IEC 60556:2006/AMD1:2016

IEC 60556 ®
Edition 2.0 2016-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
AM ENDMENT 1
AM ENDEMENT 1
Gyromagnetic materials intended for application at microwave frequencies –
Measuring methods for properties

Matériaux gyromagnétiques destinés à des applications hyperfréquences –
Méthodes de mesure des propriétés

IEC 60556:2006-04/AMD1:2016-03(en-fr)

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IEC 60556 ®
Edition 2.0 2016-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
AM ENDMENT 1
AM ENDEMENT 1
Gyromagnetic materials intended for application at microwave frequencies –

Measuring methods for properties

Matériaux gyromagnétiques destinés à des applications hyperfréquences –

Méthodes de mesure des propriétés

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 29.100.10 ISBN 978-2-8322-3274-3

– 2 – IEC 60556:2006/AMD1:2016
© IEC 2016
FOREWORD
This amendment has been prepared by IEC technical committee 51: Magnetic components
and ferrite materials.
The text of this amendment is based on the following documents:
CDV Report on voting
51/1064/CDV 51/1089A/RVC
Full information on the voting for the approval of this amendment can be found in the report
on voting indicated in the above table.
The committee has decided that the contents of this amendment and the base publication will
remain unchanged until the stability date indicated on the IEC website under
"http://webstore.iec.ch" in the data related to the specific publication. At this date, the
publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
_____________
Add, after Clause 11, the following new Clause 12 and Annex A:
12 Gyromagnetic resonance linewidth ΔH and effective gyromagnetic ratio γ
eff
by non resonant method
12.1 General
So far the gyromagnetic resonance linewidth ΔH and the effective gyromagnetic ratio γ have
eff
been measured by using the resonant cavity as described in Clause 6. Therefore, the
measuring frequency is restricted to the frequency specified by a cavity resonator.
Meanwhile, various kinds of ferrite devices have been developed in a wide frequency range.
Accordingly it is desirable to measure the gyromagnetic resonance linewidth ΔH and the
effective gyromagnetic ratio γ easily at any frequency demanded for the development of
eff
ferrite materials or devices. Moreover, there are two problems in the cavity resonator method
described in Clause 6. One problem is the insufficient resolution of a magneto flux density
meter, which is apt to cause poor accuracy in the measurement of the narrow resonance

© IEC 2016
linewidth. Another problem is that a ferrite sample becomes too small to be shaped into a
sphere or a disk, because it is necessary to reduce the size of a ferrite sample to keep the
resonance absorption increasing with the reduction of the resonance linewidth to proper
values in order to ensure a sufficiently small cavity perturbation. In Clause 12, the measuring
methods of the gyromagnetic resonance linewidth ΔH and the effective gyromagnetic ratio γ
eff
at an arbitrary frequency are described.
12.2 Object
To describe methods that can be used for measuring the gyromagnetic resonance linewidth
ΔH and the effective gyromagnetic ratio γ of isotropic microwave ferrites at an arbitrary
eff
frequency over the frequency range of 1 GHz to 10 GHz by the measurement of the changes
in transmission and reflection characteristics with frequency sweep.
12.3 Measuring methods
12.3.1 General
The measurements are performed by measuring the changes of transmission characteristics,
such as complex reflection coefficients or scalar transmission coefficients, in a transmission
line loaded with a ferrite sample with frequency sweep. The advent of a frequency synthesizer
and a receiver with low noise figure and a wide dynamic range in the microwave region has
made it possible to perform these measurements accurately.
Strictly speaking, the linewidth measured under frequency sweep and a constant external
magnetic field is not the same as the one measured under external magnetic field sweep and
a constant frequency as described in Clause 6. However the difference between two
measured values is small to the extent that it causes no problem in practical use.
As the measuring method, two methods can be considered as follows:
1) Reflection method – method measuring the reflection coefficients from the short-circuited
transmission line loaded with a ferrite sample.
2) Transmission method – method measuring the transmission power through a ferrite-
loaded coupling hole made in a common ground plane of the transmission lines crossing
at right angle.
These two methods have advantages and disadvantages in comparison with each other from
the standpoint of practical use. The reflection method has the advantage of a simple test
fixture’s structure, easier sample mounting and simpler measuring circuit arrangement due to
one port measurement, which is convenient for the measurement of temperature dependence
of the resonance linewidth. The transmission method has the advantage of being able to
measure the resonance linewidth by one ferrite sample in a wide frequency range and gives
more accurate measuring values of the resonance linewidth due to simpler measurement, i.e.
the measurement of the transmission power only, under careful making of a test fixture.
These two methods are enumerated in 12.3.2 and 12.3.3.
12.3.2 Reflection method
12.3.2.1 Measurement theory
The recommended method for measuring the gyromagnetic resonance linewidth ΔH and
effective gyromagnetic ratio γ is based on the measurement of the reflection coefficient S
eff 11
of a short-circuited transmission line with the specimen as proposed by Bady [20]. In this
standard, the short-circuited microstrip line is used as schematically shown in Figure 27.

– 4 – IEC 60556:2006/AMD1:2016
© IEC 2016
Reference plane (virtual)
z
Stripline
Connector
for µ = 1
for FMR
y
H
H cal
ext
x
Short end
Ground
Specimen
IEC
Figure 27 – Schematic drawing of short-circuited
microstrip line fixture with specimen
The reference plane is defined by the length of the specimen from the short end. Seen from
the reference plane of the test fixture, the lumped element equivalent circuit can be assumed
to be a L C parallel circuit as in Figure 28a) when the strong magnetic field is applied
o o
parallel to the plane of specimen (x-direction) to achieve the situation of µ = 1. After removing
this field, the field is applied perpendicularly to the specimen plane for gyromagnetic
resonance. Figure 28b) shows the equivalent circuit for gyromagnetic resonance [21], where
L is an air core inductance and C is a parasitic capacitance. The values of L and C are
o o o o
designated “fixture constants”. The method to calculate “fixture constants” is shown in
12.3.2.8. When a gyromagnetic resonance occurs, it is considered that some portion η of air
core inductance L is replaced by the complex relative permeability µ’ µ”, and the coupling
o
coefficient η is almost invariable within the measurement frequency range. The half value
width of the resonant curve of the imaginary part µ” is defined as gyromagnetic resonance
linewidth. By measuring the S parameters of Figure 28a) and 28b), the quantity ηµ”L
11 o
proportional to the imaginary part µ” can be derived based on the circuit theory analysis as
shown in 12.3.2.5.
Consequently the gyromagnetic resonance linewidth ∆H is derived from the resonance curve
of ηµ”L .
o
ηµ’L ηωµ”L
o o
S ←
S ←
11o
(1 − η)L
C L C
o
o o o
a) b)
IEC IEC
Figure 28a) with µ = 1 under strong magnetic
Figure 28b) with gyromagnetic resonance
field parallel to r.f. magnetic field
Figure 28 – Equivalent circuits of short-circuited microstrip line
12.3.2.2 Test specimens and test fixtures
The structure of the all-shielded short-circuited microstrip line as test fixture is shown
schematically in Figure 29. A disk shape or square slab specimen is set at the end of the
short-circuited portion. To avoid disturbance from outside, the shielded covers are set up on
the upper side and both sides of the test fixture. The impedance of the test fixture except the
short end should be made at 50 Ω ± 2 Ω by adjusting the gap between the connector and the
strip line. The typical dimensions of the test fixture are shown in Table 1.

© IEC 2016
Side shield cover a
Gap
L
(a) Top view
Side shield cover b
Microstrip line
Reference plane
Upper shield cover
Connector
L
2 (b) Side view
Z
Y
X
Specimen
Ground
(thickness t)
IEC
NOTE The thickness of the strip line is 0,3 mm.
Figure 29 – Cross-sectional drawing of all-shielded
shorted microstrip line with specimen
Table 1 – Typical dimensions of test fixture
h w h gap w L L
1 1 2 2 1 2
2,0 7,0 3,7 20 8 5
0,35 ± 0,15
NOTE Dimensions in mm.
The shapes of specimens are a disk or a square slab. The typical dimensions of specimens
are shown in Table 2.
Table 2 – Specimen shape and typical dimensions
Disk Diameter D Quotient of diameter and thickness
D ≤ 5 mm φ up to 10 GHz t/D ≤ 1/20 (t = thickness)
Square slab Side length Quotient of side length and thickness
L ≤ 5 mm up to 10 GHz t/ L ≤ 1/20 (t = thickness)
2 2
12.3.2.3 Measuring apparatus
Figure 30 shows the block diagram of this measurement method. The test fixture with a
specimen is located between pole pieces of permanent magnets or an electro magnet to
generate gyromagnetic resonance. In case of a disk or square slab, in order to apply a static
magnetic field in normal to plane, the test fixture and pole piece should be capable of rotating
along two different axes which are orthogonal to each other. Under the constant static
magnetic field, the absolute value and phase of the S parameter of the test fixture are
measured by the sweeping frequency of the vector network analyzer (VNA).
w
h
w
h
– 6 – IEC 60556:2006/AMD1:2016
© IEC 2016
Rotation
VNA
Magnet a
H
ext
S
Cable
Rotation
Test fixture with specimen
Magnet b
IEC
Figure 30 – Block diagram of measurement system
12.3.2.4 Measuring procedure
The measuring procedure is as follows:
1) The VNA is calibrated on the cable end using an “open”, “short”, and “load” jig.
2) The total sweeping frequency points are selected so as to get more than 10 points within
the half linewidth ∆ f of the frequency defined below.
3) A specimen should be contacted and fixed on the corner of the short end and the ground.
4) To sustain the situation of µ = 1, a static magnetic field H larger than 3,2 × 10 A/m
cal
should be applied in parallel to the x-direction of the r. f. magnetic field.
5) The absolute value and phase of S are measured as shown in Equation (64).
11o
S = G exp(jδ ) (64)
11o o o
6) After removing H , the static magnetic field H is applied along the z-direction.
cal ext
7) The gyromagnetic resonance curve is observed in S .
8) The direction of H is adjusted to obtain the lowest resonant frequency, namely to be
ext
normal to the plane of the specimens, by rotating the test fixture and pole pieces
individually.
9) The minimum value S is measured at the resonant frequency. This value should be
11m
less than –1 dB.
10) Then the absolute value and phase of S are measured all over the frequency range as
shown in Equation (65).
S = G exp(jδ) (65)
12.3.2.5 Derivation of gyromagnetic resonance linewidth ∆H [21]
The derivation of gyromagnetic resonance linewidth is obtained as follows:
1) By dividing Equation (65) by Equation (64), E and F are defined as Equation (66).
S /S = G/ G exp{j(δ−δ )} = E + j F (66)
11 11o o o
2) Next, the calculations should be done.
C = y (E +1) + F X (67)
11 c
© IEC 2016
C = X (E−1) − y F (68)
12 c
C = y { y (1−E) − F X } (69)
10 c
C = y { X (1+E) − F y} (70)
20 c
where
y is a characteristic admittance, usually y = 0,02 S.
X is defined by X = ω C −1/ωL (71)
c c o o
3) Also, the following calculations should be done.
C C − C C
10 11 20 12
A = (72)
2 2
C + C
11 12
C C + C C
10 12 20 11
B = (73)
2 2
C + C
11 12
4) The imaginary part ηµ”L of the complex inductance is calculated.
o
A
′′ (74)
ημ L =
o 2
ϖ{A + (B −ϖC ) }
o
5) The value of ηµ”L is directly proportional to µ”. With ηµ”L being on the vertical axis and
o o
the frequency being on the horizontal axis, the resonance curve can be drawn as shown in
Figure 31. In general, the curve is not always bilaterally symmetrical on the central
frequency axis. The resonant frequency f of the main peak and two half line widths of ∆f
r l
on the left and ∆f on the right could be derived. However, the smaller value of ∆f on the
h l
left side than of ∆f on the right side is adopted as a correct half width ∆ f because the
h
smaller one is considered to be less influenced by a higher magneto static mode. The
method to derive ∆f using the least square method is shown in 12.3.2.6.
6) The relaxation constant α is derived by the Equation (75) [22].
α = ∆f / f (75)
r
7) The gyromagnetic resonance linewidth ∆H is derived through Equation (76) [23].
∆H = 4π∆ f /(µ γ ) (A/m) (76)
o eff
where
µ is the permeability of vacuum;
o
γ is the effective gyromagnetic ratio.
eff
– 8 – IEC 60556:2006/AMD1:2016
© IEC 2016
0,7
Max
α = 0,014 7
0,6
−4
∆Η = 23,5 x 10 [T]
0,5
0,4
Max/2
MSW
0,3
(n = 3)
∆f
h
0,2
∆f
0,1
l
f
2,1 2,2 2,3 2,4 2,5
r
Frequency (GHz)
IEC
Figure 31 –Observed absorption curve of imaginary part ηµ”L of inductance
o
for a 5 mm square garnet specimen with 0,232 mm thickness and Ms = 0,08 T
NOTE If the amplitude and phase of S are measured with an accuracy of ±0,02 dB and ±0,075° respectively, the
static magnetic field strength is measured with an accuracy of ±1 %, and L and C are determined with an
o o
accuracy ±10 %, the relative error of γ becomes equal to ±1 % and the relative error in the determination of ∆H
eff
becomes equal to ±5 %, respectively.
12.3.2.6 The derivation of half line width ∆f by the least square method
First, as an example, the measurement values ηµ”L of about 10 pieces on the lower
o
frequency side and of about 4 pieces on the higher frequency side including the maximum
value of (ηµ”L ) are gathered. Next, the inverse value of (ηµ”L ) is denoted as a(0) and
o max o max
the inverse values of ηµ”L (i) on both sides are denoted as a(−10), a(−9), … a(−1), a(1), a(2),
o
and a(3). The corresponding frequencies are f(0), f(−10), f(−9), … f(−1), f(1), f(2), and f(3)
respectively, where the lowest frequency is f(−10). Then the new frequency sets of
F(i) = f(i)−f(−10) are introduced. The value of a(i) obeys the parabolic relation as in Equation
(77) because ηµ”L (i) has Lorentzian characteristics.
o
y(i) = P F(i) + Q F (i) + R (77)
where P, Q, and R are the coefficients which should be determined by the least square method.
The error function of E is defined as follows:
2 2 2 2
E = Σ{y(i)−a(i)} = Σ{ P F(i) + Q F(i) + R −a(i)} (i = −10, −9,… 0, 1, 2, 3) (78)
The partial differentiations are performed regarding P, Q, and R to minimize E .
Eventually, the coefficients of P, Q, and R could be determined by the next equations.
P = D /D, Q = D /D, R = D /D (79)
P Q R
where
X X X X A X X X X A X X X X A
4 3 2 2 3 2 4 2 2 4 3 2
D = X X X Dp = X A X X D = X X A X D = X X X A (80)
3 2 1 1 2 1 3 1 1 R 3 2 1
Q
X X n A X n X A n X X A
2 1 1 2 2 1
Imaginary part of inductance ηµ”L (nH)
o
© IEC 2016
where
4 3 2 0
X = Σ F(i) , X = Σ F(i) , X Σ F(i) , X = Σ F(i) , n = Σ F(i) (81)
4 3 2 = 1
X A = Σ F(i) a(i), X A = Σ F(i) a(i), A = Σ a(i) (82)
2 1
where n is the total number of the data. In this example n = 14.
As a result, the resonance frequency f is given by the Equation (83).
r
f = − Q /(2 P)+ f(−10) (83)
r
The half line width Δf is also given by the Equation (84).
4PR − Q
(84)
∆f =
P
12.3.2.7 Calculation of effective gyromagnetic ratio γ
eff
The value of γ could be derived through the next procedure.
eff
1) By changing an applied magnetic field from H to H , the resonant frequency f and f
1 2 r1 r2
can be measured correspondingly.
2) The effective gyromagnetic ratio γ is derived by Equation (85).
eff
2π( f − f )
r1 r2 −1 −1
γ = (T s ) (85)
eff
μ (H1 − H 2)
o
where
the frequency difference (f − f ) should be larger than 600 MHz.
r1 r2
12.3.2.8 Calculations of fixture constant L and C
o o
The equivalent circuit seeing a specimen with µ = 1 from the reference plane is assumed to
be a parallel circuit with L and C as shown in Figure 32.
o o
S ←
11o
L
o
C
o
L
Reference plane Shorted end
Specimen
IEC
Figure 32 – Assumed equivalent circuit of the test fixture
If the test fixture impedance is designed to be 50 Ω except the short end and the effect of the
loading sample with µ = 1 is negligible, the fixture constants of L and C are calculated as
o o
follows:
L = L L (H) (86)
o 2
– 10 – IEC 60556:2006/AMD1:2016
© IEC 2016
C = 0,38 C L (F) (87)
o 2
where
L is the length of the sample, and L = 166,9 nH/m and C = 66,67 pF/m [24] are the
inductance and the capacitance per unit length of the 50 Ω transmission line. The factor of
0,38 in Equation (87) was determined to minimize the lumped element model error in the
wide measurement frequency range up to 10 GHz.
Table 3 shows the calculated fixture constants for 5 mm long specimens.
Table 3 – The fixture constants for 5 mm long specimens
Length of specimen L C
o o
mm nH pF
5 0,834 0,127
12.3.3 Transmission method
12.3.3.1 Theory
A method recommended for the evaluation of ΔH and γ at an arbitrary frequency is based
eff
on the measurement of the off-diagonal element of relative tensor permeability, κ, through a
signal transmission [25]. A test fixture model used in this measurement is shown in Figure 33.
The test fixture is constructed by two tri-plate lines stacked at right angle and a common
ground plane between them with a coupling hole at the cross point of the two lines. One line
used to apply an r.f. magnetic field to a specimen is terminated by a matched load to generate
a uniform r. f. magnetic field. The other line used to detect a signal from the specimen is
grounded at the edge of the coupling hole to avoid an error caused by leakage of an electric
field from the coupling hole. A grid parallel to the driving r. f. magnetic field is provided in the
coupling hole for further suppression of the electric field leakage.
Ferrite Coupling hole
Upper ground plane
Common ground plane
Detecting line
Driving line
Lower ground plane
Electric field leakage suppressing grid
IEC
(A part of the ground plane is cut away to show the bottom part of the test fixture.)
Figure 33 – Structure of test fixture to measure resonance linewidth by transmission
A ferrite specimen is positioned on the electric field leakage suppressor grid, facing the
detecting line. A magneto-static field orthogonal to the driving r. f. magnetic field is applied to
generate a precession of the electron spin in the ferrite and a gyromagnetic resonance. The
spin precession induces a signal in the detecting line. These relationships are shown in
Figure 34.
© IEC 2016
Magneto-static field
z-axis
Spin precession
Induced magnetic flux (m )
x
r.f. magnetic field (h )
y
Induced signal (b)
y-axis
x-axis
Driving line
Ferrite
Electron spin
Detecting line
Driving power (a)
IEC
(A part of the ground plane is cut away to show the bottom part of test the fixture.)
Figure 34 – Model to measure resonance linewidth by transmission
Through the precession of the electron spin, the application of the magneto-static field to the
test fixture results in a coupling between the driving and the detecting lines as shown in
Equation (88) [25].
C = C + 20log(κ ) (88)
where
C is the coupling coefficient in dB defined by the diameter wavelength ratio of the hole;
κ is the off-diagonal element of relative tensor permeability of the ferrite specimen in the
coupling hole.
Equation (88) shows that the signal intensity obtained from the test fixture is proportional to
the absolute value of the off-diagonal element in the relative tensor permeability, κ , of the
magnetized ferrite. The resonance is defined by the magneto-static field strength and the
frequency to maximize the transmitted power, and the relationship between the resonance
frequency and the internal magnetic field of the specimen is written as shown in Equation (89).
γ H
eff i
(89)
f =
r
2π
where
f is the resonance frequency;
r
γ is the effective gyromagnetic ratio;
eff
H is the internal magnetic field of the specimen.
i
The linewidth in the frequency, ∆f, is defined as the difference between the two frequencies f
and f at which the transmitted power by the ferrite material is one-half the maximum
transmission as shown below.
(90)
∆f = f − f
1 2
The line broadening by the external load is included in the linewidth. The broadening is
adjusted from the maximum value of the transmission as described in 12.3.3.5. The linewidth

– 12 – IEC 60556:2006/AMD1:2016
© IEC 2016
described in the frequency is converted to the conventional linewidth in the magnetic field
strength by using the gyromagnetic ratio, γ . γ is a constant to define the resonance
eff eff
frequency from the internal magnetic field as shown in Equations (26) and (27) in Clause 6.
Considering that γ is independent from the shape of the specimen, it is calculated by two
eff
resonance conditions as shown in Equation (91).
2π( f − f )
r1 r2
(91)
γ =
eff
H − H
r1 r2
where
and f are the first and the second resonance frequencies, respectively;
f
r1 r2
H and H are the magnetic field strengths corresponding to the resonance, respectively.
r1 r2
The obtained linewidth in the frequency, ∆f, is converted to the conventional linewidth in the
magnetic field strength, ∆H, using γ . The details of the conversion are shown in 12.3.3.5 as
eff
well.
12.3.3.2 Test specimens and test fixtures
The test specimens for this method may be either spherical or disc-shaped. The specimen
dimension shall be small compared with the wavelength in the specimen. The spherical
specimen resonates at a lower magnetic field than the disc-shaped specimen. However, the
linewidth broadening due to the insufficient saturation magnetization of the specimen and spin
wave loss as referred to in Clause 6 will be observed in the spherical specimen. For disc
specimens, the quotient of the diameter and the thickness shall exceed 15. Although the
magnetic field should be increased, the ambiguities of the linewidth appearing in the spherical
specimen become less so in the disc-shaped specimen shaped as described above. For
specimens with a relatively narrow linewidth, the measurement result depends strongly on the
surface state of the specimen. It is recommended to finish the surface of the specimen by
referring to 6.4.
By way of an example, Figure 35 illustrates the whole structure of a test fixture to evaluate the
resonance linewidth for 1 GHz to 10 GHz by transmission.
Detecting port Specimen
A
Holder
Specimen mount
Detecting conductor
Driving conductor
Driving port
Clamping screw
Termination
Driving chamber
Detecting chamber
Common ground plane
A
A-A
IEC
Figure 35 – Test fixture for measurement of resonance linewidth by transmission
The test fixture is constructed with a driving chamber, a detecting chamber, a ground plane
with a coupling hole and a mount to maintain the transmission between them at a minimum
when the magnetic field is not applied. The transmission with no magnetic field is called the
isolation of the test fixture. A specimen is glued on a sample mount put in the detecting line to
be positioned at the centre of the coupling hole.

© IEC 2016
The characteristic impedance of the test fixture should be the same as the impedance of the
network analyzer, 50 Ω. It is favourable to adjust to 50 Ω ± 2,5 Ω for the transmission line of
the test fixture. The characteristic impedance of a transition from a connector to a
transmission line should favourably be adjusted to 50 Ω ± 5 Ω. The error caused by a long line
effect which appears in the cable connecting with the test fixture and the measuring
equipment will be reduced by decreasing the standing wave in the cable. For accurate results,
it is essential to adjust the isolation of 35 dB or more between the input and output ports of
the test fixture when a specimen is installed and no magnetic field is applied. An example of
the driving chamber, the detecting chamber and the coupling hole providing the electric field
leakage suppressor grid is shown in Figure 36. It was confirmed that the requirements
described above were satisfied when the test fixture is assembled as shown in Figure 35. A
specimen mount is a styrene foam block which would be expendable.
Connector
Connector
[Electric field leakage suppressor grid]
ø0,16 Wire
ø4
Inner conductor
Inner conductor
Enlarged view
[Driving chamber] [Coupling hole] [Detecting chamber]
IEC
Figure 36 – Example of a test fixture (tolerance: Class f)
The measured linewidth includes a line broadening caused by the external load and this
should be adjusted. The adjustment described in Equation (101) is made to obtain a loose
coupling between the load and the specimen. It is favourable to adjust the maximum
transmission coefficient of the test fixture to lower than -25 dB from the reference level
excluding the attenuation by the pad. On the other hand, a small resonance peak will be
modulated by a signal leaked directly from the input line. The resonance peak higher than
25 dB from the background signal level will improve the accuracy of the evaluation. The two
requirements for the transmission described above will be satisfied by adjusting the volume of
the specimen. Considering the favourable conditions described above, the maximum size of
the sample diameter will be 80 % of the coupling hole diameter. The quotient of the diameter
and the thickness shall exceed 15.
12.3.3.3 Measuring apparatus
A block diagram of the equipment required for the measurement is shown in Figure 37.

– 14 – IEC 60556:2006/AMD1:2016
© IEC 2016
Test fixture
Detecting port
Pad
Constant current
(fixed attenuator)
DC power supply
Network
Analyzer
Port 1 Port 2
Magnetic
flux meter
Termination
Driving port
Magnetic flux meter probe
Electromagnet
IEC
Figure 37 – Block diagram of the equipment for measuring the resonance linewidth
RF power from the driving channel of a network analyzer is fed to the driving port of the test
fixture, and the output power from the detecting port of the test fixture is sent to the receiving
channel of the network analyzer through a pad. A magneto-static field perpendicular to the r. f.
magnetic field is applied to the specimen. To obtain a favourable stability in the measurement,
a stabilized constant current power supply is recommended for the power source. A detecting
probe of the magnetic flux meter shall be positioned between the test fixture and the pole
piece.
The accuracy of the half power linewidth evaluation in the frequency domain is influenced by
standing waves in the cables of the measuring apparatus called a long line effect. Insertion of
the pad of 10 dB or more at the detecting port of the test fixture is recommended to reduce
the error caused by the long line effect. In the same way, the length of the cables between the
network analyzer and the test fixture should be made as short as possible.
12.3.3.4 Measuring procedure
The accuracy of digitalized measuring equipment is very high but sometimes the function of
the digitalized frequency synthesizer makes it difficult to adjust the frequency to the half
power points accurately. The measuring procedures in 12.3.3.4 are based on a method to
obtain the accurate half power points using numerical analysis. Theoretical details of this
analysis are shown in 12.3.3.5. When the measuring frequency range is new, the calibration
of the measuring apparatus without the test fixture should be made at first. It is supposed that
the network analyzer provides marker functions to show the frequency and the signal level of
the marker position and to search the maximum of the trace on the display as well. The
calibration procedure will be made as shown below.
1) Take off the two cables and pad shown in Figure 37 from the test fixture.
2) Connect the two cables including the pads with a jack-to-jack adapter.
3) Move the marker to the frequency at which the resonance will be measured, f .
1r
4) Record S at the frequency f as the reference signal level, A .
21 1r 1r
If the flatness of the signal level is less than ±1 dB within the expected frequency range of the
linewidth, the reference level could be represented by the value at the centre of the
measuring frequency. The flatness of the reference level larger than ±1 dB suggests some
loose connections in the cable caused by the poor flatness. The recovery of the flatness
would be made by checking the cable connection.
The linewidth measurement starts from here and this will be carried out by the steps shown
below. The measurement shall be made for two frequencies to obtain the accurate value of
γ .
eff
© IEC 2016
Prior to the linewidth measurement, the isolation of the test fixture with the specimen should
be maximized. The procedures are shown from step 5) to step 8). The procedures to measure
the linewidth are described from step 10) to step 13).
5) Position a specimen at the centre of the coupling hole. This positioning will be
accomplished by pasting the specimen to the corresponding position on the specimen
stage facing the coupling hole.
6) Take off the jack-to-jack adapter from the cable and substitute the test fixture between the
cables after the reference level measurement. The pad should be installed at the output
port of the test fixture.
7) Loosen the clamping screw and change the angle of the driving chamber and the
detecting chamber until the transmission between two ports becomes minimum. Usually
the transmission will be smaller than -80 dB.
8) Tighten the clamping screw of the mount.
9) Set up the test fixture carefully in the gap of the pole pieces of the electromagnet to make
the two centres of the specimen and the pole pieces coincide with each other.
10) Apply the magnetic field and adjust so that the maximum of the transmission comes to the
frequency at which the reference level was taken.
11) Search the accurate frequency of the maximum transmission using the search function of
the marker and record the frequency and the amplitude as f and A , respectively.
12 12
12) Move the marker to the lower frequency and adjust the amplitude at 3 dB lower from A .
Read and record the frequency and the signal level as f and A , respectively.
11 11
13) Move the marker to the higher frequency side from the peak and adjust the amplitude at
3 dB lower from A . Read and record the values as f and A , respectively.
12 13 13
The whole procedures described above are shown in Figure 38.
Although the adjustment of the marker may be coarse, the recording of the data shall be
accurate. Repeat the procedure from step 10) to step 13) for the measurement of the other
frequency as A and f . It is favourable to select the frequency more than 300 MHz apart
2i 2i
from the former measurement to obtain an accurate γ .
eff
A
1r
≈ 3 dB
≈ 3 dB
Reference level
A
A
A
Resonance
curve
f f f f
1r 11 12 13
Frequency Frequency
IEC
Figure 38 – Measurement procedures
12.3.3.5 Calculation
The gyromagnetic linewidth is defined as the difference between the two frequencies at which
the transmission level becomes 3 dB lower than the maximum transmission, and the
resonance frequency is given as the average of the two frequencies. A method to decide the
resonance curve accurately by numerical analysis is described in 12.3.3.5. This method will
fully bring the features of the digitalized measuring equipment.
Transmission coefficient (dB)
Transmission coefficient (dB)

– 16 – IEC 60556:2006/AMD1:2016
© IEC 2016
Equation (88) means that the transmitted power from the test fixture is proportional to |κ| and
this is written by Equation (92).
(2πµ f M / γ )
0 s
κ = (92)
2 2 2 2 2 2 2
(H − 4π f / γ ) + (2π∆f / γ ) H
i i
where
H is the internal magnetic field strength of the specimen;
i
f is the frequency of the driving r. f. magnetic field;
M is the saturation magnetization of the specimen;
s
Δf is the half-power linewidth;
γ is the gyromagnetic ratio.
When x = H -2πf/γ and the relationship |x|<<2πf /γ are confirmed at the frequency close to the
i
resonance, Equation (92) is rewritten as follows:
2 2
(µ M ) (µ M )
0 s 0 s
(93)
κ = =
2 2 2 2
4(H − 2πf / γ ) + (2π∆f / γ ) 4x + (2π∆f / γ )
i
This means that |κ| is expressed by a Lorentzian function when the frequency change is
small enough compared to the resonance frequency. The linewidth will be given by solving the
equation after the acquired data are adapted to a Lorentzian function. However, this cannot
be solved analytically because the Lorentzian function is a fractional function. As the inverse
of the Lorentzian function is parabolic, the inverse of the acquired data is reduced to a
parabolic equation in terms of the frequency as shown below and can be solved analytically.
(94)
I = = af + bf + c
i i i
P
i
where
th
P is the i acquired power;
i
th
f is the i frequency.
i
The half-power points of the resonance curve correspond to the points twice the minimum
value of Equation (94). The equation to be solved is defined as shown in Equation (95).
2 2
b b b
2 2
(95)
af + bf + c ≡ a( f + ) + c − = 2(c − )
2a 4a 4a
This equation has two solutions . The resonance frequency is given by
f = (−b ± 4ac − b ) / 2a
the average of the two, and the linewidth in the frequency is given by the difference of the two.
The procedure to obtain the parabola will be carried out as follows. Firstly, the measured
signal amplitudes in dB around the resonance, A , are converted to the linear scale and the
i
inversed power of the resonance is calculated by using the reference signal level, A .
r
( AA− )/10
i r
(96)
I = 10
i
Four determinants shown below are calculated from the values given by Equation (96).

© IEC 2016
2 2 2
( f − f ) ( f − f ) 1 I f − f 1 ( f − f ) I 1 ( f − f ) ( f − f ) I
1 2 1 2 1 1 2 1 2 1 1 2 1 2 1
(97)
D = 0 0 1,D = I 0 1,D = 0 I 1andD = 0 0 I
a 2 b 2 c 2
2 2 2
( f − f ) ( f − f ) 1 I f − f 1 ( f − f ) I 1 ( f − f ) ( f − f ) I
3 2 3 2 3 3 2 3 2 3 3 2 3 2 3
where
th
f is the frequency of the output power at the i measurement;
i
th
I is the inverse of the output power at the i measurement.
i
In this procedure, the frequencies were converted to the shifted frequencies from the
resonance frequency to avoid rounding errors caused by the product of the values with high
figures. The coefficients of the parabolic equation to be obtained are written as shown in
Equation (98) using the determinants of Equation (97).
D D D
a b c
(98)
a = ,b = andc =
D D D
The procedures to obtain the resonance linewidth described above are illustrated in Figure 39.
A
I
A
I
Δf
A A A
1 3 3
A
0,5
Δf
I
f f f
1 2 3
Frequency Frequency Frequency
IEC IEC IEC
(a) Transmission characteristics (b) Normalized output (c) Inverse normalized output
Figure 39 – Steps to obtain resonance linewidth by numerical analysis
The resonance frequency, f , and the loaded linewidth in the frequency, ∆f , are given as
r l
shown in Equations (99) and (100). The frequency shift to avoid the rounding error is
recovered in this equation.
b
(99)
f = f −
r 2
2a
4ac − b
(100)
∆f =
l
a
The obtained resonance linewidth in the frequency is a linewidth including the linewidth
broadening caused by the external loads and this should be adjusted as shown in Equation
(101) [26].
(101)
∆f = (1− I )∆f
u 2 l
The effective gyromagnetic ratio is calculated to convert the resonance linewidth in the
frequency to that in the magnetic field strength, and the coefficient is written as shown in
Equation (102) if the measuring frequencies are two. The suffixes 1 and 2 of the resonance
frequency, f and the magnetic flux density, B mean the order of measurement.
ri, i,
Transmission coefficient (dB)
Normalized output power
Inverse normalized power
– 18 – IEC 60556:2006/AMD1:2016
© IEC 2016
f (MHz) − f (MHz)
r2 r1
(102)
γ = 2π
eff
795,8[B (mT) − B (mT)]
2 1
Finally, the resonance linewidth in the magnetic field strength is given by Equation (103).
2π∆f
u
(103)
∆H =
γ
eff
-9
NOTE If the frequencies are measured with the accuracy of 10 , the amplitudes with the accuracy of 0,01 dB and
the magnetic field strengths with the accuracy of ±1 %, the relative errors in the determination of ∆F and γ
eff
become ±1 % for both. The error caused by the leakage of the electric field from the coupling hole has been lower
than ±3 % if the isolation is higher than 35 dB. Finally, the overall accuracy of the ∆H evaluation becomes ±5 %. It
has been confirmed that the difference between the results measured by the method descri
...