# Gas station without pumps

## 2017 September 2

### Correcting reasoning on buck regulators

Filed under: Robotics — gasstationwithoutpumps @ 13:10
Tags: , , ,

In More on cheap buck regulators, I wrote

We can fix the windup problem by either reducing the integrator coefficient (reducing the capacitor size on the COMP node, whose current size I’m uncertain of) or by using a larger inductor, so that the current changes less when the FET switches, and the time constant of the system is better matched to the integration time constant set by the RC value.

I was worried even as I wrote that claim that my reasoning was wrong.  Increasing the inductance would make the voltage on the output capacitor adjust more slowly, meaning that the system was even more under-actuated, resulting in more integrator windup. But I went ahead and bought some surface-mount 10µH inductors and put one on the board that I had taken the 1.5µH inductor off of.

In testing under light loads, the larger inductor works fairly well, though regulation is sometimes lost for short bursts even with a 145mA load.

resistance current 1.5 µH ripple 10 µH ripple
∞Ω 0 mA ±7mV ±18mV
40Ω 145 mA ±32–50mV ±36–45mV
32Ω 184 mA ±37mV ±36mV
24Ω 245mA ±60mV ±63mV
16Ω 374 mA ±50mV ±126mV
740mA ±65mV ±805mV
1388 mA ±435mV ±1186mV

So larger inductors give similar control at low currents, but hit the integrator windup problem at lower current levels.

I can think of two fixes:

• Making the capacitor of the compensation circuit smaller, so that there is less integrator windup.  I’m not sure what that will do to the stability of the regulator.
• Adding an LC filter to the output, to remove the ripple.  Because of the resistance of the inductor, this will entail some loss of efficiency.

I tried add a 1.5µH and 10µF low-pass filter to the output of the regulator, measuring current and voltage after the filter:

resistance current 1.5 µH ripple 10 µH ripple
∞Ω 0 mA ±7mV ±12mV
40Ω 146 mA ±3.6mV ±3.5mV
32Ω 185 mA ±4.3mV ±4.5mV
24Ω 246mA ±5mV ±8.5mV
16Ω 376 mA ±7mV ±12mV
740–760mA ±7mV ±194mV
5.3Ω 1090mA ±12mV–±220mV ±500mV
1388 mA ±314mV ±510mV

Adding LC filtering seems to be a big win, but the original 1.5µH inductor is still the better choice.  I get good regulation at 0.75A, but ripple starts gets big at 1.4A.  At 1A, I sometimes get a very steady output and sometimes a large 123kHz ripple, unpredictably

The voltage drop across the 1.5µH filter inductor is about 0.2V at 1A, so I’m losing about 3% in efficiency, but the 200mW loss is not enough to cause heating problems in the inductor.  For the application I’m looking at, I don’t expect continuous currents

Changing the compensation capacitor will be harder, as it seems to be an 1005 capacitor (0402 Imperial), which is a little small for my clumsy fingers and tweezers—changing the much larger inductor was enough of a challenge for my dexterity.  I don’t know exactly how many pF  the capacitor is, either, so I’d probably have to do a lot of trial-and-error fitting, or take the capacitor out and try measuring it not in the circuit.  Getting probes onto such a small part is going to challenging when it is not on a board.