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DC Transformer Saturation
Revision History
Original 01 March 2009
02 March 2009: Revised to add data for six homebrew transformers
06 April 2009; Added 3rd order IMD data for DC in the core; added table of
contents
Table of Contents—this page
PWB1010-L_Frequency_Response_with_DC_Current
Home_Made_Transformers
Intermodulation_versus_DC_Current_PWB1010-L_Transformer
Broadband transformers are common items in the RF
projects I work on. If the transformer handles only RF, obtaining wideband
response is not all that complicated. Grab a couple of feet of small gauge
magnet wire, twist it into a twisted pair transmission line, wrap a dozen
or so turns around a high permeability ferrite core and your transformer is
done.
Of course, it isn't quite that simple, but it's really
pretty close to this description. I've described a simple broadband transformer
at
http://www.cliftonlaboratories.com/easy_broadband_transformer.htm for
example. Doug DeMaw's book
Ferromagnetic-Core Design and Application Handbook is a good starting
point for understanding small ferrite core transformers. The book is still in
print and available from its publisher, MFJ Enterprises as well as other
suppliers.
Things become more complicated when the transformer must
carry DC as well as RF. The DC current pushes the core's operating point out
along the BH curve, so that the core's incremental inductance drops, sometimes
significantly. This shows up as increased loss at low frequency. A second
problem is that the incremental flux may be centered on a non-linear portion of
the BH curve giving rise to increased intermodulation and harmonics. I've
written about transformers in general, ferrite transformers, BH curves in
several places on this site, including:
http://www.cliftonlaboratories.com/ferrite_transformers.htm
http://www.cliftonlaboratories.com/estimating_q_of_ferrite_cores.htm
http://www.cliftonlaboratories.com/type_43_ferrite_b-h_curve.htm
http://www.cliftonlaboratories.com/estimating_q_of_ferrite_cores.htm
http://www.cliftonlaboratories.com/non-linear_transformer_behavior.htm
http://www.cliftonlaboratories.com/inductor_choice_for_band_reject_filter.htm
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PWB1010-L Frequency Response with DC Current
Let's look at an example of DC current altering a ferrite
core transformer's frequency response. I'll use a small commercially available
transformer, Coilcraft's PWB1010-L device, specifications available at
http://www.coilcraft.com/pdfs/pwb.pdf. The performance I'll discuss is not
unique to this particular part, but rather is present to some degree or other in
all transformers.
The PWB1010-L is rated for a
typical 3 dB frequency response from 3.5 KHz to 125 MHz, with a 50 ohm source
and termination and a current carrying capacity of 250 mA. The figure below,
extracted from the data sheet, shows an impressive frequency response. |
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However, even modest amounts of DC current significantly
reduce the low frequency response as reflected in the plot below. (The test
setup I used to inject DC current into the PWB1010 causes about a 1 dB insertion
loss regardless of frequency.) At 50 mA DC current,
for example, the -3 dB response is increased to 300 KHz or more. Or, looked at
another way, 50 mA DC current increases the loss at 10 KHz from 0.5 dB to nearly
35 dB.
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The lower the transformer design frequency, the worse the DC
saturation can be. This is because achieving good low frequency response calls
for a high permeability core, usually a ferrite with a relative permeability in
the 800 - 10,000 range. Hence, even a small DC current can drive the BH curve
into saturation. And, the smaller the core is physically, the less the current
required for saturation, all else being equal. Thus, the PWB1010 has two strikes
against it when it comes to DC current handling capability—low frequency
response and a physically tiny package. Hence, it's not surprising that even a
small amount of DC current causes a problem. As the data shows, even 5 mA DC
current causes the PWB1010 to fail to meet its frequency performance
specification. What then of the 250 mA DC
current rating? This seems to be a fusing requirement, based on the wire size
used in the windings.
As remarked at the outset, the PWB1010 is a very good
transformer so long
 as it is not carrying DC. The lesson to be learned here is
that if an RF transformer or, for that matter, any inductor such as an RF
choke, that carries DC must be examined when carrying the rated current, not
just with zero current. Of course, if it's an air core device, DC saturation
isn't a problem. But, where a ferrite or powdered iron core is used, care must
be taken to verify the device's performance when operating at the rated DC
current and RF voltage. The PWB1010 is a tiny
transformer, wound on an even smaller core. The photo on the right shows the
PWB1010's core on a ruler with 1/32nd inch (0.8 mm) divisions. The core diameter
is around 0.10 inch, which is way too small for me to wind comfortably.
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Home Made Transformers
To see if it's possible to improve on the DC saturation performance of the
PWB1010, I measured an assortment of transformers I've built, selected from my
experiments box. I looked at six transformers:
|
ID Number |
Core Type |
Turns |
Inductance uH |
| T00 |
FT50-61 |
5 |
2.04 @ 7.9 MHz |
| T01 |
FT50-43 |
10 |
45 @ 2.5 MHz |
| T02 |
FT37-43 |
9 |
20.6 @ 2.5 MHz |
| T03 |
FT50-43 |
25 |
278 @ 790 KHz |
| T04 |
35T0501 |
13 |
not measured |
|
T05 |
35T0501 |
8 |
not measured |
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The 35T0501 cores are from Steward
http://www.steward.com/default.asp and are similar in size to Fair-Rite's
cores popularly known as "T50" types, although that's not Fair-Rite's
designation. Steward's 35 material has a relative permeability of 5000, so a few
turns results in a lot of inductance, compared with the commonly available 43
material (μr 800) or 61 (μr 125). Steward's nomenclature is the core material
[35] followed by a letter identifying the shape [T = toroid] and then the
diameter in 1/1000th of an inch [0501 ] 0.501 inches]. A selection of Steward
cores is carried by DigiKey and the prices are typical of these products,
depending on volume and core size, somewhere between 10 and 25 cents each for
cores of 0.5 inch and smaller.The price paid for 35
material's permeability is that these cores undergo dimensional resonance at a
relatively low frequency, in the 5 to 10 MHz range depending on the core size.
Dimensional resonance may or may not be a problem depending on the application.
The photo below shows the relative sizes of the PWB1010,
T02 and T03. (T01, T04 and T05 are essentially identical in size with T03.) |
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How then do these home brew transformers stack up against the PWB1010 when
carrying DC current? Based on nothing other than the physical size of the cores,
we expect all of these transformers to suffer much less low frequency loss. Of
course, core material has an important effect upon DC handling ability, as we'll
see.Let's start with the six transformers with no
DC current. The image below is reduced size and clicking on it will bring up a
larger image.
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Transformer T00 is was not intended to have low frequency response, and is
optimized for 2-100 MHz. T01 and T02 were designed with a low frequency response
target in the 100 - 200 KHz range, whilst T03, T04 and T05 are designed for low
frequency response down to 20 KHz. At the high frequency end, all transformers
are more than adequately flat to 30 MHz and beyond. The insertion loss in the
passband is 1.5 dB or so, which includes both the transformer insertion
loss and about 1.0 dB loss due to the bias tee used to inject current into the
transformer under test.The figure below (click on
the image for a larger version) shows what happens when these transformers also
carry 50 mA DC current. |
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T00 shows essentially no change in response when carrying 50
mA DC current; the other transformers suffer some reduction in low frequency
response, with the greatest loss increase being associated with the higher μr
material. This can be seen more clearly with the individual transformer plots
provided below at 100 mA. I've also provided
individual plots for each of the six homebrew transformers with 0 mA and 100 mA.
Click on the associated thumbnail image below for the large plot.
Individual Plots of Home Made Transformers
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T00 |
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T01 |
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T02 |
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T03 |
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T04 |
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T05 |
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Intermodulation versus DC Current PWB1010-L TransformerIn addition to
reducing low frequency response, DC in the transformer winding can also cause
intermodulation distortion. Or, perhaps more accurately, since all transformers
have some degree of intermodulation distortion even without DC, DC in a winding
can increase the transformer's intermodulation products.
We'll use the PWL1010-L as an example. In general, the smaller the core, the
less DC required to cause problems, all else being equal. Hence, it's easier to
see changes with IMD at low values of current injection.
The figure below shows the test setup. The 8904A generates two test tones and
also provides an adjustable bias current via summing a DC offset with the two
test tones. |
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The figure below shows two things:
- Increased bias current in a winding increases intermodulation products
(reduced 3rd order intercept IP3)
- For a given DC bias current, intermodulation is reduced with increasing
frequency (improved IP3).
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Why is this?
I've covered non-linear transformer action in detail
at Non-Linear Transformer Behavior
and I won't repeat the analysis on this page. The figure below is
copied from the Non-Li near
page and represents a typical B-H curve for an audio transformer. RF
transformers, such as the PWB1010-L have a similar B-H curve.
The horizontal axis is proportional to current (it is the
driving magnetic flux density, H) whilst the vertical axis is proportional to
the magnetic flux, B.
The AC input, be it at power frequencies, audio
frequencies or RF, cycles the magnetic flux density symmetrically about
the horizontal axis zero. The induced voltage in the transformer secondary is
proportional to rate of change (derivative) of the magnetic flux, B. Hence, if
the H field is constrained to the portion of the B-H curve where the curve
is straight and symmetrical, there is no distortion in the output.
As can be seen in the B-H curve, as H increases, B is
driven into non-linearity.
For a given voltage, B decreases with increasing
frequency. The classic relationship is:
B is the peak flux density in Gauss
E is the applied voltage; RMS sine wave assumed
f is the frequency in Hz
N is the number of turns
Ae is the core cross section in square centimeters
For our purpose it is sufficient to note that as the
frequency increases, B decreases. This means that as the frequency increases,
the transformer flux reduces and hence operates closer to the linear area near
the origin. Hence, intermodulation products should decrease with increasing
frequency, exactly as noted in the plot above and as also demonstrated at the
Non-Linear transformer page.
How does DC bias enter into this? DC bias, in essence,
shifts the zero or origin to one side. The greater the DC bias, the
greater the shift. Hence, the greater the bias, the greater the proportion of
the field forced into the non-linear part of the B-H curve.
The next figures illustrate the DC bias effect, with data taken at 50 KHz
center.
The first figure below is taken with a direct connection between the 8904A
synthesizer and the R3463 spectrum analyzer; the transformer is not used. Note
that there is no detectible 3rd order intermodulation product within the 70+ dB
spectrum analyzer range. |
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The next figure shows the effect of adding the PWB1010-L transformer with no DC
bias applied. The 3rd order intermodulation products are distinctly visible at
-60 dB from a single tone. The IP3 is therefore +30 dBm. |
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With only 10 mA DC current in the primary, the 3rd order intermodulation product
increases significantly, with a corresponding IP3 of 18.6 dBm. Note also there's
a slight reduction in tone amplitude, as expected from the frequency response
versus DC bias found in the earlier part of this page. |
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With 30 mA DC bias, each individual tone has dropped around 8 db and IP3 has
increased to +12.5 dBm. |
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