Here is the easiest way to put video on an old analog oscilloscope that has "Z axis" inputs (usually on the back of the scope:
It uses an LM1881 integrated chip and nine other little components to display live video on an oscilloscope screen.
You'll need the following:
(3) 0.1uF caps
(1) 4.7Uf cap
(1) 1000pF cap
(1) 680k resistor
(2) 100k resistors
(1) LM1881 chip
(2) IN4148 diodes
Plus: an oscilloscope with a Z input; a video camera with a composite video out (usually a yellow RCA plug); two thin wires to go to Z input; a DC power supply that can be adjustable to +5vDC (you'll probably need around 3-4vDC); a composite RCA cable to run from camera to circuit; a breadboard or soldering iron; breadboard jumper cables; wires from power supply.
Here's my version on a breadboard. It's only 10 components but I used a lot of jumper cables to keep things simpler for me to see.
Below is a drawing of the end of the RCA cable coming from the video camera (or TV or VCR or DVD player or videogame console, etc.). The pointy tip is the positive signal. When you're all done you could run a ground wire from the ring/barrel negative part of the RCA plug--but I found it made zero difference on or off, so I'd leave it off.
You'll see nothing until you hook up the wires to the Z axis (intensity) of the oscilloscope. The picture was black and green, upside down and mirror-image flipped. I pointed the video camera at a TV set. Here is a Voltoren medicine commercial.
This photo is of a episode of The Three Stooges. It's hard to see in the photo, but it's the episode where Larry dresses in lady's clothing and tries to seduce members of the Nazi Upper Eschelon. Shown is "Admiral Boring" (Goering) giving the Hitler-salute to Reich's-Fuhrer Moe! It was a weird episode.
User caveats:
1. Use XY mode on the oscilloscope.
2. The black (negative) bands of the diodes should be closer to the LM1881 in the circuit path.
3. Z axis are not reversed, like other versions of this circuit in books. Z Axis + goes to the center pin tip of the RCA plug. Z Axis - goes to the ring/barrel/negative/ground of the RCA plug. When I reversed them I got no picture.
4. The camera (mine was a 1980s JVC) had to be "zoomed in" for this to work. I don't know why! If I zoomed out to wide-angle the circuit stopped working.
5. You only get a small portion of the video that the video camera sees!
6. I set the video camera exposure control to "+" for a brighter image.
7. With 3.6vDC to 4.1vDC I had much less noise in the video than running at 5vDC. Fiddle with the voltage.
8. The oscilloscope probes I used are newer ones that have 1x and 10x. Use the 1x setting, it got a much better signal for this usage. If your probes don't have a switch on them--they're probably 1x anyway.
Some random shots of my self-assembled Elenco kit power supply (from Amazon or eBay). My $5 HP analog oscilloscope from an antiques store/resale shop. The settings on the scope aren't exactly what I ended up using, but they're in the ballpark. As you can see my X and Y are actually A and B on the scope! There's also an unused horizontal input. The "Z axis" is in the back of this scope: so I ran two wires to the two screws in the back and have them wrapped around the front handle for easy access (instead of reaching behind this super heavy scope all the time).
I set the inputs to "DC" which gave a better image. I think "AC" worked by spread out the the signal and made it way worse. The "BW limit" was off (made a small difference). X vs Y setting. Scope was set to "CONV" which is the normal display setting on this scope (your scope probably won't even have that option). In the end my X and Y (or A and B) were BOTH set to ".2" on the knobs.
In the end I realized my dream of watching an episode of Columbo in Black and Green on an oscilloscope. My bucket list (other buying a new 2021 Ford Bronco) is pretty much complete.
This is one of the chickens that rampaged all over the neighborhood:
I hate breadboards, oscillating circuits never seem to work, so here is my point-to-point wired beauty:
Ground clips from oscilloscope probes went to gathered ground wires from the op amp (which actually came off the positive output pins!). Clipped the probes onto the legs of a couple of the ceramic capacitors to take a reading.
Connected the two 9 volt batteries together and then ran positive wire and negative wire from the appropriate free battery posts.
Simple layout:
Good old TL084 pinout. I think I actually used TL084ACN (newer version):
Resistor R1 = 13kΩ,
All other resistors are 10kΩ.
All the capacitors are 0.01µF monolithic ceramic capacitors.
At first I kept getting the 'flying hotdog' which in the report of Liu, Sprott, Wang and Ma they accepted as a valid output. I was only getting it when nothing else was responding. Here is a pic of it, but it's not cool or interesting:
This is where the awesomeness starts! I had to touch my finger to the negative 9v battery output to get this circuit ring (actually it's a jerk circuit, so maybe it jerks?). This is because I didn't put a potentiometer at the double 9volt battery supply. It was full +/- 9 volts.
It is close to a chaotic attractor associated with a type I class 3 eigenvalue patttern.
This mimics (well, gets close anyway to) another valid response according to Liu et al's paper. It rarely showed up, because I wasn't varying the power supply much:
Chaos is a steady-state behavior possible in any nonlinear continuous
system, if its order is above 2 in a forced circuit; or 3 in certain autonomous
circuits.
We're just waiting for the thunder storm to pass by.
This smart card reader sends and receives 13.56Mhz signals for Near Field Communication. To test it I put a little LED chip that lights up by harvesting 13.56Mhz energy.
I wanted to see these waves on my oscilloscope. I found one super simple way to sniff NFC signals and another that was almost as easy.
The first thing I did was plug my RFID smart card reader thing into a cell phone AC wall charger outlet. Luckily, that made the card reader constantly send out a continuous NFC signal. This way I didn't have to hook it up to a computer and keep clicking "read" to get a signal. Nice!
Next I turned my oscilloscope probe into a signal tracer antenna sniffer loop. How did I do this? I clipped the alligator ground clip to the tip of the probe. That's it! Oh, I also set the probe to 10x instead of 1x. That's not a big deal, but the readout on screen looked nicer, because I had the scope set to 10x for no particular reason I can recall.
Anyway, then on my Rigol oscilloscope I clicked "Clear" button and all of a sudden all 4 channels came on. I shut them off one-by-one except for channel 1. I must have had some weird settings leftover from last time I was playing with it, because after seeing nonsense information all of a sudden I was treated to this:
Big waves with tiny little waves jiggling around inside them. If you look at the center of the photo you'll see toward the bottom "Freq = 13.7MHz". This would constantly go from 13.56MHz to slightly above and below. There was my Near Field Communication signal from the card reader right on screen.
Then I thought, what if I used an actual antenna made for NFC--instead of my home made loop? So, I fished around in a junk drawer and phone a broken phone I found in the garbage that had an NFC antenna. This antenna is pictured below. It's actually technically not an antenna: it's an NFC and wireless charging induction coil.
As you can see by my drawings I took a multimeter and did continuity tests. It turns out the little copper connection boxes (which I arbitrarily numbered 1-7) aren't all connected.
Boxes 1, 2 and 4 connect to each other.
Boxes 3 and 7 connect to each other.
So, I hooked my oscilloscope probe tip and ground clip up: one went to 1 or 2 or 4; and the other went to 3 or 7.
When I slammed this induction sniffer onto the card reader I got a way cooler looking set of waves and the frequency readout at the bottom of the oscilloscope screen read 13.56MHz most of the time.
In this way I sort of proved that the smart card reader was putting out 13.5MHz waves, but also that the phone induction coil wasn't just self-resonating at 13.5Mhz: because my crappy sniffer loop in the first part of this experiment also gave me 13.5MHz.
If you have an oscilloscope that's 50-100Mhz you can do this too. However, older scopes that don't go up that high (I have many scopes that are under 10Mhz) won't show you 13.5MHz waves. I think you're supposed to have an oscilloscope that is rated about 5 times the signal you're trying to see. Theoretically, my oscilloscope would be just under this...but it still worked.
If you want to do this the correct way, you'd by a $9000 spectrum analyzer or one of those cool hand-held "RF Explorer" boxes that go up to 6GHz (GIG! not Meg) so like 6000MHz. RF Explorer has units that are weirdly advertised and named so you think you're getting a certain range of frequency, but it's not really that range. For this I think they have a model that's only $180 that would do the trick, for a little more you can get a 2.4GHz model to play with Wifi signals (but I don't think that model can go down to 13MHz. The RF Explorer units range from $120-$500 and up.
The best thing they have is a signal generator that can go up to 6GHz. I thought about getting one of those for doing this same stuff with WiFi signals, but my oscilloscope can't go up to the Gig range (only MHz). Then I came up with an idea: the router I used for my last post about lectennas puts out 2.4 and 5Ghz signals: just plug an ethernet cable into one port and then into another of it's output ports: create a loop back into itself: this creates a packet storm and plenty of WiFI waves flooding the room. This might also be a way to stress-test a WiFi system, lol: no anechoic chamber and spectrum generators needed.
Anyway, after clearing the settings the frequency stopped bouncing around from 60-100Hz and went to 13.5MHz, and cool waves appeared. Not sure why that didn't happen until I hit "clear" on the oscilloscope. Keep fiddling with buttons and sometimes stuff just works out!
Here's a phase portrait of a beautiful single scroll chaotic attractor from my oscilloscope! I was able to also confure up a multiple scroll attractor and also a teeny-tiny double scroll illustrating the classic chaotic circuit output. A Strange Attractor is when a bounded chaotic system has some kind of long term pattern that isn’t a simple periodic oscillation or orbit.
Here is how two superimposed attractors form the famous double-scroll attractor:
Here is a video:;
Nice Mobius strip attractor, the only possible attractors in this pattern are limit cycles:
Here is a multile limit cycle attractor as it adds more ovals to become a single scroll chaotic attractor.
My oscilloscope settings for my "newer" scope. There is a progression from steady state to limit cycle to chaos and bifurcation. Steady state is a dot; an oval signifies a 1 period limit cycle; multiple overlapped ovals show 2 or 3 or 4 limit cycles; once the ovals are plentiful and have a sort of inverted rounded pyramid shape (like mine above) it's a single scroll chaotic attractor. The famous double scroll chaotic attracot can have two appearances depending on your setup and equipment: the single chaotic attractor with some extra, lighter ovals underneath it; or sort of a figure 8 shape.
The circuit build is towards the bottom of this post. Chua's Circuit is basically an oscillator that outputs waveforms that never repeat: chaos! Chua's Circuit is the simplest circuit that can output real chaos. Chaos in the form of a double swoosh set of circles on an oscilloscope screen. This waveform is called an attractor, which demonstrates chaos in a continuous time dynamical system...I like the idea of a waveform generator / oscillator that never repeats. A continuouly evolving, periodic output that never repeats: chaos! What defines chaos in a system like this: extreme sensitivity to initial conditions; cause and effect are not proportional; and it is nonlinear. This circuit will also display bifurcation: small, smooth changes lead to a sudden huge change in the system. Tuning a silent radio with a knob that you're barely moving, you keep trying to nudge the timing knob and you all of a sudden loud music starts playing. Or slowly as possible applying more pressure to a mousetrap until it springs shut. The straw that broken the camel's back. We will make it less simple by replacing the supposedly hard to find, but definatly hard to choose thet correct value for inductor-with a gyrator circuit which acts as an ideal inductor. Just a couple extra cheap parts and it still works.
First off when looking at schematics to build your very own Chua Circuit you need to ignore 99% of the useless schematics out there. The schematics you'll see are for explaining this circuit, but not building it. Here is an example of the classic circuit...that doesn't tell you what you need to know:
You will see on the left side an "L". That denotes a simple 18mH inductor. These inductors are sort of hard to find. You could try and swap in and out various 18mH inductors with less than 30 ohms resistance and play around with that. They are pricey and might not be exactly the spec your circuit needs to operate. We will replace the "L" with a TL082 op-amp acting as a gyrator inductor simulator. It works like an inductor (in this circuit at least) and operates ideally. Simple! The gyrator is known as "The Fifth Linear Element" and basically couples voltage from one source to the current from a different source...and then does the same with the remaining devices' current and voltage. Once working I plan on replacing the gyrator with an actual inductor, since I just found a pile of different sized ones in a drawer. An actual inductor will add parasitic resistance that will have to be counteracted in the circuit. You will see on the right side of the circuit "NR". That is Chua's Diode...except that there is no such thing as a Chua Diode. You can't buy one in a store, you have to make it. Luckily we can make our own Chua Diode using a second TL082 op-amp. There are versions of this circuit which leave the inductor and replace this Chua diode with a memristor, but it involves more potentiometers (knobs) than this way. You will soon learn of my hatred for wiring pots. Anyway Chua’s diode has nothing in common with a diode; it has a non-linear voltage-current characteristic that makes the oscillator output “unrepeatable”.
Then we'll add in some resistors, capacitors (use metal film, not carbon, for best results), a couple of knobs (potentiometers), and a DC power supply instead of two 9v batteries oddly wired together in many of the circuit designs. The only other fancy "thing" I've made has been a scanning tunneling electron microscope. This project is very similar in that it used op-amps and the x, y and z inputs on an old oscilloscope. Because this is low voltage you can use a PC computer-based oscilloscope without blowing stuff up-as long as it can handle 9vDC. However if you use a modern fancy standalone digital oscilloscope the swooshing waves of the the output (a Chaotic Attractor) turns into swarms of ugly dots that are really hard to interpret. After the annoyance with the schematic above I became annoyed with the build schematics I found for one simple reason: they show 4 triangles that are op-amps. So, I assumed I needed four op-amps, but the TL082 is a double-op-amp: each black box with 8 legs (pins) sticking out actually has twotriangles inside of it. Four triangles on the schematic = two TL082 op-amps. Nice. Also, the schematic didn't label the triangles as being A/B pairs. Which I'm not used to. So, when I scribble out my diagrams I'm labeling them A and B. One A/B triangle pair is a single TL082. This will make total sense once you read the next few lines and check the pinouts. So, the first thing to get straight is the op-amp circuits. While it might look like we'll be using four TL082 circuits we're really only using two of them!
Here's a simple pinout that is for a different op-amp, but which has the same pinout as a TLN082, but it's drawn better. It's much easier to see how each little TL082 microchip is actually a double op-amp. One amp is "A" triangle and the other is "B" triangle. Look at this and the build schematic will make sense:
You can see that there is an "A" op-amp, and a "B" op-amp. A = pins 1, 2 and 3. B = pins 5, 6 and 7. Pins 4 & 8 power the entire TL082 (both A and B together). Inverting inputs are negative (-) inputs. Non-inverting inputs are positive (+) inputs. So, in the schematics for Chua circuits (done without an inductor, using a gyrator instead) you will see four triangles. They represent the A & B portions of only two TL082 op-amp circuits. You will see two triangles near each other, and two other triangles paired up on the other side of the schematic. Each pair of triangles near each other represents a single TL082! You must treat each triangle as an A or B regarding pins. Decide which triangle in a pair is the "A triangle" and which is the "B triangle". Anything that goes to the A triangle will only use pins 1, 2 and 3. Anything that goes to the B triangle will only use pins 5, 6, and 7. Pins 4 and 8 get the input from your power supply/batteries. It doesn't really matter which triangle those go to, but for simplicity we'll put the 4/8 power to the "A" triangles. So, on the left side of the circuit where we are not using an inductor, but building a gyrator instead we have two triangles. Left Side of Schematic-Gyrator Inductor Simulator Triangle A is on the right: Pin 1 = OUT A Pin 2 = Inverting Input A (negative -) Pin 3 = Noninverting Input A (positive +) Pin 4 = Negative Power Supply input Pin 8 = Positive Power Supply input Triangle B is on the left: Pin 7 = OUT B Pin 6 = Inverting Input B (negative -) Pin 5 = Noninverting Input B (positive +) There, now you have all 8 pins on one of the TL082 op-amps wired up! Right Side of Schematic-Chua Diode Triangle A is on the right: Pin 1 = OUT A Pin 2 = Inverting Input A (negative -) Pin 3 = Noninverting Input A (positive +) Pin 4 = Negative Power Supply input Pin 8 = Positive Power Supply input Triangle B is on the left: Pin 7 = OUT B Pin 6 = Inverting Input B (negative -) Pin 5 = Noninverting Input B (positive +) There, now you have all 8 pins on your second TL082 op-amps wired up! BREADBOARD WIRING Wire Jumpers:
c18-c24
e18-f19
g19-g25
e21-f21
he21-h24
d23-d29
e29-f29
i26-i32
j28-j29
c25-c31
h32-h39
h42-h49
g48-g49
i48-i54
e49-f49
h52-h56
c48-c52
d49-d53
b51-b55
a55-a56
f56-f57
d3-g3
j50 to right power right outside
left power rail inner to b3
left power rail outer to a54
left power rail outer to a26
j50 to right power rail outer
j10 to right power rail inner
j51 to right power rail inner
left power rail outer to a10
j23 to right power rail inner
left power rail inner to b3
i3 to right power rail outer
left power rail outer to a54
left power rail outer to a26
j50 to right power rail outer
j10 to right power rail inner
j51 to right power rail inner
left power rail outer to a10
j23 to right power rail inner
TL082 Chips
Top of chip (with half circle dimple) pins 1 and 8: e23 and f23
Top of chip (with half circle dimple) pins 1 and 8: e51 and f51
Capacitors (film metal not ceramic)
10nf j42 to right power rail outer
100nf a21-a25
100nf j26 to right power rail outer
LEDs
left power rail inner to to a13
j13 to right power rail outer
Batteries
9v Battery 1: red positive to c3 / black negative to c10
9v Battery 2: red positive to h10 / black negative to h3
Ground wire for oscilloscope probe ground clips
right power rail outer (last bottom, right hole)
Oscilloscope probe to leg of capacitor sticking out of hole j26
Oscilloscope probe to left of capacitor sticking out of hole j42
Potentiometers/Trim Pots
Pot 1: middle pin b31 / either other pin left power rail innter / 3rd pin unused
Pot 2: middle pin f39 / either other pin f42 / 3rd in unused
The left side of the breadboard usually has positive and negative...but in this circuit both columns are negative.
The right side of the breadboard is positve on inner column, negative on the outer column closest to the edge of the board.
10k linear potentiometers are recommended because they're easier to turn and are more precise. I used 10k trim pots with are less precise and have to be turned with a screwdriver--bad choice!
Connect the two halves of the circuit with some wires, knobs, outputs to oscilloscope or a USB PC computer-based oscilloscope (with a huge resistor on the outputs so you don't fry your computer or digital scope) and you're good to go. I have real oscilloscopes that are analog/tube and can handle high voltage inputs. Your digital and computer PC scopes might blow up if you try and put more than 3v into them. Read your specs. This thing basically has two 9vDC input spots that may total 18vDC if you mess things up. As always my nemesis is the humble potentiometer (volume knob). On some projects you need to use all 3 pins, but some only 2...and the circuit schematics almost never tell you which. Is it a voltage divider (might be 3 pins) or is it a current adjuster (2 pins?) or is it a volume knob for audio (3 pins?) or a variable resistor (2 pins!)? ************On the most popular "fritzing" diagram for Chua circuits they show 3 wires going to the potentiometers but in the explanation 8 pages later they state that the third wire isn't wired to anything, it's just there to physically keep the pot from moving on the table as you spin the little knob!!!!!!!!!!!!!!!!! I'm so annoyed I spent so much time trying to figure out why/where that third wire was going to!!!! Use only two wires for your Chua circuit pots/knobs: the middle one and one on either side.
I had similar issues with my scanning electron microscope build: five pots labeled V1-V5 for variable resistor, and one of them showing connection to: ground, -negative voltage (which in a DC circuit is the same as the ground) and then the incoming wiper wire from ??? Ugh! Anyway, here we go: PARTS
Analog oscilloscope with two probes (or three if you use the "z" input on the back too). Or coax cables with fittings at one end (probably RG-58 BNC-connector 50ohm) to plug into analog scope inputs, and cut off the other ends to hook to the Chua Circuit. Or you could get some BNC female sockets and put them in your Chua's Circuit...but short lengths of coax wire with BNC connectors are super cheap on Amazon and eBay, so I buy them and cut them in half quite a bit: each coax cable cut in have gives me: two BNC to bare-wire cables. BNC plugs into oscilloscope or function generator or Geiger counter, etc. and the other end I solder to whatever circuit I'm building. Some of them were 75ohm, and some were even old 1970s cable TV wires that weren't marked. Whatever.
Bits of wire, wire strippers, solder and iron if you're going to not use breadboard.
Two 1M resistors only if hooking up to digital oscilloscope
or computer. Old analog oscilloscope don’t need them.
Just hook old analog oscilloscope probes to Capacitor 1 and
Capacitor 2 (the two near each other) and then ground the probe ground clips to
-9vDC (black) on the side rail of the breadboard.
This will be my first ever breadboard project, so I’ll be
following Valentin Siderskiy’s instructions pretty much step-by step, but adding my own
clarifying notes. Such as: you can leave a wire off of each potentiometer, they
only need two in this circuit! Or the ever popular "I think LEDs are polarized so you have to stick them in the right way or they won't light up."
Also, you could easily (I think) leave off: On/off switch; Two LEDs; Resistors for the LEDs; Two more resistors that just smooth down the 5k pots to 2.5k--but then you'd need to probably buy actual 2.5k pots. Dumbing down 5k or 10k pots to only 2.5k makes it easier to make slight adjustments to the circuit while turning the knobs. Since this is my first breadboard I'm going to leave all that stuff in--when I point-to-point wire it up I'll be able to actually tell how to leave them off without breaking connections. I still think in "point-to-point" and not breadboard or circuit board layouts. Running the circuit I used a couple different oscilloscopes. One had 3 inputs: channel a and b (verticals) and a horizontal channel. I just used a and b and set the dial for A vs B to plot the voltages against eachother to get the single scroll chaotic attractor. This gave the same results as my older oscilloscope with a single vertical and single horizontal input (x vs y). The slightest turn of the potentiometers resulted in HUGE changes to the image on the oscilloscope. This is called bifurcation. One of my potentiometers measured only 1.3k instead of 10k when tested on a multimeter: so I replaced it and immediately got better results. I'll probably invest in two full sized pots with convenient knobs to twist. I had two old mismatched batteries, I'll add new ones. When I unhook the oscillscope ground clips from the ground wire the whole circuit becomes very sensitive to hand movements. Bifurcation was observed: tiny, smooth changes to a paremeter (knob twist) results in huge changes to the output (dot turned into a chaotic attractor). Hysterisis (like my previous post about neon lamp bulbs) was observed: the spot where the chaotic attractor turns on is different from where it turns off--plus there's two knobs that influence eachother. Unplugging the inside leg of the 10nf capacitor gave an extremely small, single trace of the famous double scroll attractor. It was very low resolution: it looked like a number "8" written in Old English font! Here are some attractors that resulted when I changed one, then both of the pots from 10k to 5k:
Here are some sweet toroidal Class 1 Eigenvalue = 10 (sort of) attractors.
Here are some results after putting in two 5k pots, then replacing one of the batteries with a 9vDC power supply...but varying the DC voltages from around 1.3vDC to 10vDC:
Here is the shape you see right before the classic double scroll: I was playing with the voltage (I replaced one of the 9v batteries with a DC bench power supply and going from 1.3vDC to 10vDC. One of the IC chips was getting pretty warm though):
It's a homoclinic bifurcation, the periodic orbit grew units it collided with the saddle point.
Multiscroll attractor:
You can see how this double-double scroll attractor developed from multiple loops:
The Logusz Attractor (double-double or chaotic quad-attractor as I'm thinking of naming it)...although it's actually pretty close to what others have found as a projection of the Vc2 / IL plane or the Vc / IL1 plane. The literature on this and others:
Anshan, H. [1988] "A Study of the Chaotic Phenomena in Chua's Circuit," Proceedings of 1988 IEEE International Symposium on Circuits and Systems (Cat. No.88CH2458-8). IEEE. vol.1, pp.273-276.
Bartissol, P., Chua, L.O. [1988] "The Double Hook (Nonlinear Chaotic Circuits)," IEEE Transactions on Circuits & Systems, vol.35, no.12, pp.1512-1522.
Anshan in particular backs up what I discovered myself: op-amp voltage adjustments can lead to lots of new patterns and attractors. Of course he found this out in the 1980s--and I'm just playing around in my basement as something to do besides mow my lawn...it's nice to see my "weird" non-perfect, non-double scroll attractors have actual mathematical explanations in eigenvalues (weird math) but also voltages.
Great sources of information that I ripped off:
Professor Leon Chua, the inventor of this chaotic circuit.
"Jim" who made http://www.chaotic-circuits.com/
Valentin Siderskiy, Vikram Kapila and Aatif Mohammed of http://www.chuacircuits.com and published
papers and a great Instructable post. Check out "Chua's Circuit for experimenters using readily available parts from a hobby electronics store".
"Chua’s Circuit for High School Students" by Gandhi, Gauruv.,
Muthuswamy, Bharathwaj2 and Roska, Tamas.
This list of awesomeness; hover your mouse over the titles and you can click and be rewarded with actual PDFs of the articles (and not just crummy citations): http://people.eecs.berkeley.edu/~chua/circuitrefs.html
