Transformer's Theory question
Transformer's Theory question
(OP)
I have difficulty to understand the theory of how the transformer acually works and have a question regarding to that:
The primary winding of a transformer consists of two parts:
1- Primary leakage inductance Lp1
2-Primary coupling inductance L1
neglect the wiring resistance.
So the total primary inductance Lp=Lp1 + L1
The voltage across L1 must be constnat all the time = N1*d@m/dt
where @m is the mutual magnetizing flux, which is constant for all loads.
Now,if the primary is connected into a constant AC supply voltage V1 and the secondary is connected into resistive load,then:
V1 = Lp1*d i1/dt + N1*d@m/dt
V1 and N1*d@m/dt are constants while the first term of the equation Lp1*d i1/dt
is variable depends on the primary current !
Any one can explain that conflict in the equation ?
Thanks
The primary winding of a transformer consists of two parts:
1- Primary leakage inductance Lp1
2-Primary coupling inductance L1
neglect the wiring resistance.
So the total primary inductance Lp=Lp1 + L1
The voltage across L1 must be constnat all the time = N1*d@m/dt
where @m is the mutual magnetizing flux, which is constant for all loads.
Now,if the primary is connected into a constant AC supply voltage V1 and the secondary is connected into resistive load,then:
V1 = Lp1*d i1/dt + N1*d@m/dt
V1 and N1*d@m/dt are constants while the first term of the equation Lp1*d i1/dt
is variable depends on the primary current !
Any one can explain that conflict in the equation ?
Thanks





RE: Transformer's Theory question
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Transformer's Theory question
So, the induced secondary voltage E2= E1(N2/N1)=N2(d@/dt) remains constant and does not depend on the voltage drop on the primary leakage inductace.
@ is the magnetizing flux which is constant.
RE: Transformer's Theory question
RE: Transformer's Theory question
Increased load current also means increased primary current (I really hope you agree to that). So, increased current in an inductor (the primary leakage inductance) means less voltage across the primary winding.
Why do you think that the magnetizing flux, which you for some strange reason call @, is constant? It is not!
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Transformer's Theory question
RE: Transformer's Theory question
Does the hysteresis loop change its shape and reduces its two peaks with the increase of the load current?
RE: Transformer's Theory question
However, a real transformer does have winding resistance (until we have superconducting wire) and so even the flux on the core and the B-H curve (hysteresis etc) will change with load current.
boB
RE: Transformer's Theory question
RE: Transformer's Theory question
Any model is a simplified version of reality. It is important to understand the limitations of the model.
RE: Transformer's Theory question
There are several levels of complication involved. Simplest model has no leakage inductance at all. And no resistance. Then flux ix constant when load changes.
Next model (a little more complicated, and closer to reality) contains primary and secondary leakage inductance. Those elements behave just as ordinary circuit elements and can be treated as such. You can use RMS and do not need to bother about B-H curve. This is the model used in most real-world calculations.
Next model contains more details - but still working with RMS and no B-H curve thinking involved.
Still higher in model complexity, you find differential equations and instantaneous values - but still no B-H curve involved. Core is regarded as lossless and linear.
It is only when you are doing doctorate work and pure research that you start bothering about hysterisis loops. You are then working with non-linear partial differential equations. You are a long way from that.
Accept simple and proven facts.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Transformer's Theory question
I read the theories with interest....but think of a common mode choke at the input of a switch mode power supply........
...That is a transformer, but since the Hot & Neutral are effectively "differential" lines, then which is the primary and which the secondary?
....And which coil is it that passes the magnetising current?....is it both?.
I know that the fields of each coil cancel each other out...but there must be some magnetising current whose flux is not cancelled else the thing wouldn't work as a transformer and NIp = NIs wouldn't apply.
This is one of the most confusing transformers of all...so you are right to get confused
RE: Transformer's Theory question
That current is the common mode current. That is the high-frequency current leakage current, to which the common mode choke represents an inductance.
Normal mode currents are not affected by the choke. There's nothing mystical or confusing about that. Just pure physics.
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Transformer's Theory question
V1 = Lp1*d i1/dt + N1*d@m/dt
Both V1 and N1*d@m/dt cannot be constants.
Your rate of change of flux "d@m/dt" (or better written as simply "voltage per turn") is not constant, it is the load current times the load resistance.
DH
RE: Transformer's Theory question
I1+I'2=Io1 where I'2 is I2 referred to primary and Io is a virtual parameter which means Io is I1 when I2=0.
If I1could be =0 [ideally] than U1=E1o [E=FEM]. As I1>0 then E1=U1-I1*(Rp+j*Xp) so E1<E1o.
Since E1=-ke*d (magnetic flux)/dt=ke*omega*Flux*no.turns1 [omega=2*pi*freq.] also the magnetic flux will less than Flux[o].
In order to balance the presence of I2 the transformer will draw more I1 from the Grid and if U1 will be the same:
I1+I'2=Io2 <Io1 .
The equilibrium is unsteady –steady for each value of I1 but for other E1 and Io.
Regards
RE: Transformer's Theory question
This thread was tipping towards superstition. A PLS for you!
Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Transformer's Theory question
Best Regards
RE: Transformer's Theory question
After this long round of discussion my origional question did not receive a clear definite answer:
Does the magnetizing current (Im) change with load current or it stays constant ?
That is my question- I wish to find clear answer.
Thanks
RE: Transformer's Theory question
RE: Transformer's Theory question
RE: Transformer's Theory question
Primary impedance changes the amount of voltage drop depending on the load current (VD= IL x Zp). Since Im is a function of Em (magnetizing voltage= Vsupply - VD), a bigger load current creates a larger VD, and therefore a lesser Em! Im changes with load current!
Crystal!