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.
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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 ©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.
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 ©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.
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
©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
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
©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
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