Transcript PSMA Magnetics Committee Proposed Projects for 2008

PSMA Magnetics Committee
Proposed Projects for 2008-2009
1. Validate and promote new format
for core loss data.
2. Validate, refine and promote
SPICE model for transformers.
Edward Herbert
February, 2008
PSMA Magnetics Committee
Proposed Projects for 2008-2009
• The slides can be viewed at
http://fmtt.com/PSMAmag1.ppt
(note: file names are case sensitive)
• The paper can be viewed at
http://fmtt.com, click the link for
“Transformer Spice Model” (pdf, 1,020 k),
to view or download.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
• Project 1.
• Validate and promote new format for
core loss data.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
The graph on the right shows core loss data
for Magnetics, Inc. material F. The blue lines
are the original data.
Magnetics, Inc. also provides core loss
approximation formulae:
mW/cm3
Where a, c and d are constants,
f is in kHz and is in kG.
The dashed lines in the graph are the core
loss approximations, color coded.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Note the slopes of the lines. On a log-log
graph, the slope is the exponent, “d”. Note the
differences, almost 2 to 3.
Note the line spacing. On a log-log graph, the
spacing is the exponent, “c. Note the
differences, almost 1 to 2.
This shows that the loss mechanisms are
different, and the slope is a clue as to which to
use.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
To be useful for SPICE, we need the core
losses in the time domain.
The same core loss data can be plotted vs
frequency for curves of equal Bmax.
Using the core loss approximation, and
ramping the frequency, the solutions are
shown on the graph on the right, color coded.
The blue lines are my best approximation at
curve fitting.
No accuracy is claimed, this is a qualitative
exercise.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
It is interesting to divide the loss density vs
frequency through by the frequency. This gives a
graph of the loss density per cycle for various
Bmax.
Note that the curves are fairly flat on the left,
indicating that frequency does not much affect the
losses.
This is the classic model, that the losses are fixed
for a given Bmax. This breaks down above about
10 kHz.
No accuracy is claimed, this is a qualitative
exercise.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Substituting into the loss equation and
solving for log steps of E gives the graph on
the right, loss density vs frequency for E.
Log steps of volt density,
Volts per turn cm2.
No accuracy is claimed, this is a
qualitative exercise.
The solution is blanked for
Bmax > 3,000 gauss.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
“d” varies from almost 2 to 3,
“c” varies from almost 1 to 2.
Using these as limits, asymptotes
for the loss density vs frequency for
log steps of voltage can be plotted.
The fit is not too bad.
Log steps of volt density,
Volts per turn cm2.
No accuracy is claimed, this is a
qualitative exercise.
The solution is blanked for
Bmax > 3,000 gauss.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Making a left-right mirror image of the plot,
frequency is converted to period.
I chose to use the half-cycle on-time for
the x axis, that is, the period of the pulse
for an ac square-wave.
This is NOT the instantaneous loss vs
time, as the formulae are in terms of Bmax.
We still need an expression in the time
domain for a SPICE model.
This curve may be very useful for the
design of transformers, especially pwm
transformers.
No accuracy is claimed, this is a
qualitative exercise.
Log steps of volt density,
Volts per turn cm2 vs
“on-time” for ac square waves.
The solution is blanked for
Bmax > 3,000 gauss.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Proposed presentation for core loss data:
Core loss data presented as loss density
vs on-time for log steps of volt density
should be easier to generate, and should
be more useful to transformer designers.
Hypothesis: I believe that a more
accurate result for pwm transformers is to
use the actual voltage and on-time of the
pulse. Find the loss density from the
graph, then factor it by the duty-cycle D.
PL = PL(E,t) * D
For 100 volts on 10 turns on a core of 2
cm2, use the 5 V line (100 V / 10 * 2).
No accuracy is claimed, this is a
qualitative exercise.
Log steps of volt density,
Volts per turn cm2 vs
“on-time” for ac square waves.
The solution is blanked for
Bmax > 3,000 gauss.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
To get an expression that is
useful in SPICE, the data
must be converted to the
time domain.
The graph at the left plots
loss density for a family of
square wave on-times with
100 mV per turn cm2.
Sorting out what it means, it
really is a crude step-wise
integration.
So, the time the expression
in the time domain is the
derivative of the curve.
No accuracy is claimed, this is a
qualitative exercise.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Taking the derivative of the
curve is daunting, as I do not
have an expression for it.
However, taking the
derivative of the asymptotes
is easier.
No accuracy is claimed, this is a
qualitative exercise.
Thus, the high frequency
SPICE model for core loss is
just a resistor.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
No accuracy is claimed, this is a
qualitative exercise.
Thus, the low frequency
SPICE model for core loss is
a resistor, but a special
resistor that varies as 1/B.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
• Project 2.
• Validate, refine and promote SPICE
model for transformers.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
• Basic ideal transformer:
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Multiple-winding
ideal transformers:
A separate ideal transformer
model is made for each
winding, and they are
connected through a “linking
winding” at the terminals Vc.
If two or more windings are
connected to make a tapped
winding, it is preferred to
model each winding
separately, then connect them
through a low resistance, to
preserve the node names.
R13 connects V1r to V2.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
• Magnetizing inductance, saturation and hysteresis,
Simple model:
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
• Curve fitting:
Lm is varied to adjust the slope of the curve at the origin. Use the
measured or estimated magnetizing inductance.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
• Curve fitting:
The exponent is varied to adjust the corner of the curve as the
core saturates.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
• Curve fitting:
Rh is varied to adjust the width of the hysteresis loop.
Adjust Lm, the exponent and Rh as necessary to get a good
approximation.
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PSMA Magnetics
Committee
Proposed Projects
for 2008-2009
SPICE model, 4 turn
transformer with
hysteresis and core
losses, simple model:
The hysteresis and core loss
model is connected to the
transformer through the “core”
connection, Vc and the return.
If the transformer has turns
connected to make a centertapped winding, it is preferred
to connect them through a very
low value resistor, so the node
names do not change.
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PSMA Magnetics
Committee
Proposed Projects
for 2008-2009
SPICE model: Winding
resistance and leakage
inductance, simple model;
Loss and energy test
points.
For a simple model, the winding
loss is modeled as a resistor,
and the leakage inductance is
modeled as an inductor.
Behavioral voltage sources
calculate the losses and stored
energy in the various
components.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Thus, the high frequency
SPICE model for core loss is
just a resistor.
Core loss, low and high
frequency effects.
Thus, the low frequency SPICE
model for core loss is a resistor, but a
special resistor that varies as 1/B. 24
PSMA Magnetics Committee
Proposed Projects for 2008-2009
Core loss, low and high
frequency effects.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Core loss, low and
high frequency effects.
Curve fitting;
The hysteresis curves show the effect of varying Rb. To start, Rb is set to a
very high value, 1e6. The green graph shows the effect of Rh. The blue graph
shows Rb = 0.1 . The red graph shows Rb = 0.05 . Note that the
hysteresis loop fattens as a wedge as Rb is decreased.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Skin effect:
A wire is modeled as five concentric segments of equal area. Because the
area is equal, the dc resistances are equal, and are 5 x the dc resistance of
a wire per a wire table, in m per unit length times the length.
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PSMA Magnetics
Committee
Proposed Projects
for 2008-2009
Skin effect:
The wire size (AWD or mm),
wire length and temperature
are entered as SPICE
parameters.
The resistance Rw1 is
calculated in the behavioral
voltage sources.
The inductors are the value
that gives the correct time
constant for the depth, given
the resistance.
The inductances seem to be independent of wire size, at least approximately.
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PSMA Magnetics
Committee
Proposed Projects
for 2008-2009
Proximity effects:
A step change in current I1 induces an
equal and opposite current Ie in an adjacent
conductor. The current Ie dies out
exponentially.
Rigorously, a coupled inductor and a wire
with skin depth should be modeled, but that
is pretty complex.
The SPICE model on the right is a
reasonable approximation, and is quite
simple.
However, the loss in Rw is NOT Ir12 * Rw, it is (Ie2 + I12) * Rw. In the simple
model, Rw is also a surrogate for Re, so the calculation must recognize the two
resistors of the more complex model. The voltage drop, Ir1*Rw is correct.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Proximity effect:
A step change in a current I1 induces an equal and opposite current Ie in an
adjacent wire. Ie dies out exponentially. The waveform of Ie is modeled below
as Vjd, for use in a behavioral current source, scaled appropriately.
If the shape is not quite right, a different filter can be used in place of C1R1.
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PSMA Magnetics
Committee
Proposed Projects
for 2008-2009
Proximity effects:
Assuming that the eddy
currents are mostly on the
surface of the conductor,
the exponential current
transient is applied to the
outer layer resistor R1 of
the model for the skin
effect, scaled if necessary.
The parameters are
adjusted to fit measured
circuit behavior if it is
available.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Proximity effect:
The currents in the layers are shown, and the total winding losses Pw.
Note that some currents go the “wrong” way following a transient, and that
some currents and losses persist after the input current goes to 0.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Proximity effects,
multi-layer windings;
For a multi-layer winding, model each layer as a separate wire with
proximity effects, all connected in series. The injected current transient
increases for each layer, approximately as 1x, 2x, 3x, etc.
Proximity effects,
losses in another winding or a shield;
The losses are modeled in the winding in which the current changes, and
can be approximated by increasing the injected current Ie.
If the winding is a multi-layer winding, assume that the losses are only in
the layer adjacent to the other winding or the shield.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Transformers with coaxial
or interleaved windings:
The simple models given
above are not adequate
for modeling the leakage
inductance and proximity
effects in coaxial and
interleaved windings.
In the top core on the right, the first primary has very
good coupling to its coaxial secondary, and it is
similar for the second primary to the its coaxial
secondary.
However, the coupling from primary to primary has a much higher leakage
inductance, important for an accurate SPICE model.
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PSMA Magnetics Committee
Proposed Projects for 2008-2009
Transformers with coaxial
or interleaved windings:
The behavioral current and voltage sources B1
and B2 model the first primary and its coaxial
secondary winding. The leakage inductances
are very low. Similar for B3 and B4.
The secondaries link through a higher
inductance, L6 and L7, center-tapped for
symmetry, and winding resistance R9 and R10.
The leakage inductance primary to primary
reflects this higher inductance, while each
primary to its coaxial secondary winding is very
low.
An interleaved transformer is modeled similarly.
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