After doing some reading online, it seems that you can't really build a step-down converter with only a filtering capacitor and without an inductor, because the losses occuring during charging of the capacitor would lead to low efficiency.

However, I'm looking at a application note from Zilog: "AN0259 - Low-Cost NiMH Battery Charger Using the Z8F0830": https://www.zilog.com/docs/z8encorexp/appnotes/AN0259.pdf which is using exactly that circuit - a capacitor is charged with a 10 kHz PWM signal, which in turn charges the NiMH battery. No inductor is present in the circuit.

What makes this circuit work in that situation? Or maybe it acts as I described above - it has high losses, but the designers just roll with it?

After doing some reading online, it seems that you can't really build a step-down converter with only a filtering capacitor and without an inductor, because the losses occuring during charging of the capacitor would lead to low efficiency.

However, I'm looking at a application note from Zilog: "AN0259 - Low-Cost NiMH Battery Charger Using the Z8F0830": https://www.zilog.com/docs/z8encorexp/appnotes/AN0259.pdf which is using exactly that circuit - a capacitor is charged with a 10 kHz PWM signal, which in turn charges the NiMH battery. No inductor is present in the circuit. What makes this circuit work in that situation? Or maybe it acts as I described above - it has high losses, but the designers just roll with it?