Exercise 7.
Four Terminal Electronic Components
Required knowledge
•
Calculation of inductance of toroidal and solenoidal inductors.
•
Knowledge of basic definitions related to magnetism and magnetic materials, e.g.,
magnetic field strength (H), magnetic flux density (B), permeability, B-H curve,
hysteresis loop, saturation, core loss, copper loss, inductance factor.
•
Interpretation of quantities at the end of this guide, and interpretation of any of the
quantities that are mentioned in the laboratory exercises.
•
Connection between the current and induced voltage in an inductor. Calculation of H
and B in an inductor. Calculation for sinusoidal excitation.
•
Kinds of losses in a transformer/inductor, e.g., copper loss, core loss (hysteresis loss,
eddy current loss). Why laminated cores are used? How the skin effect changes the
copper loss?
•
In circuit measurement.
•
Parameters and models (equivalent circuit) of transformers, e.g., how core and copper
losses, leakage/magnetizing reactances are modeled, dependency between turn ratio and
secondary/primary voltage and current. Insertion loss.
Aim of the measurement
You will learn how to model impedances and four terminal electrical components. The
measurement is primarily connected to test of materials, parameter identification and incircuit measurements.
Web links
http://en.wikipedia.org/wiki/Ferromagnetic_material_properties
http://en.wikipedia.org/wiki/Toroidal_inductors_and_transformers
http://en.wikipedia.org/wiki/Transformer
http://en.wikipedia.org/wiki/Saturation_(magnetic)
http://en.wikipedia.org/wiki/Ferromagnetism
http://en.wikipedia.org/wiki/Insertion_loss
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indtor.html
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcon.html#c1
©BME-VIK Only students attending the courses of Laboratory 1 (BMEVIMIA304) are allowed to download this file, and to
make one printed copy of this guide. Other persons are prohibited to use this guide without the authors' written permission.
Laboratory exercises 1.
Measurement instruments
Precision Magnetics Analyzer
Wayne Kerr 3260B
Main features of the Magnetics Analyzer:
Frequency: 20 Hz – 3 MHz
Drive Level: 1mV to 10 V rms into open circuit, 50 µA to 200 mA rms into short
circuit
Source Impedance: 50 Ω
Test board
Test Board No VIK-02-01:
Transformer with poor coupling, Tr-1
Transformer with improved coupling, Tr-2
RC-network
Telecom transformer, Tr-3
Laboratory exercises
1. Measurement of ferromagnetic parameters
Technical data of the DUT:
Type: TDK H5A
Core material: ferrite
Form: toroidal
Dimensions: D = 68 mm, d = 44 mm, h = 13,5 mm
Frequency: max. 0,2 MHz
Initial permeability, µi : 3300 -0….+40%
Max flux density, Bm: 410 mT
Inductivity factor, AL: 4300±25% nH
1.1. Measure the coil impedance at 1V in the range of 100 Hz500 kHz!
1.2. Measure the resonance frequency and the self-capacitance of the coil!
1.3. What is the max. measurement frequency if the systematic error caused by the
resonance is not higher than 1%?
1.4. Measure the coil impedance at 150 Hz in the range of 1 mV10 V using the
Graph-mode of the Analyzer!
1.5. Calculate µr(Bm) and AL(Bm) from the Z(U) characteristics!
2. Measurement of model parameters of transformers
Technical data of DUT No Tr-1 and Tr-2:
Type: TDK H5A
Core material: ferrite
Form: toroidal
Dimensions: D = 68 mm, d = 44 mm, h = 13,5 mm
6
©BME-VIK Only students attending the courses of Laboratory 1 (BMEVIMIA304) are allowed to download this file, and to
make one printed copy of this guide. Other persons are prohibited to use this guide without the authors' written permission.
Four terminal electronic components
Frequency: max. 0,2 MHz
Initial permeability, µi : 3300 -0….+40%
Max. flux density, Bm: 410 mT
Inductivity factor, AL: 4300±25% nH
Number of primary turns, Np: 110
Number of secondary turns, Ns: 110
Cross section of the copper wire, ACu: 0,05 mm2
Diameter of the isolated wire dv: 0,6 mm
2.1. Measure the model parameters at Ueff = 5V and f = 1 kHz! Measure the dc
parameters! What are the differences between the two transformers?
2.2. Estimate the measurement uncertainties of the copper resistances and that of
the magnetizing inductivity!
2.3. Measure the primary impedance Z(U, f) of the unloaded transformer!
3. In-circuit measurement on RC-network
Technical data of the RC-components:
R1 = 100 Ω ±0,1%
R2 = R4 = 1 kΩ ±1%
R5 = 10 kΩ ±2%
C1 = 1 µF ±5%
C2 = 100 nF ±5%
R4
IN
R5
R1
R2
C1
C2
OUT
Fig. 7–1. RC filter to be measured
3.1. Measure all of the RC components using in-circuit technique! Are the measured
values within the specified tolerance bands?
4. Measurement on Telecom transformer
Technical date of the DUT No Tr-3:
Type: PCM-40
Core type: M30 Permalloy
Turn ratio, Ns/Np: 408:384
Frequency band: 200 Hz…220 kHz
Insertion loss, IL: max. 0,1 dB
Max. voltage level: +10 dB
Terminating impedance: 600 Ω
4.1. Measure the turn ratio of the Telecom transformer!
3
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Laboratory exercises 1.
4.2. Measure the Insertion Loss and Reflection Loss of the Telecom transformer at
given frequency using direct coupling!
4.3. Measure the Insertion Loss and Reflection Loss of the Telecom transformer at
given frequency using direct coupling and RC-damping!
4.4. Measure the Insertion Loss and Reflection Loss of the Telecom transformer at
given frequency using capacitance coupling!
6
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make one printed copy of this guide. Other persons are prohibited to use this guide without the authors' written permission.
Unit
Calculation
A (mA)
1
A (mA)
m (cm)
A/m (A/cm, mA/cm)
A/m (A/cm, mA/cm)
T, Wb/m2 (mT)
T, Wb/m2 (mT)
V·s/A·m
V·s/A·m
1
1
1
1
Θ = NI
for a closed core.
H = Θ/l = NI/l H = ReH + jImH
Hm = √2 H for sinusoidal H
B = µ0 µr H B = µ0 µr H B = ReB + jImB
Bm = √2 B for sinusoidal B
µ = B/H = µ0 µr
4π·10-7 .
µr = µ / µ0 = µ0-1B/H can be a nonlinear function, i.e., µr = µr(H)
µa = µ0-1Bm /Hm for variable excitation, Hdc=0.
µ = µ'-j µ" describes phase shift between B and H in non-ideal circumstances.
µ' = Re µ
1
- µ" = Im µ
1
|µ| = sqr ( µ'2 + µ"2 )
µi
µ4
µmax
µe
Current, excitation current
Number of turns
Magnetic excitation
Average length of magnetic field
Strength of magnetic field
Maximum strength of magnetic field
Magnetic flux density
Maximum of magnetic flux density
Absolute permeability
Permeability of vacuum
Relative permeability
Amplitude permeability
Relative complex permeability
Real value of relative complex
permeability
Imaginary value of relative complex
permeability
Absolute value of relative complex
permeability
Relative initial permeability
Initial permeability @ Hm= 4 mA/cm
Relative maximal permeability
Relative effective permeability
1
1
1
1
A
Φ
L
AL
Cross section area of core
Magnetic flux
Inductivity
Inductance factor, AL
m2 (cm2)
Wb, V·s
H, Wb/A
nH
µi = µa= µ0-1Bm /Hm at limiting case Bm, Hm →0
µ4 = µa= µ0-1Bm /Hm measured at Hm= 4 mA/cm by definition
peak value of curves µr (H) or µr (B)
kind of equivalent permeability of a core that has, e.g, irregular shape, mixed
material, air gap or any non-ideal properties.
Note: it can be less than the physical cross-section, e.g., laminated core
Φ = BA
L = NΦ /I L= µ0 µr N 2A/l = 10-9N 2AL
AL = 109 µ0 µr A/l (inductivity can be calculated as L = 10-9N 2AL, see above)
Zs
Serial impedance of an inductance
Ω, V/A
Q
tgδ
Zs'
Quality factor
Tangent of loss angle
Corrigated serial impedance
1
1
Ω, V/A
I, I
N
Θ
l
H, H
Hm
B, B
Bm
µ
µ0
µr
µa
µ
µ'
- µ"
|µ|
Zs = Rs+jωLs = jω µ0 (µ'-j µ")N 2A/l, Ls = µ0 µ'N 2A/l Rs = ω µ0 µ"N 2A/l
|Zs| = sqr (Rs2+ω2Ls2) = ω µ0 |µ| N 2A/l
Q = ωLs /Rs = µ'/µ"
tgδ =1/Q = µ"/µ'
Zs' = Rv +jωLs = jω µ0 (µ'-j µ")N 2A/l, Ls = µ0 µ'N 2A/l Rv = ω µ0 µ"N 2A/l
|Zs'| = sqr (Rv2+ω2Ls2) = ω µ0 |µ|N 2A/l, Rv=Rs-RCu
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Four terminal electronic components
5
Some quantities related to magnetic materials
Notation Name
Laboratory exercises 1.
Calculation
Ωm, Ω mm2/m
RCu
Rh
Rö
Rv
Rs
P
PCu
Ph
Pö
Pv
Pv /f
m
pv
Electrical resistivity (also called specific
electrical resistance)
Resistance for DC current
Hysteresis resistance
Eddy current resistance
Loss resistance
Serial resistance
Power loss
Copper loss
Hysteresis loss
Eddy current loss
Core loss
Loss per period, Bm = constant
Mass of core
Specific core loss
Ω, V/A
Ω, V/A
Ω, V/A
Ω, V/A
Ω, V/A
W (mW)
W (mW)
W (mW)
W (mW)
W (mW)
W/Hz (mW/Hz)
kg (g)
W/kg (mW/g)
Rcu = ρ lCu /ACu
It models the hysteresis loss
It models the loss caused by eddy current
Rv = Rh + Rö = Rs – RCu
It models the core loss.
Rs = RCu+ Rh + Rö = RCu + Rv Models the core and copper loss
P = I 2 Rs = I 2 (RCu+ Rh + Rö)
PCu = I 2 RCu
Ph = I 2 Rh = c1Bmpf
p= 1…3
Pö = I 2 Rö = c2Bmqf 2
q= 1…3
for sinusoid B
Pv = I 2 Rv = Ph + Pö = c1Bmpf + c2Bmqf 2 for sinusoid B
Pv /f = c1Bmp+ c2Bmqf Bm = constant!
J
δ
Current density
Skin depth
A/mm2
mm
J=I/ACu
δ = sqr (ρ/(π µ0 µr f ))
ρ
Excercise 7
Some quantities related to magnetic materials (cont.)
Notation Name
Unit
pv = Pv /m
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Four terminal electronic components
6