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I assume your referring to the actual phase angle lag if both the primary and secondary windings are in a like phase configuration.
Under no load they will appear to be near equal a few degrees of lag will be between the secondary and the primary at most.
As the load increases the phase angle lag will get greater and greater.
To visually see it a dual trace oscilloscope is needed.
This may not be the most technically accurate explanation but its how I learned it.
When the alternating current power going into the primary winding starts creating the magnetic field there is a slight time delay as the magnetic flux lines are created and start moving through the iron core.
Until the magnetic field begins to move there is no induced power being formed in the secondary.
That time lag can be calculated and related to a phase angle lag of sorts.
Once the input power starts to decrease and eventually reverse the magnetic field in the iron core also has to decrease and reverse. Being inductance acts like a flywheel it wants to keep going even when the input power drops. That creates a lag effect on the reversing part of the cycle.
As the secondary load increases it creates a work load drag on the magnetic field that further increases the lag from when the input power is applied until the magnetic field is created and begins to move.
I'm afraid I missed you on the last part where you explained why the load increases the phase between the two voltages of the primary and secondary coils.
All the alternating magnetic flux in the secondary coil does is to create an induced voltage which its direction is opposite to the magnetic flux's growth direction, and its size is N×dθ/dt, right?
This induced voltage called ε.
If I was correct, then when there's no load, there is still ε exsists, but there is no current since the secondary circuit is an open circuit (no load).
when there's a load, Z, the only difference is that now there is also current I = ε / Z.
I dont see how Z changes the voltage's phase, if the voltage's phase is determined by the primary voltage's phase.
I recall asking the college professor who explained it to me way back then something similar. His response was,
" It just does, so dont worry about it, just know that as the load increases the primary phase to secondary phase lag angle gets bigger."
I have never worried about it since.
I jes use dem tings, I donts tinks bout em. I eez simple dat way.
Not to nit pick but does the simulator make the correct adjustments and assumptions for actual winding Resistance, core losses and induction saturation rates?
I dont use the simulator stuff because its usually ideal conditions based and never real life based.
Life likes to toss in a load of variables that Sim software can not accurately reproduce.
The 90 degree voltage to amp ratio is correct but what about the primary to secondary phase lag differential?
That is what I had problems with on my early GTI setups. There is always a small time lag from primary to secondary that is very measurable when tracking on/off switching points when synchronizing the primary side wave form to the secondary side.
I thought so!
I have had countless arguments with so called electrical and electronics experts that have told me I am wrong countless times because their computer simulator said so.
And when I have offered to prove it in real life working conditions I got the deaf ear and blind eye treatment because 'the computer is right since its simulations are based on mathematical formulas and my stuff is just based on casual observation and clearly I do not know electrical physics.'
Hence my rather quick dropping of simulation software and never turning back!
Imagine if I had tried to Sim my GTI circuits! I would probably never had came here!
Depending on what was simulated tcm I might argue for the simulator, BUT they are not perfect, and 'real life' devices often have quirks that can't be properly simulated. Many a time I've kicked or banged on a device to get it working again. I've as yet to find a 'nudge' button in LTSpice though =)
If you can tolerate their quirks though simulators are great tools for optimizing existing designs.