3rd or 4th failed soldering attempt
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The circuit is required to switch on the relays 2 at a time in sequence, at a regular interval, so that each battery is charged in turn. There are many timer kits available, and the idea for this circuit comes from this one. The only thing I've added is an inverter and counter to give the sequential triggering of several pairs of relays.

The schematic reads left to right. The first component is a 555 used to generate a square wave once every second or so - configurable with the potentiometer. The output of the 555, pin 3, feeds to the input of the 4020, a binary ripple counter, on pin 10. The 4020 counts the number of square waves from the 555, and itself outputs a high signal on different pins for different counts. The output I chose was on pin 1, which counts to 2048. The 4020 wouldn’t be necessary if the 555 could output a really long square wave, once every 2 hours or so. About the longest one I could get out of it was a few minutes. The output of pin 1 on the 4020 is low until the count of 2048 is reached, at which point it goes high.

Pin 1 of the 4020 is connected to the 4069 hex inverter, on pin 1. The hex inverter just flips the signal, high to low and vice versa. The reason for this will be obvious (hopefully) after I get to the last piece, the 4017 decade counter.

The output from the 4069, on pin 2, feeds to the input of the 4017, on pin 14. The 4017 counts from 1 to 10 - with pin 3 giving a high signal after 1 high input from the 4069, pin 2 giving a high signal after 2 high inputs, through intuitively enough pins 4, 7, and 10. This works well for what I need, as I want to charge one battery at a time. When pin 3 is high, the first 2 relays switch on via a transistor, allowing the a path for the charger to get to the first battery. I need pin 3 to go high right away, as I want to start charging right away, so the signal must be high to start, hence the 4069 inverter. The next battery is charged when pin 2 is high, and pin 3 returns low.

It's possible to charge up to 10 batteries with this circuit by adding more relays, as the 4017 counts to 10.

I find this description a little bewildering myself, so here's a picture of how the outputs look from the various components.

Here it is on the breadboard, where I wish it could have stayed:


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