Electrical – Linear power supply + zero-crossing detection on transformer secondary

EDIT - Answer totally rewritten!

If we consider the equivalent circuit of a transformer below, at low frequencies the response is dominated by the effects of the primary resistance and the primary inductance which form a high-pass filter. The cut-off frequency of this filter is given by \$f_c=\dfrac{R_P}{2\pi.L_P}\$.

Qualitatively, at low frequencies, the primary current is proportional to the input voltage since the primary appears as a resistance. As Olin says in his comment, the secondary voltage is 90° out of phase with the current (it is proportional to the rate of change of current) so we get an overall 90° phase shift.

As the frequency increases, the primary impedance becomes more inductive producing a phase shift in the current. This phase shift subtracts from the original shift and the overall phase shift falls towards zero (but never quite getting there).

If there is a resistive load on the secondary, the leakage inductance eventually comes into effect forming a low-pass filter with the reflected load resistance. This will cause the phase shift to lag further, towards -90°

To take a worked example, I tried to find some specifications for the inductance of mains transformers but manufacturers don't seem to specify this. So I measured a random transformer with a hand-held inductance meter and got 2.5H (hopelessly underestimated since the meter is a cheap audio frequency type). The primary resistance is 47\$\Omega\$. This gives a cutoff frequency of around 3Hz, at which the phase shift will be 45°. At 60Hz, this would have fallen to 2.9°

So that's the "why", but whether this error is significant depends on the application. As others have noted, an opto-isolator may well be a better solution.

Simplified Equivalent Circuit :-

You cannot smoothly dim a normal incandescent light bulb with zero-crossing control of normal 50/60Hz single-phase mains- the filament (even a really fat high-power one) will visibly flicker to an objectionable degree with even a small number of possible levels of control. Similarly, radiant heating is problematic with zero-crossing control because the temperature can change significant within a small number of cycles. In those cases, phase control is typically used.

Normally for zero crossing control we would like a cycle length of several seconds or more (up to maybe 30-60s), so that the number of half-cycles is at least in the low hundreds. That limits the applications to those where the low-pass filter formed by the heat capacity of the various elements will smooth out the power, so generally those applications with a time constant in the 1minute + range.

Phase control has problems that zero-crossing switching does not have (more EMI, there may filtering required for EMC compliance, undesirable audible noise from lamp filaments, nonlinear response power-vs-trigger angle). On the other hand, zero crossing switching of high current loads can cause visible light flickering (otherwise independent lights that happen to be powered from the same mains circuit).

For phase control or for zero crossing switching you need zero crossing detection. In the case of zero crossing switching, the micro can delegate that job to the triac driver and just tell it roughly when it wants the triac on or off, and the driver and triac will respond with some latency depending on when the zero crossing happens to hit.

There's a third alternative- the simplest- random switching, where the triac just switches on whenever it is asked to (and switches off at the zero crossing, since that's all it can do).

If you implement a zero-crossing detector for a micro and drive the triac with a non-zero-crossing opto (or use a random switching SSR) then you can select any of the three options with firmware.