you look through a typical safety test standard, you’ll notice it breaks down the various tests in two categories. “Type” tests are conducted on prototypes and samples of the final product or its individual parts and components, and are not generally repeated unless there are changes in design or materials. “Acceptance” tests are routine verification tests conducted on 100% of the products produced. For example, a typical Type test would be used to check the fire retardant properties of the plastics used in the manufacture of the product during development, while a Routine test would be carried out to check for high voltage breakdown or leakage and touch currents on the production line.

Nowadays, a majority of countries around the world adopt standards created by international organizations such as IEC, ISO, and ITU, then fine tune them to suit local requirements. The IEC works by distributing its work across almost 170 Technical Committees and Subcommittees which are entrusted with the job of creating and maintaining standards. One of these committees is “TC89 Fire hazard testing” whose job is to provide “Guidance and test methods for assessing fire hazards of electro-technical equipment, their parts (including components) and electrical insulating materials”. These tests are why we feel safe enough to plug something in and still sleep at night.

Practically all electrical products need to confirm to this set of tests as part of their “Type” test routine. This committee produces fire hazard testing documents in the IEC 60695 series of standards. These documents range from general guidelines on several fire hazard topics to specific instructions on how to build the test equipment needed to perform the tests. It’s interesting to see how some of these tests are carried out and the equipment used. Join me after the break as we take a look at that process.

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The God Particle

March 13, 2017 by Will Sweatman 56 Comments

The Greek philosopher Plato is well known for his allegories and metaphors. Of particular interest is his Allegory of the Cave, which appeared in The Republic, written around 380BCE. In it, Plato describes a group of prisoners which are chained to a wall within a cave, and have been all of their lives. They have no direct interaction with the world outside of the cave. They only know of the world via shadows that are cast on the wall opposite of them. For the prisoners, the shadows are their reality. Though you and I know the shadows are only a very low-resolution representation of that reality.

standard_01 — Plato’s “Allegory of the Cave”, drawing by Markus Maurer

Theoretical physicist Steven Weinberg, a Nobel Prize winner who works out of the University of Texas at Austin, once likened himself to a prisoner in Plato’s cave. We are forever chained to this cave by the limitations in measurements we can make and experiments we can perform. All that we can know are shadows of the reality that exists in the sub-atomic world. We can see the shadowy figures lurking in our math and as wisps of misty vapor trails in our cloud chambers. We attempt to pierce the veil with the power of our imagination and draw nifty looking charts and animations depicting what our mind’s eye thinks it can see. But in the end, we are all trapped in a cave… staring at shadows. Reflections of a reality we can never truly know.

In our last Quantum Mechanics article, we introduced you to the idea of quantum electrodynamics, or to put it more simply — quantum field theory. In this article, we’re going to explore how QED lead to the prediction and eventual confirmation of something known as the Higgs Boson, also known as the God Particle. As usual, we’ll aim to keep things as simple as possible, allowing anyone with a curious mind to know what this God particle talk is all about. Like so many things in the quantum world, it all started with an unexpected outcome…

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