For a linear driver to not be that lossy, you need the output voltage to be as close as the input is. The input for this is the rectified and filtered mains, so a kind of triangle waveform with its peak voltage equal to the mains peak and the valey voltage the peak mi us how deep the capacitor discharges. Plus because the mains is not 100% regular sinewave, with all the power switching causing it to vary practically in a random manne (talking about a kind of noise with frequency components up to 50Hz and a strong flicker type component for low frequencies down to the tolerance itself), the voltage on the rectifier follows. Now to be efficient, the LED chain voltage must be as close to the rectifier output. But the problem is, once thd rectified voltage happens to fall below what is the LED string voltage plus the required headroom the current regulator need, the regulator is not able to maintain the current anymore and it starts to get pinched.
So with normal mains, the voltage uses to be sufficient all the time, so the current (so brightness) are perfectly constant. But when the mains voltage itself gets lower, the fluctuation noise brings it below that sufficient level, so the LED brightness is drooping. Because the voltage fluctuates (both the basic 100Hz ripple, as well as the fluctuation noise), it starts to appear as the shimmering. To combat this, some designs use bypass switches to bypass part of the string voltage, so allow the rest to light normally even with the undervoltage, so the shimmering gets less pronounced, but it still is there, the light from the bypassed section is just missing. Some even boost the current through the rest to compensate for the missing light of the bypassed section, so the fluctuation of the total output gets suppressed, but because there is nonzero distance between the segments, the light source changes its shape with that fluctuation, so still some shimmering may remain.
So a summary: Switching drivers principally have the same behavior when the voltage becomes insufficient, but because they retain efficiency even when the voltage difference is larger, it is a no-brainer to just use lower voltage LED string, so the regulator has always sufficient headroom so keeps the current constant, so no shimmering. Linear designs are forced to have the margin small, so it gets reached and the shimmering happens from time to time with still quite common voltage levels.
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