DIY Oscilloscope

For one of my projects I need to measure the frequency of an oscillator. I don't have an oscilloscope, and buying one is prohibitively expensive. I looked for alternatives, and I was intrigued to find a surprisingly full-featured and very inexpensive DIY oscilloscope kit made by JYETech; I got mine at NKC Electronics. The oscilloscope is built around an ATMega64 CPU running at 16Mhz. The oscilloscope can sample AC or DC signals up to 5M times/second, and has a variety of other nice features which cover a broad range of hobbyist uses.

This blog posts details my experience assembling and testing this oscilloscope kit, at revision 062.

This is an average complexity project, you'll need to be pretty comfortable with soldering in pretty tight spaces (around 1mm between leads). You'll need a good soldering iron, or even better a temperature controlled soldering station -- I use the XYTronic 379, which is excellent and sells for around $50 (click on any image below to see a larger version):

You'll also need the following tools:

• Rosin core solder
• Helping hands -- very helpful for holding the board while you solder some small components
• Flush cutter -- essential for trimming leads underneath the LCD to make it fit
• Long nose pliers
• Multimeter -- essential for testing intermediate voltages during assembly

The oscilloscope kit is tiny -- a little bigger than your palm:

In it you'll find the following (in clockwise order):

• Instruction sheet -- this is one piece of paper with URLs to more information online
• LCD screen
• Bottom- and Top- cover panels
• Mainboard
• Components

The mainboard comes with all surface mount components pre-soldered, which is really nice: some of these components are extremely tiny (a couple of millimeters), so soldering them would have been a nightmare.

Important note: the mainboard the revision number printed in the upper-left corner -- if you are following these instructions to assemble your own oscilloscope, make sure that you have the same exact version otherwise the steps may not match and you can damage the board!

The components can be grouped into categories as follows. First, we have the actual electronic components

• L7805CV voltage regulator (3-pins, with a screw attachment at the top)
• Heat-sink for L7805CV
• 1x 470uF capacitor
• 5x 100uF capacitors
• 1x 0.1uF capacitor (orange)
• 1x 100mH inductor (2 pins, round, no other markings on it)
• 1x 1N4001 diode (smallest component, white stripe at one side)

Then we have the switches and external connectors:

• 9x push-button switches with 9x white caps
• 3x slider switches (3 positions)
• 1x RCA input jack
• 1x power jack
• 1x RS-232 male connector
• 3x male connectors

The screws and pins that will hold everything together:

And, last but not least, the wires and connectors for the rudimentary probe you'll be using with your oscilloscope:

As I mentioned above, the documentation that comes with the oscilloscope is sparse, so you'll also want to open the following URLs in your browser, or print them out and have them nearby:

• Detailed parts list: this lists all the parts above along with the names referenced on the schematic.
• Assembly notes: this shows the final placement of the electronic components on the mainboard, referencing the parts by the names in the detailed parts list above.
• Voltage reference chart: this shows the expected voltages you should see on the board after you assemble it; very useful for testing your work before you finalize it, as well as visuall verifying the placement of parts.

There is also a helpful discussion board where you can search for answers or ask questions.

First, some definitions:

• The back of the board is the side that has all the chips and surface-mount components
• The front of the board is the side that will hold the switches and LCD later on

Start by installing components on the back of the board. The first component is the power adaptor. The leads are large, so you'll want to use a higher temperature on the iron and a fair bit of solder on the other side:

Take the voltage regulator and bend its legs using the long nose pliers at the joint:

Align the voltage regulator with the heat-sink, place the legs through the 3 holes at the top of the board, run the screw through the hole in the heat-sink (it is threaded, so you'll probably want to use a screw-driver), and put a washer on the other side. Solder it, then use the flush cutter to cut it as close as possible to the mainboard.

Take the diode and bend its legs using the long nose pliers as shown:

Place the diode on the mainboard in the D3 slot, with the white stripe towards the right (this is essential: the diode only works in one direction). Solder it:

Insert the 470uF capacitor as shown. This is the largest capacitor by size, so you can't miss it. The capacitor is electrolytic, so it's essential to get + and - correct: the capacitor has a grey stripe on it that indicates the - (negative) lead; the other lead is the positive lead. Insert the positive lead in the hole on the mainboard that has a square shape, and the negative lead in the hole that has a round shape. In this case, the grey stripe will be pointing down, towards the power plug:

Insert the other 5x 100uF capacitors as shown on the schematic. They are all the same size, so order doesn't matter, but placement, just like above, does matter. The capacitors are denoted on the schematic as C10, C14, C15, C16, and C32, along with the position of the + lead.

Important note: the C14 position is wrong on the schematic, you will want to put it in reverse, that is to say with the + lead towards the right, and the grey stripe (- lead) towards the left:

Bend the leads on the ceramic capacitor (orange) as shown:

Then place it on the right side of the board:

Install the probe connector opposite the power connector. Just like the power connector, it has large leads, so it will need more solder than usual:

Optional: install the RS-232 connector in the middle of the board. This connector can be used to hook-up the oscilloscope to a PC and take screenshots of its LCD. If you'll never need this feature, you can skip installing this, it will also make your life easier later when you install the LCD:

Short the leads across D4 (green wire, circled in the diagram below).

Important note: this step is missing from the official documentation:

It's now time to power-up the oscilloscope and do a preliminary test. You'll need a 9V DC power supply, where the jack is center-positive and outer-negative. Plug it in, and, using your multi-meter, measure the DC voltage at the "+5V" hole indicated with a red arrow in the image above. The multi-meter should read 5V DC. If it doesn't, something is wrong, the most likely causes are:

• You got the polarity wrong on one of the capacitors.
• You got the polarity wrong on the diode.
• One of your solder joints is loose.

Go back and carefully check your assembly, cross-reference with the schematic, and keep testing the voltage at the "+5V" hole above until it's right.

Once you get the voltage right, install another lead across the "JP1" connector, as shown below:

Check the "+5V" voltage hole again -- it should still read 5V DC. If it doesn't go back and check the capacitors and solder joints.

Now turn the board on its front and install the 9 push-button switches: their leads are springy, so they should snap into place, after which you can solder them. The orientation of the switches across their 4 holes doesn't matter:

Install the 3 slide-switches. Their leads are asymmetric, so they only fit in one direction:

You are now done with the mainboard for the time being. Pick up the LCD assembly and look on its back: you'll see a row of holes with labels:

Place the long strip of leads into these labeled holes, by inserting the shorter end into the holes (the longer end will go into the mainboard.) Solder them onto the LCD assembly, taking great care to keep the leads perpendicular to the LCD board, otherwise the LCD assembly won't fit right on the mainboard.

Important note: be sure to insert the strip of leads into the labeled holes, and not the other ones!

Important note: this is the hardest, most delicate part of the whole assembly. These holes are about 1mm apart, and the LCD board's holes are not pre-soldered. You need a steady hand and patience. The helping hands tool should come in handy here. A technique I found works reasonably well is to get one of the leads soldered correctly, holding the rest at the right position and angle; once you get that done, soldering the rest should be easier:

Solder the two other 2x lead strips at opposite ends of the row of holes opposite the one you just soldered. These leads are not electrical contacts, they just hold the LCD in place on the other side. Pay close attention to solder these in perpendicularly as well:

Using the flush cutter tool, cut one of the leads as shown in the image. This is because the hole into which it goes on the mainboard is obstructed by the heat-sink as shown:

Now solder the LCD assembly on the front side of the board. The LCD assembly can only go in one direction, don't force it.

Important note: you will need to use the flush cutter to cut all leads of components sticking out through the board behind the LCD very flush to the board, otherwise you risk shorting the LCD!

Screw together the two halves of the metal posts that will hold the panels above and below the mainboard. The shorter metal post goes on the front of the mainboard, the longer metal post on the back:

The final assembly should look like this:

Now comes the moment of truth: plug it in, and, if all is well, it will go through the boot sequence like this:

Place the white-caps on the push-buttons, and, using the 4 remaining screws, assemble the top and bottom panels like this. If you find that the push-buttons are sticky after installing the panels, either trim the white-caps with a knife, or loosen the screws a little:

You're almost done! The last step is to assemble the probe:

Strip the ends of the red and black wires -- these will connect to the alligator clips. Be careful to slide the shrink-wrap tube and alligator clip cover on each wire before finalizing the assembly:

Do the same with the larger black coaxial wire, and connect it to the RCA plug. Just like above be careful to slide the shrink wrap tube and RCA cover over the wire before finalizing the assembly. Connect the red wire to the inner coaxial lead (leading to the center jack), and the black wire to the outer coaxial lead (leading to the outer shield):

After everything is assembled, slide the shrink-wrap tubes over the connections and use a hair-dryer on high to shrink them into place.

Let's test that the oscilloscope can actual measure frequencies! Turn it on, and plug the probe into the RCA jack. Set the oscilloscope as follows:

• Using the SEC/DIV button, set it to "1ms"
• Using the LEVEL button, set it to "i"
• Using the V.POS button, and the +/- buttons, slide the Y level down towards the bottom of the screen

Now connect just the red alligator clip to the upper-left corner hole on the mainboard marked "500Hz/5V pp" (this hole is also marked on the top panel with the same indicator):

The oscilloscope should show you a 500Hz square wave:

You might consider getting a better probe, I like this one.

Enjoy!

No Impact Man

We watched "No Impact Man" a few days ago. I was really looking forward to the movie, as I've often thought about the same exact themes in my own life.

I found the movie to be informative, entertaining, but I also fell that it fell short in a number of important ways.

The basic idea of the movie is to ask if it's possible to live in such a way that you produce as little impact as possible on the environment around you. Impact is defined in a number of ways:

• Trash
• Personal transportation (= direct pollution)
• Food transportation, electricity generation (= indirect pollution)
• Buying stuff (= consumer culture, which also leads to direct and indirect pollution)

The movie explores how much we need in order to live a happy life vs. how much we want for the sake of convenience, or because modern society has conditioned us for to want it. The protagonist and his family take some of the following steps to reduce their impact:

• Don't buy new things as much as possible.
• Instead, buy old things that someone else no longer wants.
• For instance, no new clothes, buy all clothes used.
• This reduces direct impact (no packaging trash) and indirect impact (no resources consumed to produce new items).
• This is a reaction to modern consumer culture.
• Reuse things as much as possible.
• For instance, no kleenex (use a handkerchief), no toilet paper (use textile rags that can be washed and reused).
• This is a reaction to the culture of using something once and throwing it away.
• Buy food locally.
• Locally here is defined as a 250 mile radius around NY.
• This is a reaction to the fact that modern agriculture is very oil-intensive: food is produced using fertilizer (generally, oil-derived) and transported from far away (also using oil).
• Stop using electricity.
• Live by sun-light alone, use candles at night.
• Electricity generation is very dirty, more than 50% of electricity in the world today comes from coal.
• Don't drive anywhere.
• Bike or walk.

Overall, the family manages to pull through this year long experiment and find that their life, while radically changed in many ways, was still largely happy and enjoyable. For instance, they traded TV for more quality time with friends and family; they lost weight and got into much better physical shape from eating less sugar-rich highly-processed foods and biking/walking everywhere; and so on.

What the movie did not address, unfortunately, is that such a life-style, while possible, depends on a number of unstated assumptions:

1. Time. You need lots more time to walk everywhere, cook meals from raw materials (as opposed to buying them pre-processed), and so on. In my own life, time is a scarce commodity, even though I'm keenly aware of it and try to budget it carefully.
2. Money. You have to pay the rent, pretty much no matter where you live. The movie hardly explored the fact that the wife had a high-paying job that covered their bills, and allowed the husband to basically not work for a year and stay home to conduct this experiment (with all that entails).
3. Distance. To make such a lifestyle possible, you have to be able to walk or bike reasonable distances to get food, or to go to work, etc. This is possible in NY, since it's one of the densest cities in the world. This may not be possible in a more rural, or even less dense city somewhere else.
4. Luck. Trading the fridge turned out to be very difficult because their food spoiled fast. In my opinion, the family was lucky that they didn't get sick during the second half of the movie. They probably mitigated this by buying their food daily or every other day and not storing it over any length of time. This is possible, but requires even more time investment.

Some of these issues could be addressed by living on a self-sufficient farm -- a mostly closed-loop system that provides for most of your needs, without needing to go outside it for other stuff. It's much less clear to me if an impact-free life is possible in a modern urban environment, especially one that depends on fossil fuel for energy. After all, your food must come from outside the city, and for that you basically need oil for transportation.

Even with these shortcomings, the movie was still entertaining and informative. I liked the fact that the movie took a very optimistic tone and genuinely tried to look at these problems and see what solutions might exist.

The movie also highlighted the fact that one person's actions do matter. Many people get discouraged by the fact that they might be alone in a sea of other people who don't care or are unwilling to change, so why bother? The protagonist answers, and I agree: "Being optimistic [...] is the most radical political act there is."

In terms of our own life, it prompted me to think harder about what other changes could we make to reduce our impact:

• Could we reduce single-use items (like Kleenex, shaving cream cans) in favor of multiple-use items (like handkerchiefs, shaving soap)?
• Could we go to the farmers market down the street every week instead of buying so much packaged food at grocery stores?
• Could we reduce TV/Internet use in favor of other activities?
• Could we buy more stuff used (craigslist, antique stores, etc.) instead of new?

Given where we live and where my job is located, it is unlikely that I will be able to reduce the impact of transportation, at least for the time being. But I remain optimistic.

Diodes and demodulation

As we described before, a diode lets current flow in only one direction. This is essential for demodulation: the process of extracting information from a signal. To understand demodulation we need to first understand the first and simplest kind of radio transmission -- amplitude modulation.

The goal of radio is, ultimately, to transmit sound over very long distances. A band is playing in New York and I would like to hear it in San Francisco. One way to do this is to build a sound amplifier so loud that the sound waves themselves travel directly from the origin to my ear. This is obviously impractical: it would be intolerably loud at the origin and barely audible at the destination; furthermore, you could not have multiple radio stations broadcasting at the same time, they would all clobber each other in a cacophony of noise.

Another way to do this is:

• Convert the sound wave (anywhere from 1 Hz - 10 kHz) to another equivalent wave (measured in hundreds of kHz or even MHz).
• The equivalent wave, or modulated wave, contains the original sound wave information but in a different representation.
• The carrier wave is not audible to the human ear since it is in a totally different frequency spectrum.
• Sound waves travel by making the air vibrate. The amount of energy required to make air vibrate over long distances is enormous (think loud rock concert).
• Higher frequency waves are electromagnetic waves. They can travel much longer distances using much less energy.
• Once the modulated wave arrives at my radio's antenna, the radio translates this modulated wave back into a sound wave that I can hear. This is called demodulation, and it is made possible by diodes.

 Let's first see what a modulated wave looks like (courtesy of yourdictionary.com):

The carrier wave is basically the radio station frequency. When you tune into KFRC, you tell the radio to look for sound information embedded in carrier frequency 1550 kHz.

The modulating wave is the sound. This is what is embedded into the carrier frequency and, ultimately, the "information" we want to hear.

The modulated wave is the combined wave that travels from the radio tower to my radio. Visually, it roughly looks like a combination between the carrier wave and the modulating wave, which should hopefully agree with your intuition and some of the descriptions above.

Now, we wish to turn this modulated wave into sound. To understand how that works we need to first understand how a loudspeaker works, as shown on this diagram (courtesy of soundonmind.com):

• The magnet provides a fixed, constant magnetic field.
• The signal input provides the sound wave we wish to ultimately hear.
• When the signal input goes into the voice coil, the voice coil becomes an electromagnet.
• The voice coil's magnetic field "pushes against" the magnet's field, based on the strength of the signal input.
• The voice coil is attached to the diaphragm, which is basically a piece of cardboard.
• When the voice coil moves, the diaphragm moves, and pushes air to varying extents, generating a sound wave we can hear.
• If you've ever touched a loudspeaker that was playing music, you can actually feel the movement of the diaphragm with your fingers.

Let's step back and look at the complete picture:

• We have a modulated wave that contains the sound information embedded in a carrier wave. This modulated wave has very high frequency, measured in hundreds or thousands of kHz, so it is not audible by the human ear.
• We have a loudspeaker that can convert a wave into sound by vibrating a piece of cardboard.

What would happen if we feed the modulated wave directly into the loudspeaker? Think about it for a minute before reading on.

The answer is: absolutely nothing:

• The modulated wave has very high frequency, which means that the "peaks" and "throughs" come in rapid succession one after the other.
• When a "peak" arrives at the voice coil, it starts to move the voice coil out; this takes a bit of time, as the voice coil has to physically move in order to push the diaphragm and make a sound wave.
• However, a "through" quickly follows the "peak" and starts to pull the voice coil back in the opposite direction.
• The "peaks" and the "throughs" effectively cancel each other out as far as the diaphragm is concerned and no sound comes out the speaker.

What would happen if we feed the modulated wave through a diode first, and then feed the output from the diode to the speaker? A diode lets current flow in only one direction, so the modulated wave would basically be cut in "half":

Now, if we feed the demodulated wave into the speaker:

• The first peak will start to push the voice coil out.
• There is no through following this peak, simply an empty space, or "absence of signal".
• How is absence of signal different from a through?
• A through is a negative signal -- it starts to pull the voice coil in the opposite direction.
• Absence of signal is no signal -- the voice coil is left where it is will at most react based on its own inertia or the elasticity of the diagram.
• The next peak will start to push the voice coil further out.
• As you can see, the voice coil (and the attached diagram) react only to the peaks, in other words they both move according to a wave that follows the top of the peaks.

The wave that follows the top of the peaks is our original sound wave! Look back at the first diagram to see it, or just trace the peaks above with your finger.

The coil and diaphragm end up vibrating the air in accordance to the original sound wave, therefore producing sound we can hear. The diode demodulates the modulated wave back into sound we can hear.

My first month with a Mac

About a month ago I upgraded my company laptop from a Thinkpad to a MacBook Pro. Although I've used Apple computers in the past, it's never been my "main" computer or even close to it. I've always used Thinkpads as my work laptop and felt they were and still are exceptional laptops. I'm pretty proficient with the Mac now; I still miss the Thinkpad every so often, but overall I'm happy. Here are some of my impressions thus far from the transition.

My most important requirement for a computer is that it lets me be "productive". I define productivity as "doing my job as fast as I know how using the given tool". If the machine gets in the way (by being unreliable, slow, lacking software, etc.) then that's a deal breaker and I'm not interested. I don't have particular allegiances to certain companies or hardware manufacturers, so long as I can be productive. In that respect, the Mac got off to a surprisingly good start, and I can now safely say that I'm about 95% as productive on it as I used to be on my Thinkpad. I honestly did not expect this, so it was a rather pleasant surprise.

In terms of software, the applications I run most on my Mac are:

• Chrome = duh
• iTerm = SSH client
• TextMate = general purpose programming text editor
• OpenOffice = word processing, spreadsheet, presentations
• Eclipse/Android = work
• iTunes = streaming radio
• Picasa = photos
• VLC/QuickTime/Flip4Mac = media
  
• Skype = video conferencing
• Solitaire etc. = blow off steam

All these programs work almost flawlessly. I don't detect almost any difference from the Thinkpad, they run fast, they're reliable, they're as bug-free as they are on the PC.

The only application that took some work was iTerm -- I run Emacs in screen, and getting the keybindings to work was a bit painful. In particular, by force of habit I'd often hit Command+W to copy in Emacs, which would close the current tab. Fortunately, it's easy to re-bind the keys for any menu to some other key combination, so that's what I did. This is actually a remarkable feature of OSX, and one that I'm not sure exists on Windows -- you can specify any app and any menu entry in that app (by name), and then give it another key combination. Cool!

The main drag was getting used to the new key combinations. Command+{C, X, Z, TAB} all work the same and fairly intuitive for someone used to PCs. But that's where the similarities end:

• I used Home/PgUp/PgDn/End/Del a lot on the PC, and the Mac is inadequate here. Having to hit Fn+{Left, Right, Up, Down} just isn't the same. Not to mention that different apps interpret the key combinations differently, sometimes it recognizes Fn+, other times Command+.
• I still find it confusing to have to deal with Control, Alt, and Command. I know how they work, but I still have to think about it. Why do we need 3 keys to do what a PC does with just Control and Alt?
• Switching between applications is done via Command+TAB, switching between multiple windows of the same application is done via Command+~ Is this really necessary? Command+TAB should be enough IMO, why the extra aggravation?

Another minor drag is connecting an external monitor. I sometimes use an external digital monitor (DVI), other times an external analog monitor (VGA). Apple decided that they couldn't use a single connector for this, you need two dongles: one for DVI (DVI-D to be precise), and another for VGA. This is crazy. The mini-port can clearly put out both digital and analog signal, and DVI connectors are perfectly capable of relaying said signals. I suspect the reason Apple insisted on a DVI-D dongle is to speed the demise of VGA monitors. This is part of the general company culture (we know what's best for you, trust us), which I personally find patronizing.

Now that we got the bad out of the way, there's plenty of stuff to like:

• The touchpad is fabulous. Scrolling with 2 fingers, clearing the desktop with 4 fingers -- it's just beautiful. Furthermore, I simply could not use the touchpad on my Thinkpad, I always used the little red knob instead; the PC touchpad is so sensitive it's useless. The Mac touchpad simply works, and works well. If you've never tried to use one, I do recommend you try it.
• The laptop feels extremely sturdy and well built. I used to think that Thinkpads were the best built laptops out there, but the unibody design wins hands down. It's not even a comparison.
• The keyboard feels good, the screen looks beautiful. I'd say on par with the Thinkpad.
• The battery life is amazing. I get 4+ hours easily, which was never possible with any Thinkpad I've ever used. The magnetic power connector is really neat and has saved wire accidents a few times already.
• The wireless configuration just works. As soon as the laptop comes out of standby, it's connected to the wireless, which is fantastic (the Thinkpad used to take a good 15-20 seconds, which gets old fast). The laptop also knows to stay connected to the current SSID, unlike the Thinkpad which would switch between SSIDs seemingly randomly if more than one "preferred" network was in range (I guess they thought this was a feature?)
• Last but not least, going in and out of standby is remarkably fast and reliable -- it's almost instant ON/instant OFF. The Thinkpad would sometimes take 1 minute (yes, 60 seconds) to do this, and lock-up in the process. I've experienced this with every Thinkpad I've used.

All in all, I think the Mac has come a long way in the area I care the most about -- productivity. I would go so far as to say that if I had some Windows-only apps I needed to run, I'd run them in VMWare (which is very fast and nice to use on the Mac).


The Mac is a remarkable beautiful piece of engineering. The rumours are true, there's no laptop quite like it. It's also expensive, almost double the price of an equivalent Thinkpad. This is the reason I'd have trouble justifying the price if it came out of my own pocket. But I do love using it, and I can understand why some people never settle for less.

Vacuum Tubes

Part of the reason I worked on restoring this old radio is because I wanted to learn how vacuum tubes work, as well as how radio transmission works.

The simplest vacuum tube is a diode -- a device that allows current to pass only in one direction:

• Green element = the heater. This is a filament that gets hot when current flows through it. Its only purpose is to radiate heat onto the red element = the cathode.
• Red element = the cathode, or the emitter. This is a filament coated in a special substance that can emit electrons when it's heated up.
• Blue element = the anode, the collector, or the plate. This is a flat piece of metal which collects the electrons emitted by the cathode.

The key feature of the diode is that current can only go from red to blue, not the other way. In other words, if the heater is hot, then current can flow from red to blue as shown above. However, if we flip the polarity of the battery (the + would be connected to the red element), no current can  flow.

Notes:

1. The heater circuit operates at low voltage, around 5V.
2. The anode/cathode circuit operates at much higher voltage, frequently above 200V (in my radio, the anode/cathode rail goes up to 750V). This is because, even in a vacuum, the voltage has to be high enough to force electrons to jump across the small gap between the two leads. This high voltage makes older appliances dangerous, they can definitely kill you if you're not careful.
3. The reason tubes are vacuum'ed is because the air molecules get in the way of electrons "jumping" from the cathode to the anode.
4. All vacuum tubes "wear out" in time: the substance that covers the cathode is literally stripped away and eventually stops emitting electrons entirely. This is why vacuum tubes in old appliances had to be replaced every so often (typically measured in years, but it depends on how heavily the device is used).

This is it. All vacuum tubes are variations on this theme. They contain various additional elements that serve to amplify or dampen the flow of current between the cathode and the anode, but the basic principle is the same.

So why is a diode useful? Who cares that we have a device that lets current flow in only one direction?

To answer that question we need to look at the simplest form of radio transmission: Amplitude Modulation, or AM. More on that in the next post.

Radio Frankenstein

About 6 months ago I wrote the first post about my classic radio restoration project. The project is done, the radio is functional, but I somehow never got around to writing anything more about it. I'm going to try to fix that in the next series of posts.

I read a few useful guides on how to get started restoring an old radio. Bringing a radio up to life for the first time is risky-business, since the radio components can become compromised over time, and you run the real risk of burning up the radio (literally) if you're not careful.

The most useful I found was from Phil's Old Radios, recommending roughly the following:

• Spot gross defects first: leaks, stains, smells, etc.
• The electrolytic capacitors are probably dead: replace them.
• Use a variac to slowly turn the radio on.

At the high-level, my Philco was in reasonable shape: it was missing two vacuum tubes, but aside from that it wasn't leaking or showing other signs of gross physical damage.

I proceeded to test all the capacitors in the radio: there's about 10-15 of them total, so it's not that hard. The most important test for a capacitor is to verify that it's not shorted, in other words the resistance between its two leads should be infinite. Over time, electrolytic capacitors dry-up (literally), and as a result short circuit the leads, which can be catastrophic (it can burn up the power transformer, which is hard and expensive to replace).

My Philco has two kinds of capacitors:

1. Two very large electrolytic capacitors (8 muF each). These are visible on the top of the main board, and serve to smooth the DC coming out of the rectifier bridge. It is essential that these not be shorted as I explain above. Sure enough, when I measured them, one was shorted, and the other was on its way. I bough two replacement Sprague Atom's, disconnected the leads from the existing electrolytics and connected the new capacitors in place. Incidentally, the Spragues are very solid, high-quality capacitors, great to work with. Here's a sample:


2. Bakelite capacitors: these look like a little "vat" with 6-7 leads. Inside it are 2-3 capacitors, sealed in a hard, black, gunky insulator. Fortunately, none of the bakelites were bad, they all tested good on the multi-meter and, fortunately, ended up working in the end.

Serious radio enthusiasts try to "hide" the new capacitors inside the old electrolytics, in order to make the restoration even more authentic. This is a process called "re-capping", it works like this:

1. Use a Dremel to cut open the bottom of the electrolytic capacitor
2. Gut its contents, leaving an empty aluminum shell
3. Insert the new electrolytic capacitor in the old shell, solder each end to the two leads
4. Glue the bottom of the electrolytic back with epoxy glue

I got so far as step 2 above: the "gunk" inside my electrolytics was a very nasty, black, foul smelling tar-like substance that wouldn't come out no matter what. I read that some people use a hair-dryer to literally melt this stuff out of the shell, but I decided that was too much for me, so I just put the electrolytics back on the circuit board (without the bottom) and left it at that.

The next step was to replace the missing vacuum tubes. I got the complete set of schematics and repair bulletins from the excellent Philco Repair Bench. It was easy to detect that the two missing tubes were:

• Vacuum tube 80 -- the rectifier
• Vacuum tube 42 -- the power pentode

These are ancient tubes, in fact the names alone should give you an idea: the tube manufacturers simply started to count at 1 and worked their way up to around 100 or so, each number representing one type of tube. There were only a handful of tube manufacturers at the time (Philco, Tung-Sol, RCA), and they made a majority of all the tubes on the market.

I thought I'd be totally out of luck finding replacements for them. In fact, it turned out quite the opposite: there a vibrant community of old-timers who sell tubes like these for cheap. I was able to find both tubes for around $15. Not only that, but I was actually able to find them NOS = "New Old Stock", which means that the tubes were in mint condition, they had never been used! Imagine: these are tubes made 80 years ago and they still work. Here's what the rectifier looks like:


Notice how it says "Made in USA" on it. When was the last time you saw that printed on anything?

With both tubes in their sockets, now came the real test: turning on the radio. I don't have a variac, and I thought it too expensive to buy one. So instead I built a cheap home-made one: a dim-bulb tester. I first tested the radio with a large 100W bulb, and then with a smaller 45W bulb. In both cases the vacuum tubes slowly started to glow, and no weird smells or pops came out of the radio, so I decided it was safe to plug it directly into the wall.

Imagine my surprise and awe when, after 15 seconds of warm-up, the radio actually went on and started hissing! I kept a finger on the antenna lead, and was able to tune into a few AM radio stations (one was broadcasting a baseball commentary, and another had a show about aliens invading the earth).

A beautiful thing.

Shuffling tricks

I recently read this interesting article about an error in the EU Microsoft Browser Ballot. Briefly:

• In the EU, Microsoft must give users a choice of browsers in Windows.
• This is done via a message box with 5 top-choices (Firefox, Opera, Safari, MSIE, and Chrome), and a bunch of other intermediate-choices.
• The box should display the 5 top-choices in random order.

As it turns out, the order is not exactly random! For instance, MSIE is more likely than not to appear towards the right-end of the list, and Chrome towards the left-end.

The reason for this is programmer error, as described in the article. The programmer implemented the shuffle algorithm incorrectly by assuming that JavaScript uses QuickSort, when in reality it uses some other algorithm.

It turns out that shuffling is notoriously hard to get right.


Consider the following two simple shuffling algorithms:

1. For each entry Ex in the array: swap Ex with any other entry in the array.
2. For each entry Ex in the array: swap Ex only with entries after it.

Intuitively, it seems like either approach should produce a good shuffle. However, your intuition would be wrong: the first approach produces a non-uniform shuffle, while the second approach produces a uniform shuffle.

Better writers than I have explained how and why this happens. One good explanation of this is at Coding Horror: The Dangers of Naivete. The crux of the proof is:

• The total number of entries in a shuffle of n cards is n! (n factorial).
• The total number of arrangements of cards where you swap each card with any other card is n^n (n to the power n).
• n! does not divide evenly into n^n, so the shuffle cannot be uniform.

Prove to yourself that the 2nd algorithm above does not suffer from the problem described above. For extra credit, also prove that it is uniform.

In thinking about this problem, I was struck by one non-obvious fact: how can it be that, in the first (non-uniform) algorithm some configurations occur more than others? I mean, think about it:

• Start with an array in some order.
• For each element, randomly swap it with some other element.

Somehow, this makes it so that some configurations occur more often than others, and reliably so! Although the algorithm is random, somehow it favors certain configurations. This is quite surprising indeed. Really, spend a minute to let this sink in.

I haven't found a good "intuitive" explanation for why this favoritism happens. This explanation, from stackoverflow.com, comes close: "And that's the "intuitive" explanation: in your first algorithm, earlier items are much more likely to be swapped out of place than later items, so the permutations you get are skewed towards patterns in which the early items are not in their original places."

Magician-turned-statistics-professor Persi Diaconis has done a lot of very interesting work in randomness, nature, and our perception thereof. One interesting question he answered was: how many times do you have to shuffle a deck of cards so that it's "random"? Another is: how random is a coin flip, really? Both have surprisingly non-obvious and interesting answers.