How can I simplify this charge pump?

Question

In thinking about an answer to a different question, I came up with a likely-not-ideal solution to the following:

Given a square-wave input of 125 Hz whose minimum is 0V and maximum is somewhere between 1-7V
Assuming an ideal source with zero output impedance
Not having access to a negative rail
Needing to support an output load of at most 10 mA that varies at the same frequency but between +Vin and -Vin; i.e. zero-centered and with double the amplitude
Wanting as simple a circuit as possible, ideally with only passive, discrete components

The complex and obvious solution is a switching supply to generate the negative rail, and then a comparator. I came up with the following charge pump as a simpler solution, shown at Vin=5V, RL = 5k:

Since it doesn't need to generate a negative rail, it doesn't need an inductor. It works fine, but I don't love it, for the following reasons -

I feel like it can be further simplified
The output is asymmetric - the positive cycle is stable but the negative cycle follows the capacitor discharging

Is there a simpler solution? The alternate one below does work, courtesy @tobalt.

schematic

^{simulate this circuit – Schematic created using CircuitLab}

@tobalt Slightly smaller like 0.5V difference? If so I'd be interested in seeing it — Reinderien, May 22 '21 at 17:59
@Reinderien I'm kind of flummoxed by the difficulties. But it's probably that I didn't read you as well as I should have. I recently wrote about something like this: [here](https://electronics.stackexchange.com/a/562940/38098). The inverter part is on the right side of the circuit, there. It's what you drew, isn't it? Seems to work. Can you spot the difference? The key is the load. It totally changes the behavior, depending. So maybe you didn't compute things right? (Read the ***theory*** section there.) — jonk, May 22 '21 at 23:22
@jonk to be clear: there are two circuits above; the first works fine and the second (suggested by tobalt) does not. I'm going to try adding one more FET like he suggested in the comments. — Reinderien, May 23 '21 at 03:35
@Reinderien I guess I'm just thinking about your comment, *"the alternate one below does not seem to work when I simulate it..."* But perhaps I didn't read you well, as I mentioned. That's okay. If the link I provided isn't helpful, then it isn't. Only you'd know. — jonk, May 23 '21 at 04:13

tobalt · Accepted Answer · 2021-05-23T15:21:38.780

3

Sorry for my previous answer. It took me a while to understand what you were trying to achieve.

I think this does what you want.

edited May 23 '21 at 15:21

answered May 22 '21 at 18:05

tobalt

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I've tried to simulate it, results in my question, and it's not working - it's inverting to a DC rail instead of a square wave. – Reinderien May 22 '21 at 18:08
Could you sketch a diagram of what the FET connection would look like? – Reinderien May 22 '21 at 21:04
Brilliant! Thank you. – Reinderien May 23 '21 at 15:08
1

@Reinderien I have edited it, to use MOSFET instead of BJT. That way you get rid of the two resistors. – tobalt May 23 '21 at 15:21

How can I simplify this charge pump?

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