How does this "CD4069 smooth bargraph" work?

Question

I saw this schematic and I had problems finding out how it works:

As the voltage increases from zero, the first LED grows in brightness. Just when that LED is fully lit, the next LED begins to glow slightly. Each LED represents about 1 volt of change, when the circuit is operating from 9 volts.

According to the 4069 datasheet, the gates are not Schmidt triggers nor buffered, and the diagram for a gate seems quite simple:

If I'm right, the resistors form a voltage divider and just drive the LEDs.

I have these questions:

1. How does the circuit work? Why doesn't the next LED light up until the previous one is fully lit?
2. What does the first gate (left most gate, with two 1Mohm resistors) do?
3. What kind of modifications do I have to do, to make it work with a 5V supply? The supply would be a constant 5V and the input would be a variable 5V.

regards.

Answer 1

Have a look at the typical characteristics of a CD4069UB gate:

As you can see, the gate with no feedback (typically) acts as crude comparator that switches at approximately Vdd/2 (which is 4.5V in this case).

With feedback it can be considered an amplifier with a transfer function as follows:

Vpin1 = 4.5V, Vpin1 = (Vo + Vin)/2 => Vo = 9V-Vin

Now we can easily calculate the transition voltage for each LED from top to bottom, since it's a simple voltage divider (the gate inputs draw negligible current):

The right-hand column indicates the difference to the next LED, which is fairly constant.

It should be mentioned that this circuit works "typically" and there is no guarantee that any given gate will behave that way, in fact if you look at the worst-case characteristics:

.. it may not work very well at all. Also both the transistors are partly 'on' at the transitions (and the input gate is biased so it also has both transistors on) so the circuit draws extra mA that are wasted.

So it's an okay toy, but not really something you'd want to ship.

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To make it work from a 5V supply, you can simply reduce the supply voltage and accept that the input voltage will be scaled proportionally. Instead of 0..5V it will be more like 0..2.8V. Use a divider at the input if you want a 0..5V approximately input voltage. There is no control over how 'sharp' the transitions are, you're at the mercy of the physics and fabrication of the inverters.

Answer 2

This circuit relies on the fact that the CD4069, as well as all other "digital" logic ICs, are not really digital but analog electronics operating (usually) at the extremes of saturation and cutoff. But they can be operated linearly. Usually this is undesired operation but for an example like this, it can be useful.

The 5 individual inverters are operated as amplifiers in their linear mode until they reach either saturation on the way up or cutoff on the way down. The resistor in the "ladder" are carefully sized so that the saturation of one corresponds with the start of the linear region of the one above it.

It's easy to just assume that all circuits always behave linearly but they don't. That's a simplification to make designing digital circuits simpler.