Exact solution for resistors to increase hysteresis of 3-pin voltage monitor ICs

[hanakp]

Short version: Simple 3-pin voltage monitors usually have quite small internal hysteresis. It's possible to increase it with external resistors, i.e. choose arbitrary input threshold voltages VinH and VinL. I derived equations that allow for exact calculation of the necessary resistors. I'm attaching 3 Wolfram Mathematica notebooks (and exported PDFs) that cover 3 cases:

1. Monitor with CMOS (push-pull) output, where equations account for its supply current.
2. Monitor with open-collector output, where equations account for its supply current.
3. Monitor with open-collector output, without supply current. It's based on Texas Instruments app note SLVA360.

All schematics and design tips are inside those documents; I verified they work on physical circuits. There are also equations that calculate total supply current Idiv of the circuits. Beware that threshold voltages are sensitive to variations of IC supply current Icc. It can be suppressed by using smaller resistor value, but of course that will increase total supply current Idiv.

Long version:
I'd spent an inordinate amount of time fiddling with this, so I figured I might as well go all the way and publish it here...

I needed a low-power circuit that would turn off load if battery voltage decreased under certain threshold (and turn it back on when voltage rose above another threshold). It seemed standard 3-pin voltage monitors would suffice, but I was soon proven wrong -- they had too small hysteresis and tended to oscillate. In retrospect, it wasn't all that surprising: load turns on -> battery voltage drops -> monitor turns load off -> battery voltage rises -> repeat.

I started with Rohm BD4926G which has CMOS (push-pull) output, because I already had PCB designed for them. I couldn't find any articles or equations how to calculate necessary resistors values, so I put the state equations together myself. Then I used Wolfram Mathematica to derive equations for the resistors, as I've grown too lazy to do even such basic algebra on paper. The equations are quite simple, so you could easily re-create them in MS Excel or whatever (i.e. you don't need Mathematica to calculate resistor values).

There was more information about monitors with open-collector output. I wanted to test them too, because there are Texas Instruments TLV840xxx monitors, whose supply current is mere 150 nA. One clever way to increase their hysteresis is this application note from former Maxim which connects a single resistor into the GND lead. But that's usable only for small hystereses, because voltage drop on the resistor changes logic levels of the monitor's output. I didn't like that.

More standard solution is described in the aforementioned Texas Instruments app note SLVA360. But it contains only state equations and semi-numerical method to calculate the resistors, not the direct way. In Wolfram Mathematica, I soon found out why -- the algebraic solution is brutally complex, despite deceptively simple input. I actually thought it was just a mistake, so I put the state equations together myself, they're the ones in the 2nd notebook. But the results were identical as in the 3rd notebook. So if you don't own or use Mathematica, you'll have to use the TI way. 

In real implementation, CMOS output circuit with BD4926 exhibited lower sensitivity to Icc variations, even though TLV840 has much lower Icc. I'm not sure why it happens, but I'll probably won't use these circuits, anyway. Their accuracy can be guaranteed only with too small resistors and they would unnecessarily drain the battery. In long storage, they would eventually damage it.

As I mentioned in the notebooks, decoupling capacitors CD are absolutely necessary for stable operation. The ICs produce Icc spikes when their internal comparator flips, which will lead to oscillations in the voltage transition band. The capacitors have to be rather beefy, too: 100 nF or more is needed if R1 and/or R2 are in megaohm range. You can use smaller capacitors with smaller resistors, but always check both transition edges on the oscilloscope, preferably in your entire voltage and temperature ranges!

BTW, I know I didn't need to plug Rcc as separate variable, because it's always connected in parallel with R2. But it's more convenient when it's separate, because it allows you to quickly evaluate Icc variation sensitivity.

[temperance]

Are you aware that the BD4926 is not recommended for now designs?

[hanakp]

Yes, I used it because I recycled it from one old design. But this resistor hack is not very suitable for the intended application, so I'll replace it with something completely different, anyway. I kinda like MIC2779...

[temperance]

The question is if this will solve the problem because battery voltage depends on internal resistance (ageing) and temperature. Which type of battery are you using?

I think you will need a latching circuit and a method to reset the latch when the battery is being charged.

[hanakp]

It's LiFePo4, a single cell. It's a D-size cell with industrial temp range and quite low internal impedance, so I don't expect it to be much of a problem.

You're right that the load control should be integrated into "smarter" battery management solution, but the charger (energy harvester, actually) module was already done (by someone else). It will have to be redesigned for actual production units, but that's still rather far down the line. There was talk about using some ultra-low-power MCU...

[temperance]

In that case, you can have the undervoltage IC drive a MOSFET such that it removes its own power when the battery voltage is low. Upon charging, the switch will be closed again.