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Index |
Ferrites
in HF-applications
Measurements to core
materials (published in
Electron # 10, 2001) General This chapter is the sixth in a series of
articles on ferrite materials in HF-applications. The first article is an introduction
to this field with an overview
of some widely applied materials and most important properties. The
second article is on materials back-ground and most important
HF-application formulas. The third article is on HF inductors and transformers.
The fourth article is an introductory
to transmission-line transformers. The fifth article is on examples of transmission-line
transformers and their analysis. It is advisable to read the first three
articles in the above order first especially since next chapters are building
on information and formula's already explained earlier and referencing to
this. Introduction When designing transformers or inductors we
need to now the qualities of the constituents. In case of transistors and
integrated circuits it usually is the print on the housing that tells us the
particular type and with these type numbers the manufacturer will supply
further information. Type numbers usually are a unique coding that tells one
component from an other and manufacturers recognize and respect this coding. This is not the situation with ferrites and
other inductor core materials. Since these materials differ widely on
parameters and it is usually more than one parameter that determines fitness
to a specific application, it is important to tell one material from an other
to make sure the right material is being applied in the right application. An
impression on ferrite types and qualities may be found in the introductory
article on Ferrites in
HF applications and in Ferrite materials
and properties. Unfortunately many ferrite and iron-powder
core materials for HF applications are looking very much alike after
manufacturing. Many manufacturers only deliver bare and un-coded materials
and when some type of (color) coding is being applied, this usually is specific
to a particular manufacturer and even within this color-coding scheme, a wide
color variation from batch to batch may exist to indicate a specific material
type. When acquiring a specific material, the
supplier therefore will have to guarantee this material and it is up to the
designer and end-user to keep materials apart or marking-up locally. When
marking is lost or to determine a particular material from an unknown source,
only measurement will tell materials apart and that is what we will discuss
in this particular article. A great many materials are being around and
within a specific material one may find many different shapes. Although the
measurements in this chapter will focus on popular toroidal inductor shapes,
formulas and tests also apply to other shapes and variations. Basic formula for an inductor on a magnetic
core: L = n2 .mr .m0 .A / l
(H)
(4) To design / characterize an inductor we need
to identify n = number of turns, A = core area and l = magnetic path length.
Factor 'm0' = general permeability = 4 . p . 10-7 and mr = relative permeability, to be specified by
the manufacturer. If any of these parameters is unknown, we have to measure. This is a mechanical measurement with the
caliper and should be performed to the bare material. When factory coated,
this may be included since coating usual have a thickness of around 10 mm. The area is determined with: A
= (D - d) .h / 2 (20) and magnetic path length with: l
= (D + d) .p / 2 (21) with D = outside diameter, d = inside
diameter and h = height of the toroide, all dimensions as always in meters,
unless specifically indicated otherwise. Sometimes the toroide is not exactly round so
the average diameters should be taken; this may also apply to the core
height. In view of the usual factory tolerance, measuring A/l within 5 % is
already very accurate. Measuring relative
permeability Measuring relative permeability is a bit
tricky since this parameter is depending on the magnetic field strength
(induction), frequency and temperature. Measurements have to be performed
within a temperature range of 20 - Properties of ferrite materials are also
depending on magnetic field strength; at higher flux permeability is
following a hysteresis path with a specific shape for each (ferrite)
material. Therefore all magnetic parameters are being measured at a very low
flux of 0,1 mT (milli-Tesla)
or lower. This is an industrially agreed method to directly compare
permeability of materials by different manufacturers. Core materials however will also be applied
at large(r) field strength even up to the point where saturation sets in.
Manufacturers therefore will specify the complete hysteresis curve (B-H
curve); these measurements however are beyond the scope of this discussion. Measuring initial permeability mi Since frequency is one of the factors
determining final permeability, manufacturers have agreed to measure the
initial permeability at such low frequency that even the higher permeability
materials (lowest maximum frequency) will not be affected. This agreed
frequency is 10 kHz., with a magnetic field strength of 0,1 mT. Relative permeability of any core material
may be determined by measuring inductance of an inductor with a low number of
turns. Ideally this measurement will be performed with a dedicated measuring
bridge, running at 10 kHz. When this is not available, a very acceptable
method consists of determining resonant properties of the inductor using a
known capacitor, a LF frequency generator and an AC voltmeter. An example
of this test set-up, the magnetic core
under test and ten turns of a test inductor is schematically shown in figure
3.
In the set-up of figure 3, resonance will be
determined by changing the frequency of the LG generator until maximum
amplitude is being measured with the AC-voltmeter. Care should be taken to
not change the frequency too quickly as the quality factor of the resonant
circuit may be quite high with peak voltage to be easily missed. The
resonating capacitor of 0,1 mF should be of relatively high accuracy since the value of this
capacitor is determining the accuracy of this measurement set-up to a large
extend. Better not apply a decoupling type of capacitor as these usually are
specified with a tolerance of -20% to + 50%. Any other capacitor with a +/-
5% specification will do, since measuring frequencies will be relatively low.
From the above formula for the inductance and
the general resonance formula (2 p fr)
mi = (2 .109 .l) / (fr2
.A) (22) This measurement set-up will do nicely for a
wide range of toroide dimensions and materials with resonance frequencies to
range between 1 and 150 kHz. With the generator delivering 0,5 Vrms or below, voltage across the
inductor will be low enough to stay outside hysteresis effects, so this
set-up is measuring the real mi Measuring permeability at
frequency At higher frequencies permeability is
splitting up into two factors, of which one is the loss factor. Relative
permeability therefore may be written as: mr = m’ – j. m”, with m’ as the inductivity factor and j.m” as the loss factor. The complex factor 'j' is determining the
relative phase component of 90 ° between the voltage and current at this
component. Since pure inductivity makes voltage and current to run 90 ° out
of phase, the 'j' term in the permeability makes the inductor loss into an
in-phase term again, so we are really discussing loss that will generate heat
('Ohmic' loss). To determine both m’ and m” at a certain frequency, we need
an instrument to measure both factors at the same time. A few examples of
such instruments are the measuring bridges by General Radio, Hewlett Packard
and Marconi as very accurate and professional instruments. At a (much) lower
budget we find instruments by MFJ (e.g. MFJ-259B) and Autek
Research (RF-1, RF-Analyst). Different instruments will measure different
parameters that may usually be re-worked into and in-phase and a quadrature
component. Since most instruments operate most
accurately around a terminating impedance of 50 Ohm, we best start at the
lowest measuring frequency with an impedance around 25 Ohm. Since we are
measuring inductive loads, impedance will go up at higher frequencies. As an example we will determine m’ and m” at 1,8 MHz. When we like to see
a lower impedance XL = 25 W, impedance should be: L = XL / 2.p.f
= 25 / (2. p . 1,8. 106 ) = 2,21 mH. Say we found for the initial permeability in
our first measurement mi = 100, we determine the number of turns for
this more extensive measurement using formula 4:
since each turn through the balun hole is accounting
for a complete turn. In this example, l and A are taken
from a To avoid copper loss we will apply wire with
a diameter of Since permeability is not changing too
quickly over frequency we may spread measurements to a few well selected
points of interest, e.g. spaced-out radio-amateur frequencies. As soon as
impedance is becoming too high (say over 150 Ohm), we take-off turns to
arrive at the ball-park impedance around 50 Ohm again. In the example of
table 6 we took 4 turns starting at 1,8 MHz., and changed to 2 turns at 14
MHz.
Table 6.
Measurements to an example inductor Our measurements presented the values for Rs and Xs
in the 3rd and 4th column. With the first and fourth column we calculate
inductance in the fifth column with: L = XS
/ 2 p f
and permeability (m’, sixth column) and loss (m”) according to: m’ = XS
/ (2 p f n² m 0 A / l )
en m” = RS
/ (2 p f n² m 0 A / l) If we compare the measurement results from
table 6 with the materials overview of table As we noticed earlier, the relation between B
en H (permeability) is also determined by the absolute strength of the
magnetic field. At large(r) field strength this relation is no longer linear
so it may be useful to determine parameters under various field strength
conditions to get an impression of the behavior of this component in a
practical system. Earlier we derived a formula for maximum voltage across an
inductor to drive this component inside the linear field-strength region. One
of the parameters in this formula is saturation field strength, Bsat,
usually presented by the manufacturer, but may also be measured in the
set-up of figure 4.
The Device Under test (DUT) in this case is a
1 : 1 transformer, possibly a HF balun. In the linear region, the load Rb = 50 Ohm, is transformed from the output
tot the input of the DUT, thereby presenting the required termination
impedance to the generator. The HF voltmeter may be any device capable of
measuring at the required frequency, or an oscilloscope. Best instrument of
course is a tuned measuring system to only measure at the desired frequency
and ignoring higher harmonics. For measuring purposes, an additional, low
turns measuring coil has been added to the DUT, which will only marginally
influence measurement accuracy. The following steps are to be taken for this
measurement: With the switch in the upper position, a
reference measurement U1 is being made, to be followed by a second
measurement with the switch in the lower position to measure U2. According to Faraday's law, we may write: with: n = number of turns of the additional coil A = area of the magnetic material w = 2 p f
with f as the measuring frequency B = core induction Reworking this formula for the maximum core
induction (we are 'normally' measuring rms values):
Bmax = U2 Ö2 / (n w A) In practice it is better to express
saturation as related to input voltage U1 and transformer ratio T
= U2 / U1. Induction may than be expressed as: Bmax = U1 T Ö2 / (n w A) (24) With this set-up we determine core induction
at a specific frequency and input voltage, the latter related to system power
according to: P = (U1)2 / Zin (25) In linear application, inductions should be
lower than 0,2 Bsat, so maximum
allowable system power for this component follows directly from this test
set-up. As an example we tested the Ruthroff 1 : 2,25
transformer as in the last part of our
article on transmission-line
transformers. This transformer has been constructed using a When we are to apply this transformer in a 50
Ohm environment, at a system power of 1000 W., U1 will be 224 V. from
which we calculate: Bmax = 224 . 0,32 . Ö2 / (2 p 3,6 .106. 1,11 . 10-4)
= 20,2 mT. Since saturation of 4A11 is specified at 340 mT, we may safely apply this transformer at this system
power and frequency and still be within the linear application region. In HF
applications above 1 MHz however, it usually is the core loss-power that will
determine maximum voltage across the coil instead of the maximum voltage for
linearity, we calculated above. Formulas and example calculations may be
found at Ferrite
materials and properties. The above linearity test set-up therefore is
only is serving as a means to determine saturation level. Bob J. van Donselaar, on9cvd@veron.nl |
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