Understanding Output Voltages for a Center Tapped Transformer

[JC2000]

TL;DR Summary

Unable to put a finger on exactly why the following holds :

1. The voltage between the extreme nodes and central tap of the transformer is half of the voltage difference between the extreme nodes.

2. A 180 degree phase difference exists between the voltage at extreme nodes.

While trying to understand the working of a full wave rectifier I was unable to precisely understand the working of the central tap transformer.

Edit 1 : The voltages are out of phase by 180 degrees as voltage is alternating(?) So the only thing I don't understand is how the distribution of amplitudes occurs...

Thank you for your time!

 

[nsaspook]

It might help to think of the Center Tap transformer as two identical transformers connected like this.

The dots show phasing.

 

[zoki85]

Edit 1 : The voltages are out of phase by 180 degrees as voltage is alternating(?) So the only thing I don't understand is how the distribution of amplitudes occurs...

Thank you for your time!





View attachment 256711

The secondary winding is wound in the same direction and when excited by same AC magnetic flux, the potentials of terminals A and B with respect to the center tap point are:

V_A=V_msin(ωt)
V_B=V_msin(ωt+π)=-V_msin(ωt)

Per definition, the voltage is the difference of potentials.
So, how much is V_AB=V_A-V_B ?

 

[Merlin3189]

why the following holds :

1. The voltage between the extreme nodes and central tap of the transformer is half of the voltage difference between the extreme nodes.

Voltage is induced in each turn of the secondary. Half the turns are in each half of the secondary. So half the total voltage is in each half of the secondary.

2. A 180 degree phase difference exists between the voltage at extreme nodes.

This is due to the choice of centre tap as zero reference. On your diagram, the centre tap is shown as ground or reference potential.
Starting at one end tap, the voltage increases in magnitude linearly as you go along the winding. If either end is taken as zero reference, the voltage at half way and at the opposite end will be in phase, the halfway one being half the amplitude of the other end.
It is by choosing to refer to the centre tap that you force one half winding to have an opposite voltage to the other. The centre tap is always half way between the ends. so when the top half goes +ve, the bottom must go -ve and vice versa, so that the mid point can stay at zero.

Incidentally, I don't like Zoki's derivation, because there is no time shift causing the "phase" difference. The difference is that the amplitude is reversed simply by choosing a different zero reference point.
I would say
VA=Vmsin(ωt)
VB=-Vmsin(ωt) because VB is measured in the opposite sense to VA
That is, VB is antiphase with VA, which looks like Vmsin(ωt+π)

 

[zoki85]

The difference is that the amplitude is reversed simply by choosing a different zero reference point.
I would say
VA=Vmsin(ωt)
VB=-Vmsin(ωt) because VB is measured in the opposite sense to VA
That is, VB is antiphase with VA, which looks like Vmsin(ωt+π)

Agreed.
I wrote that solely for math purposes, in order to OP see 180° phase difference reffered to in two different ways

 

[alan123hk]

Edit 1 : The voltages are out of phase by 180 degrees as voltage is alternating(?) So the only thing I don't understand is how the distribution of amplitudes occurs..

According to Faraday's law, assuming that from A to G(ground) and from G to B have the same winding direction and number of turns, since the magnitude and phase of the magnetic flux flowing through them are the same, V(AG)=V(GB).

Because V(GB) =-V (BG), V(AG)=-V(BG), which means that V(A) and V(B) are 180 degrees out of phase with respect to G (ground).

 

[Qmavam]

TL;DR Summary: Unable to put a finger on exactly why the following holds :

1. The voltage between the extreme nodes and central tap of the transformer is half of the voltage difference between the extreme nodes.

2. A 180 degree phase difference exists between the voltage at extreme nodes.

While trying to understand the working of a full wave rectifier I was unable to precisely understand the working of the central tap transformer.

Edit 1 : The voltages are out of phase by 180 degrees as voltage is alternating(?) So the only thing I don't understand is how the distribution of amplitudes occurs...

Thank you for your time!





View attachment 256711

I modified your drawing to try to answer, "why is it that they (L1, L2) are 180 degrees out of phase, although when you use L1 and L2 without a neutral for a 240 volt circuit L1 and L2 are not out of phase?
Which is not really true it is about the reference. Anyway, here is the modified drawing that might help someone else.
Mikek