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I confess, that I did only a rough hand calculation, may be not very exact. AndrzejM kindly has drawn some typical waveforms found in the circuit. Assuming a load independant transformer voltage, the capacitor is always charging to the sine peak value (reduced by rectifier voltage drop) and (in a simplified view) discharging linear until it falls below the momentary transformer voltage. The linear falling ramp has a gradient of Idc/C. With a smaller capacitor, the intersection point with rectified sine voltage occurs more early, thus the ripple is less than doubling when using a halved capacitor value.