Journal of ELECTRICAL ENGINEERING, VOL 57. NO 8/S, 2006, 105-109
COMPUTER CONTROLLED SYSTEM FOR COMPLEX PERMEABILITY
MEASUREMENT IN THE FREQUENCY RANGE OF 5 Hz − 1 GHz
Rastislav Dosoudil* − Elemír Ušák − Vladimír Olah
Two different methods have been used to determine the complex permeability over the frequency range 5 Hz to 1 GHz of several toroidal−shaped spinel ferrite samples. Automated measurements are obtained by means of two different computer controlled
analyzers. At low frequencies (5 Hz − 10 MHz), an inductance measurement method is used. A simple method was used to eliminate the coil effects from the sample response. At high frequencies (1 MHz − 1 GHz), a coaxial transmission line measurement
method has been used. The operation principle as well as calibration and compensation procedures for both the analyzers are discussed. Measurements are optimised by the partial elimination of undesirable influences. For computer control and measurement
process, two different programs have been written in the VEE environment (Agilent technology).
Keywords: complex permeability, sintered ferrite, low−capacitance winding, coaxial line cell, impedance, reflection coefficient
1 INTRODUCTION
An automated equipment for the measurement of complex (relative) permeability µ~ = µ ′ − jµ ′′ of soft magnetic
materials has been developed by using two different analyzers (Fig. 1). The measuring frequency can be set between 5 Hz and 1000 MHz.
APC-7
test port
4 BNC
terminals
Sample
under
Network
Analyzer
HP4191A
GPIB bus
der test), also flows through resistor R. The potential at
the “Low” point is maintained at zero volts (thus called a
“virtual ground”), because the current Ir through R is balanced with Z x current Ix by operation of the I−V converter
amplifier. The measured impedance Z x is calculated using
voltage measurement at “High” terminal Us and that
across R (Ur): Zx ≈ RUs/Ur. The analyzer employs the I−V
converter consisting of sophisticated null detector, integrator (loop filter) and vector modulator to ensure a high
accuracy for a broad frequency range.
u
Terminal
adapter
16085B
test
µ
f
t
Impedance
Analyzer
HP4192A
Personal
computer
High
Test
signal
source
USB/GPIB
Interface
82357A
Zx
Low
Ix
R
Ir
Measured
impedance
G Us
V2 Ur
V1
I-V
Converter
Fig. 2. The operation principle of HP4192A.
Fig. 1. The schematic diagram of an automated system with
two different analyzers and view of set-up.
The first analyzer (HP4192A), working in the frequency
range
of
5 Hz − 13 MHz,
uses
the
auto−balancing−bridge method, Fig. 2, [1]. The current,
flowing through the measured impedance Z x (sample un-
The second analyzer (HP4191A), working in the frequency range of 1 − 1000 MHz, uses network analysis
measurement method, Fig. 3, [2]. The directional bridge
circuit has a test port (APC−7 coaxial connector) to connect the sample under test (Z x) and provides an output
signal proportional to the complex reflection coefficient
Γ~ of Z x ( Γ~ = Γ ′ + jΓ ′′ ), which is the ratio of a reflected
signal to the incident signal. To achieve accurate measurement of Γ~ , the frequency of the directional bridge
output signal is converted to 100 kHz by the sampling IF
converter. The vector ratio of the reference and test channel IF signals is detected for both of the real and imaginary component vectors, which coincide with the compo-

* Department of Electromagnetic Theory, Slovak University of Technology, Faculty of Electrical Engineering and Information Technology, Ilkovičova 3,
812 19 Bratislava 1, Slovakia, e-mail: rastislav.dosoudil@stuba.sk
ISSN 1335-3632 © 2006 FEI STU
106
R. Dosoudil et al: MEASUREMENT OF COMPLEX PERMEABILITY IN THE RF BAND
nents Γ ′ and Γ ′′ of the measured Γ~ . The other measurement parameter values (R, X, B, G) are calculated from the
values of the measured components ( Γ ′ , Γ ′′ ). Both the
analyzers (HP4192A and HP4191A) are equipped with the
microprocessor based digital control circuit, which controls the operation of the analogue measurement circuits.
The USB/GPIB interface provides a simple connection of
the computer and various GPIB compatible instruments.
u
t
Test
signal
source
50 Ω
50 Ω
G
Power divider
V1
Directional
bridge
HP4192A also the level of output signal), b) perform both
the electrical length and residual/stray impedance (admittance) compensations, c) check the level of signal − voltage across or current through the sample under test
(HP4192A only), d) recalculate the obtained measured
quantity ( Γ~ in case of HP4191A and Z x in case of
HP4192A) to corresponding values of µ~ , and view the
curves.
2 PERMEABILITY MEASUREMENT AT LOW
FREQUENCIES (5 Hz − 10 MHz)
V2
Reflected
signal
Incident
signal
Sample
Zx under
test
A toroidal−shaped ferrite core with complex (relative)
permeability µ~ = µ ′ − jµ ′′ , cross section S and average
magnetic path length ls, provided with a winding of N
turns, can be treated as an impedance Z = Rs + jωLs consisting of a self−inductance Ls and a resistance Rs in series, Fig. 4a.
a)
Fig. 3. The operation principle of HP4191A.
The measurement of complex permeability µ~ will be
discussed from the point of view of two aspects: a) the
used frequency range, and b) the used measurement
method. In the low frequency range of 5 Hz to 10 MHz
(measurements performed using the HP4192A instrument), the inductance/resistance measurement method was
used. In this method, complex permeability µ~ is obtained
by measuring the inductance (ωLs) and the resistance (Rs)
differences between a coil wound around the toroidal
sample and one wound around a non−magnetic blank
(with the dimensions identical with those of used toroidal
core). In this case we will discuss several effects (stray
capacitance, number of windings, repeatability,
λ/4−dimensional resonance phenomena, etc.). In the
higher frequency range from 1 to 1000 MHz (measurements performed using the HP4191A analyzer), a coaxial
transmission line measurement method has been used, [2].
In this case, the high−frequency permeability can be obtained by measuring the input impedance differences between a coaxial line cell loaded with a toroidal core and
the cell without the core. Two similar coaxial line cells
were used (one is a handmade for large cores and the
other is an original product of Agilent for small cores:
16091A). In the case of both measurement methods, impedance measurements were optimized by the partial
elimination of undesirable influences. Several soft magnetic materials (sintered MnZn ferrites) were used to verify the relevance of used measurement methods. The calibration as well as compensation procedures for both the
instruments will be discussed in detail. For computer control and all the necessary measurement processes as well
as evaluation of obtained results, two simple programs
have been written in VEE environment (Agilent technology). The programs allow to: a) define the measuring
conditions (test frequency, frequency step, in case of
A
A
b)
Rs
Ls
B
A
Rs
Ls
B
Cp
B
Fig. 4. Ferrite core with winding and its equivalent electric
circuits.
Therefore, the complex permeability can be derived
from the impedance measurement results using the following expressions
Rs + jωLs = jωµ o S (µ ′ − jµ ′′)
µ′ =
ls (Ls,2 − Ls,1 )
µ o SN
2
µ ′′ =
N2
ls
ls (Rs,2 − Rs,1 )
µ o ωSN 2
(1)
(2)
where Rs,1 and ωLs,1 are the series resistance and inductance of a toroidal coil without magnetic core, Rs,2 and
ωL s,2 are the series resistance and inductance of a toroidal
coil
with
magnetic
core
(Rs = Rs,2 − Rs,1
and
Ls = Ls,2 − Ls,1), respectively. This approach has some major disadvantages. First, since the measurement is based
on a handmade inductor, measurement results are affected
by how an inductor is made. If many core samples are
measured, repeatability can be a problem due to a variation of coil winding. We can get rid of this problem by
measuring impedance of an inductor with ferrite sample at
a temperature higher than the Curie point Tc of the ferrite
core, where it becomes paramagnetic, i.e. virtually a
non−magnetic material. This procedure ensures that geometry, dimensions and number of turns are identical both
in the high permeability, ordered ferromagnetic state
(T < Tc) than in the very low permeability disordered
paramagnetic phase (T > Tc). The frequency dependence
of complex permeability of ferrite sample can therefore be
separated from that of the wound coil, simply by subtract-
107
Journal of ELECTRICAL ENGINEERING, VOL.57, NO.8/S, 2006
ing point to point for each frequency the results of wound
sample evaluated at T > Tc from those obtained for the
same sample evaluated at room temperature (below Tc).
This means that the overall frequency dependence of
complex permeability is a contribution of the coil dependence plus the sample dependence. Second, as the frequency increases, physical dimensions of magnetic core
get small, making winding and quality control of the test
turns even more difficult. This effect cannot be avoided.
Third, since some spinel ferrites such as MnZn are semiconductors with low electrical resistivity 10 -1 to 10 2 Ωm,
high permeability 102 to 10 4 and high electrical permittivity 10 2 to 105, there is a possibility of arising of eddy currents that can affect the dispersion of permeability. Moreover, the cross−section of the ferrite core to be measured
may have to be kept small in order to avoid
λ/4−dimensional resonance phenomena. The reason is
that, owing to the high permittivity, it is possible that at
the measuring frequency the wave length λ in the ferrite
will be of the order of magnitude of a linear dimension,
which can give rise to standing−wave phenomena in the
core material. It is also possible that a ferrite core may
contribute to the stray capacitance of a winding. Besides
the self−inductance Ls and resistance Rs (in Eqs. 1 and 2),
the complete equivalent circuit also contains the stray parallel capacitance Cp shown in Fig. 4b. Between the terminals A and B apparent values Rs′ and Ls′ are thus measured, which are related to the true values Rs and Ls by the
equations:
Rs
(1 − ω L C ) + (ωC R )
2
2
s
(3)
2
p
p
s

Cp Rs2 

ωLs 1 − ω 2 Ls Cp −

Ls 

X s′ = ωLs′ =
2
2
1 − ω 2 Ls Cp + ωCp Rs
(
) (
)
1
4πf r2 Ls ( f r ) +
Rs2 ( f r )
Ls ( f r )
In addition, in cases where the ferrite core has a high
permittivity ε , the stray capacitance can be reduced by
winding the ferrite core beforehand with an insulating
material of low ε . The self−inductance Ls cannot be arbitrary small, since otherwise the stray self−inductances of
the supply leads would become relatively important. In
that case the core can be wound with metal strip, but it is
even better to use a single coaxial winding, a kind of box
fitting closely around the ferrite ring [3−5].
The effect of stray capacitance on the measurement of
the complex permeability was verified by means of the
following experimental procedure. First, we used one set
of winding to measure the complex permeability. Then,
two exactly same sets of windings are connected in parallel (Fig. 5) in order to make the self−capacitance Cp of
winding small. The measured results of MnZn ferrite
(with dimensions: 12×8×4 mm) with initial permeability
µi ≈ 22000 are shown in Fig. 6. In this case, the stray capacitance Cp ≈ 0.5 pF giving the self−resonance frequency
fr ≈ 56 MHz (according to Eq. 5) was obtained by a
method described in [5]. The results indicate that the
complex permeability is affected by the arrangement of
winding along the toroidal core.
(4)
25000
MnZn ferrite T46
The total stray (or parasitic) capacitance Cp can be derived
from Eq. 4 by means of the resonance condition [3]: the
self−resonance frequency fr of a winding is defined as the
frequency at which its reactance X s′ becomes zero.
Hence, from Eq. 4, the stray capacitance Cp is given by:
Cp =
Fig. 5. View of low−capacitance winding of five turns on core
and its connection to the HP4192A analyzer via a post fixture.
(5)
where Ls(fr) and Rs(fr) are the self−inductance and resistance at f of fr. The capacitance Cp is assumed to be independent of frequency. The values of µ ′ and µ ′′ derived
from Ls′ and Rs′ according to Eqs. 1 and 2 will differ all
the more from the real values the larger is the value of
ω2 Ls Cp. This is particularly the case at higher frequencies,
at which Cp and Ls must therefore be kept as small as possible. In order to make Cp small, we provided the ring core
Complex permeability
Rs′ =
with a special low−capacitance winding, in the manner
showed in Fig. 5.
µ'
20000
One set of winding
Two sets of winding
(Low-capacitance
winding)
15000
10000
µ''
5000
0
3
10
4
10
5
10
Frequency (Hz)
10
6
7
10
Fig. 6. Complex permeability spectra for sintered ferrite T46
(MnZn) measured using the HP4192A analyzer
3 PERMEABILITY MEASUREMENT AT HIGH
FREQUENCIES (1 MHz − 1 GHz)
At higher frequencies (> 100 kHz), due to arising of
stray (parasitic) capacitance of windings, it is highly recommended to use the measurement method by means of
which we can avoid the problems discussed in the previ-
108
R. Dosoudil et al: MEASUREMENT OF COMPLEX PERMEABILITY IN THE RF BAND
ous section. According to this fact, we have used the coaxial transmission line technique [2]. For this purpose,
two different coaxial line cells have been used, Fig. 7. The
first one was a user−fabricated for large cores (up to
15 mm in diameter) and the other one was an original
product of Agilent (16091A) for small cores (up to 10 mm
in diameter). The first one was terminated with N−type
coaxial connector and the second one with the APC−7
connector. The analyzer HP4191A has a test port
equipped with a fixed APC−7 connector. The HP4192A
can also be used to measure the complex impedance of
coaxial cells loaded with magnetic cores (in the frequency
range from about 100 kHz to 13 MHz). Since this instrument terminates with four BNC connectors, it requires to
use the terminal adapter 16085B, which converts BNC
outputs into one APC−7 port. Hence, both the analyzers
can employ the 50 Ω coaxial measurement technique.
When the sample is inserted into the first (handmade)
cell or the other (16091A), the whole system is completely
closed and then connected through the N to APC−7
adapter (first cell) or directly (second cell) to the previously calibrated impedance analyser. The analyser supplies an electromagnetic wave propagating in a TEM
mode. The impedance (HP4192A) or reflection coefficient
(HP4191A) is measured, permitting the determination of
the input impedance Z in of the cell with the sample. Based
on the approach presented in [2] we derive the equation
for the determination of complex permeability of any cell
equipped with the test sample, Figs. 7 and 8. Since the
construction of the cell creates one turn around the toroid
(with no magnetic flux leakage), the complex magnetic
flux of the measurement circuit including the ring core is
given by the equation
a b
µ µ~ I
~=
Φ
∫0 ∫0 2πo ⋅rx dxdy =
d2
2 b
µ I
+ ∫ ∫ o dxdy +
2
d h π ⋅x
1
d2
2 h
µ I
µ µ~ I
∫d ∫0 2πo⋅ x dxdy + d∫ ∫0 2πo ⋅rx dxdy +
a b
2
1
2
2
d1
2 b
b
µ I
µ I
∫0 ∫0 2πo⋅ x dxdy − ∫0 ∫0 2πo⋅ x dxdy
a1
(6)
2
Fig. 7. View of the cells mounted on APC−7 test port (from
left to right): Agilent 16091A cell, handmade cell along with
N to APC−7 adapter, and handmade cell with a ferrite core.
Each of the used coaxial line cells is a highly conductive rugged shield surrounding the central conductor
which terminates in a short circuit. The short circuit produces a maximum magnetic field and a minimum electric
field near the toroidal sample, thus making the
“short−circuit” technique particularly suited for the measurement of the magnetic properties of sample under test
such as permeability. The medium between the inner and
outer conductors of cells is air. The inner length b of cells
(b = 12 mm for handmade one and 20 mm for 16091A)
obeys the condition b < λ/4 for f ≤ 1 GHz in order to
avoid the λ/4−size resonance effect, Fig. 8.
where µ o is permeability of free space, and I is phasor of
harmonic time–dependent electric current. The complex
susceptibility of a sample under test is then given by
~-Φ
~ )
2π ⋅ (Φ
air
(7)
χ~ =
 d2 
h ⋅ I ⋅ µ o ⋅ ln 
 d1 
~ = (bµ I 2π ) ⋅ ln(a a ) is the magnetic flux when
where Φ
air
o
Eq. 7 we can use corresponding complex impedances Z
(measured on a cell with core) and Z air (measured on a cell
without core)
µ~r = 1 + χ~ = 1 +
b)
a)
sample y
2a1
2a
b
d2
d1
R
B
L
analyzer
b
h
i(t)
2a
Fig. 8. a) The cell with a sample and its equivalent electric
circuit, and b) its cross−section.
x
1
ferrite core is not inserted in the cell. The measured complex impedance Z of an equivalent electric circuit of the
cell loaded with the ferrite core shown in Fig. 8a is given
~ /I. Instead of fluxes Φ
~ and Φ
~ in
by Z = R + jωL = jω Φ
air
(Z - Z air )
d 
jh ⋅ µ o ⋅ f ⋅ ln 2 
 d1 
(8)
where d 1 and d 2 are the inner and outer diameters of the
toroid, respectively, h is the height of the toroid, and f is
the frequency of applied ac electromagnetic field. Complex (relative) permeability is therefore calculated from
difference between the impedance Z of the cell loaded
with the toroidal sample and the impedance Zair of the
empty cell.
The analyser HP4191A measures the complex reflection coefficient Γ~ = Γ ′ + jΓ ′′ which is recalculated to the
input impedance of the cell Z in (with or without a sample)
109
Journal of ELECTRICAL ENGINEERING, VOL.57, NO.8/S, 2006
tic impedance of the 7 mm (APC−7) test port. Resistance
(Rin) a reactance (Xin) values of the input impedance of the
cell Z in = Rin +jXin can then be calculated using the following relations:
Rin = Z o
1 − Γ ′ 2 − Γ ′′ 2
(1 − Γ ′)2 + Γ ′′ 2
X in = Z o
2Γ ′′
(1 − Γ ′)2 + Γ ′′ 2
(9,10)
It should be noted that since the handmade cell is connected to the test port via an N to APC−7 adapter, special
attention must be paid to the errors caused by these additional parts − one is residual impedance error and the
other is electrical length error. The residual impedance,
which includes distributed parameters such as residual
resistance, residual inductance, stray conductance and
stray capacitance, makes the measurement values inaccurate. The electrical length error occurs due to a phase shift
of the test signal along the 50 Ω transmission line between
the calibration plane (i.e. APC−7 test port) and the cell.
This leads to an impedance measurement error when
measuring phase. Phase shift error can be compensated
with electrical length compensation function which both
the analysers provide automatically. Residual impedance
error can be compensated with SHORT and OPEN compensation functions, which only the HP4192A instrument
provides automatically. The second analyzer (HP4191A)
does not have such a possibility. In this case, we can remove the residual impedance error from the measurement
results by computing the SHORT and OPEN compensation values using the user−developed software through an
external computer. The details of residual impedance and
electrical length compensations are discussed in [2].
Without these compensations spurious geometrical resonances might be present in the measured data.
As an example, figure 9 shows the frequency dependences of real µ ′ and imaginary µ ′′ parts of complex relative permeability µ~ = µ ′ − jµ ′′ calculated using Eq. 8
from measured impedance values for sintered ferrite H40
(MnZn). We also checked the level of ac current passing
through the coaxial cell, i.e. the amplitude of ac magnetic
field intensity Hac which should not be higher than about
0.5 A/m in order to fulfil the initial permeability condition. For the MnZn ferrite in its sintered form it is just
about 0.4 to 0.5 A/m. The dimensions of toroidal sample
used here were 10×6×4 mm. The thickness h = 4 mm of
sample satisfies the condition, at which λ/4−dimensional
resonance effect cannot occur in the measured results:
h < λ/4. The value of Hac was investigated because both
the analysers do not have the constant−current mode. The
change of real part of complex permeability with frequency is called the dispersion of permeability and the
change of imaginary part with frequency is known as absorption. MnZn sintered ferrite H40 showed a resonance
type of frequency dispersion of permeability, the low fre-
quency real part of complex permeability is about 5600
and the critical resonance/relaxation frequency at which
the imaginary part µ ′′ has its maximum is about 1 MHz.
7000
Complex permeability
according
to
the
following
equation:
~
~
Z in = Zo(1 + Γ )/(1 − Γ ), with Zo = 50 Ω the characteris-
MnZn ferrite H40
µ'
6000
Data measured
on HP4191A
(1 MHz - 1 GHz)
5000
Data measured
on HP4192A
(1 kHz - 10 MHz)
4000
3000
2000
µ''
1000
0
10
3
10
4
10
5
6
7
10
10
Frequency (Hz)
8
10
10
9
Fig. 9. Complex permeability spectra for sintered ferrite H40
(MnZn) measured using both the analyzers
4 CONCLUSION
We have described a computer controlled system for
the measurement of complex permeability of soft magnetic materials using two different analyzers. The described system gives us the ability to perform measurements over a wide range of frequencies in order to achieve
better understanding of resonance/relaxation processes
particularly in spinel ferrites and related materials. The
data treatment is discussed, paying special attention to the
proper conversion of the impedance/reflection coefficient
measurement to permeability spectra. The used sample
coaxial cells can be connected with the test port via a precision coaxial cable in order to provide measurements in
the dependence on temperature (in a convenient furnace)
and/or dc bias magnetic field (in a suitable electromagnet). All measurement processes are computer controlled
by the developed VEE programs.
Acknowledgement
This work was supported by VG-3096-Slá-SK1 grant of
VEGA agency of the Slovak Republic.
REFERENCES
[1] Agilent 4192A, LF Impedance Analyzer, Operation manual
[2] DOSOUDIL, R. − OLAH, V.: Measurement of Complex Permeability in the RF Band, Journal of Electrical Engineering 55, No. 10/S,
(2004), pp. 97-100.
[3] KAZIMIERCZUK, M. K. et al: High−Frequency Small−Signal
Model of Ferrite Core Inductors, IEEE Trans. Magn. 35, No. 5 (1999),
pp. 4185-4191.
[4] SMIT, J. − WIJN, H. P. J.: Ferrites, Philips Technical Library, Eindhoven, Netherlands, 1962. (in German)
[5] YURSHEVICH, V. et al: Measurement of Self−Capacitance for
Windings on High−Permeability Ferrite Cores, Measurement Science
Review 1, No. 1 (2001), pp. 219-222.
Received 2 November 2006