An Intuitive Derivation/Proof of the Sum of an Infinite Geometric Series based on Zeno’s Paradox

A geometric series is a series of numbers where each number in the series is equal to the previous number multiplied by a constant multiplication factor. For example: 2, 4, 6, 8, 16… is a geometric series with a constant multiplication factor of 2.

The sum to infinity of such a sequence, then, can be represented as:

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Project: Nixie Clock (upgrade) – Final Schematic and PCB

One big change since I did the first version of the clock is my access to professionally made PCBs. At the time, I was only able to produce PCBs via hand etching or using my home-made PCB mill. A board like this requires at least a double sided design which is not easy using the above methods and so I used veroboard. This is painfully slow and messy.

 

For the new version I will use a professionally made two layer PCB.

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Project: CRT Oscilloscope LCD Mod – Choosing the replacement LCD

I’m replacing the screen on the logic analyser for a few reasons:  The CRT is heavy and bulky – replacing it would make the whole thing lighter, an LCD could be brighter and I can add colour to the monochrome display, and on top of this it’s just an interesting project. The most important thing is that the replacement screen is not worse than the old one!

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Project: CRT Oscilloscope LCD Mod – Simulating signals

After putting this project on the back burner, I am focusing on it once again. Brian HG on the EEVblog forums suggested that a simple line doubler would make the signal compatible with most modern VGA displays. What that means is that each line in the frame needs to be repeated twice, at double the speed.

Currently we get a new line every 40 microseconds, but this is too slow for most displays to be happy about. Therefore, if we record each line and output it twice at 20 microseconds each most VGA displays will be ok with it.

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Project: Robox – Buttons: Interrupts or Polling?

The robot box needs to know when it has reached the limit of it’s motion. If motion continues past this point, the machine will literally rip itself apart. To stop this happening, I am using a limit switch that will be pressed if the robotic finger move too far. However, it seemed that a good portion of the time the robot would ignore this button and continue to rip itself apart. The reason for this lies in the way I was using interrupts to detect the pressing of the button.

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Project: Nixie Clock – MC34063 Boost Converter (upgrade)

I really like my Nixie Clock that I built two years ago – but I don’t like to leave it on when I’m not around. The reason for this is that the Nixie tubes are powered directly from the mains which means that touching the Nixie tubes could result in a dangerous electric shock. While the tubes are protected under glass I don’t like the thought of someone accidentally tripping over it and getting electrocuted. So I decided to redesign the clock.

I am going to power the clock from a 9V wall supply and boost that voltage up to 180V to light the Nixie tubes. While this is still quite a high voltage, it is isolated from the mains and is much less dangerous.

My design is largely based on Threeneuron’s Pile o’Poo.

power_supply_schematic.png

The schematic for the 180V power supply

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Micro Motor Controller – Code and Gerbers

For the Robox project,  I needed a board to program and control a servo and a DC motor – I could probably have used something off-the-shelf, but I prefer to have a board specialised for the job.

The board I designed features an ATtiny828 microcontroller with 16 general use IO, two PWM outputs to control two 6V servos and an Allegro A3916 dual h-bridge to control two DC motors (or one stepper motor) at up to 1A per channel. This is more of a general use motor control board and could be useful in a bunch of projects.

Schematic-v1.0.png

Schematic

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