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Anonymous Poster #1

# Transformer Saturation Curve

02/28/2017 10:30 AM

Transformer Saturation Curve is a relation between transformer current and transformer primary Voltage RMS. For the point on the curve that represents current at the nominal transformer primary Voltage RMS, Which current is this? Is this the excitation current in the transformer magnetization circuit? or it is the primary current at no load so it includes no-load losses current?

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#1

### Re: Transformer Saturation Curve

02/28/2017 11:58 AM
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#2

### Re: Transformer Saturation Curve

03/01/2017 3:02 AM

This is transformer schematic. Since [EMF] E=k*F F=B*Sfe the magnetic flux will decrease from no-load to full load due to voltage drop from Vp to E. However, this voltage drop is negligible usually and you may consider E=~Vp.

If Vp will stay constant from no-load to full load the excitation current [considering no-load current-reactive part Im]will be constant.

But if you will vary the Vp from 0 to Vp rated and above you'll get increasing excitation current for approximate 0 to rated and more.

It is difficult to measure the excitation current directly, so a separation between magnetic losses-including hysteresis and supplementary losses- current and excitation current calculating the equivalent losses current and extracting this from Io[usually considering sinusoidal waves and then using complex numbers: Io=Ife+jIm j=sqrt(-1)].

Magnetic field strength H[A/m] depends on current H=wp*Im/(magnetic circuit length) [wp=primary coil number of turns].The magnetic circuit includes the transformer magnetic core but also the surrounding air, oil or else.

The magnetic flux density B[Wb/m^2] to H[A/m] ratio is noted miu=miuo*miur [H/m-Henry=Wb/A]where miuo is the permeability of vacuum [or air] and miur it is the relative permeability of different materials with respect to vacuum [or air].Usually for iron [or steel] is about 1000 to 2000. This it is why the most of magnetic flux will flow through magnetic core and a leakage flux will flow in the surrounding vicinity.

Since miur is variable with field intensity H -and from an elevated value and above will be almost constant-a H_B curve-magnetic curve-is characteristic for each magnetic material-transformer laminates.

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#3

### Re: Transformer Saturation Curve

03/01/2017 3:42 AM

You have the wrong concept. The saturation curve represents the inductance between the Instantaneous current and the Instantaneous voltage. Simplifying equations for sine waveforms can be done assuming the saturation curve is linear. So no more saturation curve for you.

For transformers it refers to the magnetizing impedance.

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#4

### Re: Transformer Saturation Curve

03/01/2017 4:16 AM

See[for instance]:

http://www.electronics-tutorials.ws/electromagnetism/magnetic-hysteresis.html

By the way, I am not sure Anonymous1 referred to current transformer.

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#5

### Re: Transformer Saturation Curve

03/01/2017 4:24 AM

And still a correction: the inductance is the ratio between magnetic flux and the current producing the magnetic field. L=F[Wb]/I[A] [Henry=Wb/A].

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#6

### Re: Transformer Saturation Curve

03/01/2017 9:10 AM

Transformer Saturation Curve is a relation between transformer current and transformer primary Voltage RMS . . . e.c.

http://www.dissident-audio.com/Transfos/Papers/Wolpert_Audio_Xfmr_Design_Manual.pdf

http://www.dicks-website.eu/coilcalculator/index.html

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#7

### Re: Transformer Saturation Curve

03/01/2017 10:28 AM

The second link [coil calculator] describes so the inductance:

“The inductance of a coil is the property which describes the relation between the voltage across the coil, and the change of current through the coil.”

L = V / (di/dt)

It is correct if instead of "voltage" it would written “ back- EMF” [back-electromotive force]. It is not the supply voltage but it is the voltage induced in the coil [E] .The above formula neglect the leakage inductance and the circuit resistance.

V=[R.I+j2.π.freq.(Lleak+Lm).I] Lm=magnetic core inductance Lleak=leakage[in vicinity air] inductance; j=√-1

Indeed if L.i=Φ [by definition] and dΦ/dt=E [by definition] then Ldi/dt=E and L=E/(di/dt) .

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#8

### Re: Transformer Saturation Curve

03/03/2017 8:17 AM

The current at rated primary voltage, no load, is both the things you state, but the second is less accurate...

The magnetising force is the primary current x primary turns - this is not affected by consideration of losses in primary winding resistance or magnetising losses which change the "back-e.m.f." opposed to the applied supply voltage. The primary current is the magnetising current. It may be convenient for analysis to represent losses as a parallel resistance, but this is accurate for engineering purposes only because losses are small and can be considered almost constant over normal supply voltage range.

Actual magnetising current is not sinusoidal and drawing an equivalent transformer circuit, which is assumed to be linear and work at just fundamental supply frequency, is a convenient simplification which is accurate enough to understand what is happening.

The following image is oscilloscope voltage and current into primary of a toroidal transformer. These, as you may know, usually give more extreme saturation behaviour than the typical E-I lamination construction.

Note that the current wave is far from sinusoid - the distortion of voltage, flattening at the peaks, is in the house mains supply.

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#9

### Re: Transformer Saturation Curve

03/03/2017 9:09 AM

Thanks,67.I agree with you.

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