# Curent transformer spice model?

Discussion in 'Electronic Design' started by Clarence_A, Feb 5, 2005.

1. ### Clarence_AGuest

Does anyone have a web reference to a spice model of a current
transformer or a site where creating such a model is discussed?

Also, I will eventually need a Saber model of the same part.

Thanks to the serious engineers on this list!

2. ### Winfield HillGuest

Clarence_A wrote...
Current transformers have the same linear spice model as other
kinds of common transformers, with DC winding resistances, the
turns ratio, leakage inductance, magnetizing inductance, etc.

.. ---Rp---, ,---+--Rs--###----
.. | | | Lell
.. #||# #
.. #||# # Lm
.. turns #||# #
.. ratio | | |
.. -------' '---+----------

Not all of these parameters play a significant role, e.g. the
magnetizing-inductance component may not be significant, and
it's not a linear parameter anyway. You can assume Rp = 0.
A wideband transformer (>10MHz) may also suffer from winding
capacitance and ac copper losses, but you can ignore them.

Generally the primary is a single turn, from the wire being
measured going through the core. So the turns ratio N is
the number of secondary turns. You can measure or calculate
Lm = A_L N^2 for the secondary inductance in the spice model
and divide that by N^2 for the primary inductance, thereby
setting up the turns ratio for spice (isn't that awkward?).

The leakage inductance Lell is important; it's easily measured
by shorting the transformer, showing as k = sqr[Lm/(Lm+Lell)]
in the classic spice model, but I prefer to leave k = 1 and
add external inductances for Lm and Lell, so their presence
and effect is more clear in the drawing.

When you use a current transformer the load resistance is a
critical item. It's transformed down by N^2 to an effective
series resistance to the circuit being monitored, so you want
to use a relatively low load resistance. The low frequency
limit occurs when Lm shorts out the load, the high frequency
limit when the Lell reactance equals the load.

3. ### Clarence_AGuest

"Winfield Hill" wrote

Thanks Win.
I was using a five winding transformer model, the Current
transformer is a three phase unit, with a test winding and the
sense winding. But I didn't trust the results since I have never
seen any reference to what the model of a current transformer
would be. Again, Thanks.

4. ### JoergGuest

Hello Winfield,
That cannot be emphasized often enough. Woe to those who allow that load
resistance to fail. That can result in a serious kaboom situation
especially when large RF currents are measured. Once I blew a coax when
the load resistor failed. The toroid was gone, too. From then on I
always used two load resistors so at least you have a chance to detect a
mysterious jump in the readout and shut things down.

Regards, Joerg

5. ### Tony WilliamsGuest

I use MacFadyen's model for CT's, which did seem
to give predictable results for a series of
measurements on 1000:1 NiFe CT's, at 0-400Arms,
over the frequency range 400-700Hz. This was
a comparison of low-level measurements (and
predictions) against the actual CT performance
using a precision AC current source.

2
Rp (1-k )Lp Rs
o---/\/\--))))))))--+ +---+-----+--/\/\---o
| | | | |
)||( ) \ \
Np)||(Ns )Ls /Rc /Zl
)||( ) \ \
| | | | |
o-------------------+ +---+-----+---------o
2
Inductance Ratio= k.(Lp/Ls)

Shifting the leakage inductance over to the primary
side puts it in series with the (constant current)
source and allows it to be ignored.

MacF only had an Ls, which could be assumed to be complex
to allow for (inphase) iron losses, but I found it easier
to add a separate Rc for core loss.

In fact, (at 400-700Hz, on those 0.004" NiFe cores),
iron loss was the largest single factor in the departure
of current ratio from turns ratio. At 10Vrms across Rc,
each 8mW of iron loss was 0.8mA of shunt current, which
was 0.2% of Iout, or equivalent to a 2-turn error.

...... and the out_of_spec troubles on the CT's were
because the core mfr was supplying (expensive!) cores
with iron losses that could range from 3mW to 15mW.

I did a similar exercise with 15KHz/30mArms CT's, on
ferrite cores. MacF's model worked quite well there
also, although there were some common-mode (capacitive)
effects (reduced by using screened cable for the 2-turn
primary).

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