Electronics > Beginners
Hitting the ground running
rstofer:
--- Quote from: 0culus on March 26, 2019, 09:58:43 pm ---Haha, thanks. I'm one of those weird people who does math for fun. :-DD My personal favorite courses of my math degree were complex analysis and differential geometry. I'm looking forward to flexing those muscles again.
As to doing all that with a slide rule, my hat is off to you, sir. :-+
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Here's a project that will tie together math, op amps and general electronics. But it's the math that is fun.
Breadboard up a couple of 1 second integrators (from op amps) using 1 ufd capacitor and 1M Ohm resistor. You need two. Then breadboard up a couple of summer/inverters and use some kind of toggle switch to set the initial conditions of an analog computer simulating damped harmonic motion.
Hint: Lord Kelvin's method works well. He was an absolute genius re: analog computing based on his brother's mechanical integrator. Isolate the highest derivative on the left and divide out the coefficient. Then, assuming you actually have the second derivative, use integrators, summers and potentiometers to build the right hand side. Then we have the MAGIC of the '=' sign: Take what was created on the right hand side and route it back to the first integrator as y'' because the '=' sign shows we just created y''. Absolute genius!
See attached PDF of MATLAB Simulink implementation of Damped Harmonic Motion.
Since the op amps are inverting, that -1 inverter comes free with the summer ahead of it. The damping and spring constants are just potentiometers.
The point of the exercise is to use op amps as they were intended: Operational Amplifiers. Analog computing and, of course, the solution of certain types of differential equations. And modeling the rocket nozzle controls of the Atlas missile. That was kind of important... We can't have the thing falling down! Car suspensions use a similar equation - probably dolled up to consider physical limits and so on.
See Vernier Rocket:
https://www.grc.nasa.gov/www/k-12/rocket/rktcontrl.html
I had nothing to do with the Atlas control system but my Control Systems instructor did!
You can see my first analog computer here:
http://www.analogmuseum.org/library/vogel_schaltplan.pdf
http://www.analogmuseum.org/library/vogel_ar_beschreibung.pdf (German but easy to translate from context)
BTW: The Vogel Analog Computer has enough resources to work the Predator-Prey problem.
That ought to keep you busy!
rstofer:
--- Quote from: Phuzzy112 on March 27, 2019, 10:31:19 am ---Oh, that looks like a winner! I think I will be placing an order for that book pretty soon. The components though... not sure. The full bundle costs more than some of the secondhand kit I have been eyeing so I will probably have to cherry-pick the designs I want to tinker with and order just those.
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I would look a couple of labs ahead and order what I needed. I might pay extra in shipping but DigiKey offers Priority Mail and it's only about $7 and it's FAST!
As to learning AC (mentioned above), you can learn a lot with a simple variable frequency sine wave generator, a resistor and capacitor. Maybe pick the values for a 100 Hz low pass filter (calculators all over the Internet). Use at least a 1k resistor to protect the generator. Remember: At high frequencies, that capacitor will look like a short circuit. The resistor protects the generator.
Now, hook up the low pass filter and measure the voltage across the capacitor as you measure frequency (how?). Plot the results with Excel (or anything else) and you have some idea of the impedance of the circuit versus frequency.
Now reorganize the circuit into a high pass filter and measure the voltage across the resistor. Overlay the first plot.
Now cascade the low pass and high pass filter (second schematic here)
https://www.electronics-tutorials.ws/filter/filter_4.html
In the end, you will understand where the breakpoint is and if you can plot the frequency on a log scale, you will have a real Bode' plot.
Everything in AC is based on impedance which is usually a function of frequency.
There's a lot to learn from a couple of resistors and capacitors.
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