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Home Brew Analog Computer System

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GK:
One of the synchronizer scopes I have in mind used polar coordinates of sorts to indicate the beat between a ref. frequency and a signal input.

My 3-D projective unit could be used to produce spherical polar coordinate displays.  It would just be a simple matter of first transforming the spherical polar coordinates to Cartesian ones:

http://keisan.casio.com/exec/system/1359534351

I could build a separate unit for doing that, or I could just patch a computer program to do it (summers combined with sin/cos function generators and 4-quadrant multipliers). The former would be more practical in use of course, which is why I have gone through the trouble of constructing the current projective unit. Could be an interesting project.................

 

GK:
Come to think of it a 2-dimensional polar coordinate oscilloscope, where time is the independent variable, represented by the angle of rotation about the pole, would be a rather simple thing to make.

Firstly, you'd need to design a triggered timebase that produces a "sweep" consisting of a single cycle of a sine-wave, rather than a ramp voltage. From this an all-pass filter could then be used to generate the cosine "sweep" term. Simply multiply these two signals independently with the uni-polar signal input voltage representing the distance from the pole and you have your X and Y deflection signals respectively.   

GK:
Although my priority right now is to complete the construction of my Fourier synthesis display unit and write it up on my website, it seems I just can't help myself. This evening I got half way to having a functional polar coordinate oscilloscope. I knocked up a quick and dirty triggered timebase generator which produces sin and cos sweep terms, for time as the independent variable represented by rotation about the pole:



The top waveform is the trigger pulse and the lower two waveforms are the subsequent (rising-edge triggered) sin and cos "sweeps". The slopes/breakpoints haven't been calibrated yet and I still have to breadboard the shaping circuit(s) that will transform these triangular waveforms into smooth sine and cosine curves. I will probably use BJT long-tail pair shapers. However that will have to wait for another spare evening.

In the meanwhile, here is a very quick play in SPICE, of sine, sawtooth and square waves displayed in polar coordinates:

GK:
You say polar coordinate oscilloscope, I make polar coordinate oscilloscope (in 2 free evenings  ;D ).

As I had to use parts that I had at immediately at hand the bread-boarded prototype circuitry is still very crude and there is still plenty of scope for improving the phase and amplitude linearity of the generated displays. For shaping the sine and cosine "sweeps" for the angular deflection I used logarithmic shapers that exploit the non-linearity of a BJT long-tail transistor pair. I am not overall happy with this approach. No matter how the circuit constants are tweaked, the lowest THD null always results in a sine function with excessively pointy nipples (well that is what they look like to me). This non linearity is quite visible when plotting the circumference of a circle on the CRT. However there are other (better) ways to do that job. I'm also using quite crappy and obsolete (EXAR) multiplier chips that had to be compensated down for breadboard stability to the extent that phase distortion in the display is not insignificant at even modest operating frequencies. However the fundamentals are covered/proven and now it's just matter of refining the design. I intend to make an instrument with a full oscilloscope-like front-end, with comprehensive timebase, triggering, radial (rather than "vertical") input sensitivity and offset controls - though this will go on the back burner for the time being while I get back to finishing some other stuff.
     

GK:

--- Quote from: GK on January 30, 2014, 11:21:16 am --- For shaping the sine and cosine "sweeps" for the angular deflection I used logarithmic shapers that exploit the non-linearity of a BJT long-tail transistor pair. I am not overall happy with this approach. No matter how the circuit constants are tweaked, the lowest THD null always results in a sine function with excessively pointy nipples (well that is what they look like to me). This non linearity is quite visible when plotting the circumference of a circle on the CRT. However there are other (better) ways to do that job.
--- End quote ---


The squaring technique using a 4-quadrant multiplier (X & Y inputs connected together) looks like the most viable alternative right now........ Mathematically perfect sine curves..............

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