Difference between revisions of "Permittivity and Permeability of Materials Obstacle Course"
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== Permanent Materials == | == Permanent Materials == | ||
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== Materials to Borrow When Necessary == | == Materials to Borrow When Necessary == | ||
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+ | - Milling machine<br> | ||
+ | - Lathe<br> | ||
+ | - RF Lockin<br> | ||
+ | - Active Probes<br> | ||
== Activities == | == Activities == | ||
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=== Reading === | === Reading === | ||
# Read the Wikipedia articles on [https://en.wikipedia.org/wiki/Permittivity permittivity] and [https://en.wikipedia.org/wiki/Permeability_(electromagnetism) permeability]. With the help of the instructor or TA try to achieve a physical understanding of just what the permittivity and permeability mean in a bulk material. | # Read the Wikipedia articles on [https://en.wikipedia.org/wiki/Permittivity permittivity] and [https://en.wikipedia.org/wiki/Permeability_(electromagnetism) permeability]. With the help of the instructor or TA try to achieve a physical understanding of just what the permittivity and permeability mean in a bulk material. | ||
− | # Read the first three sections of [[Media:Measuring_the_Permittivity_and_Permeability_of_Lossy_Materials_-_Solids,_Liquids,_Metals,_Building_Materials_and_Negative-Index_Materials_.pdf |this paper]] (pages 1-27). | + | # Read the first three sections of [[Media:Measuring_the_Permittivity_and_Permeability_of_Lossy_Materials_-_Solids,_Liquids,_Metals,_Building_Materials_and_Negative-Index_Materials_.pdf |this paper]] (pages 1-27). Pay particular attention to the permittivity (<math>\epsilon</math>) / capacitance and permeability (<math>\mu</math>) / inductance associations. |
− | === Permittivity of a Lossless Material From a Capacitance Measurement === | + | |
+ | === Capacitance Techniques (Below 10MHz) === | ||
+ | |||
+ | === * Permittivity of a ''Lossless'' Material From a Capacitance Measurement === | ||
+ | |||
+ | [[File:Epsiloncap1.png |right |350px]] | ||
+ | |||
+ | # Place three samples (air, Teflon, glass) between the aligned and polished ends of two 3/8" diameter, 1/2" lengths of 6061 Al rods (as shown at right). <math>d</math> should be on the order of 1 mm. Measure the capacitances and, from the known surface area <math>A</math> and spacing <math>d</math>, determine the material's relative permittivity. <math>C = \epsilon_r \epsilon_0 \frac{A}{d}</math> (for a capacitor with no fringing fields). | ||
+ | # How do your measured permittivity values compare to standard reference values? | ||
+ | # [https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html Use this web applet to build a capacitor and observe the field lines ]. Are there fringing fields? | ||
+ | <math>\epsilon_r</math>(air): 1.000536<br> | ||
+ | <math>\epsilon_r</math>(Teflon): 2.1<br> | ||
+ | <math>\epsilon_r</math>(glass): 3.7-10<br> | ||
+ | |||
+ | === * A Better Permittivity-Capacitance Measurement of a ''Lossless'' Material === | ||
+ | |||
+ | [[File:Epsiloncap2.png |right |350px]] | ||
+ | # [https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html Use this web applet to build a ''guarded-electrode'' capacitor (as shown at the right) and observe the field lines ]. Are there fringing fields? | ||
+ | # Measure the three permittivities (air, Teflon, glass) again using this guarded-electrode setup. | ||
+ | # How do these results compare to your first (unguarded) measurements? | ||
+ | # How do these results compare to the standard values? | ||
+ | <br><br><br> | ||
+ | |||
+ | The measurements above for a lossless material amounts to requiring the permittivity to be real (as opposed to complex). However, for a lossy material, the permittivity is complex and we need an additional characteristic (beyond simply the capacitance) to characterize the material. This additional characteristic is the conductance <math>G</math>. The measurement below will include the conductance of the material. | ||
+ | <br><br><br><br><br><br><br> | ||
+ | |||
+ | === * Permittivity of a ''Lossy'' Material From a Capacitance Measurement (up to 10 MHz) === | ||
+ | |||
+ | [[File:RCVdivider.png|right|800px |thumb]] | ||
+ | |||
+ | # Employ the guarded-electrode setup above and measure the lossy material's capacitance <math>C</math> and conductance <math>G</math>. <math>C=\epsilon^'\frac{A}{d}</math> and <math>G=\omega \epsilon^{''} \frac{A}{d}</math>, where <math>\epsilon^'\text{/}</math><math>\epsilon^{''}</math> are, respectively, the real and imaginary parts of the complex permittivity. | ||
+ | ## Simultaneously measure the voltage and phase across the resistor <math>V_R</math> and capacitor <math>V_C</math>. | ||
+ | ## The current through the capacitor is given by <math>I_C=V_R/R</math>. The voltage across the capacitor is given by <math>V_C=Z_C I_C</math>, where <math>Z_C</math> is the capacitor's impedance. Solve for the impedance <math>Z_C</math>. | ||
+ | ## The capacitor's [https://en.wikipedia.org/wiki/Admittance admittance] <math>Y_C</math> is given by <math>Y_C=\frac{1}{Z_C}</math>, where the <math>Re(Y_C)=G</math> (the [https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance conductance]) and the <math>Im(Y_C)=B</math> (the [https://en.wikipedia.org/wiki/Susceptance susceptance]). Calculate <math>G</math>. | ||
+ | ## Read section 13.1 (pages 106-107) in this [[http://hank.uoregon.edu/wiki/images/b/b5/Measuring_the_Permittivity_and_Permeability_of_Lossy_Materials_-_Solids%2C_Liquids%2C_Metals%2C_Building_Materials_and_Negative-Index_Materials_.pdf paper]]. | ||
+ | ## Calculate the relative permittivity <math>\epsilon_r</math> as <math>\epsilon'_r=\frac{C}{C_{air}}</math> and <math>\epsilon''_r=\frac{G}{\omega C_{air}}</math>. | ||
+ | ## Do the above procedure for three frequencies at 0.1 MHz, 1MHz and 10 MHz. | ||
+ | ## Plot <math>\epsilon'_r</math> and <math>\epsilon''_r</math> as a function of frequency. | ||
+ | <br><br><br><br> | ||
+ | |||
+ | Beyond 10MHz lumped circuits become non-ideal (resistors start exhibiting capacitive and inductive effects - analogously with capacitors and inductors - even plain wires). So, to go beyond 10MHz, we need to consider how the lumped-component model fails for determining the permittivity. We can put the RC voltage divider circuit on a ground-plane surface-mount PCB for higher frequencies or move to the transmission-line method or the waveguide method (next three sections below). | ||
+ | |||
+ | === * Permittivity of a ''Lossy'' Material From a Capacitance Measurement (up to ~ 500 MHz) === | ||
+ | small surface mount components on a ground-plane PCB... | ||
+ | === Transmission Line Techniques (above 500 MHz) === | ||
+ | coming soon... | ||
− | + | === Waveguide Techniques (above 500MHz) === | |
− | + | coming soon... | |
− |
Latest revision as of 10:00, 24 May 2018
Contents
- 1 Permanent Materials
- 2 Materials to Borrow When Necessary
- 3 Activities
- 3.1 Reading
- 3.2 Capacitance Techniques (Below 10MHz)
- 3.3 * Permittivity of a Lossless Material From a Capacitance Measurement
- 3.4 * A Better Permittivity-Capacitance Measurement of a Lossless Material
- 3.5 * Permittivity of a Lossy Material From a Capacitance Measurement (up to 10 MHz)
- 3.6 * Permittivity of a Lossy Material From a Capacitance Measurement (up to ~ 500 MHz)
- 3.7 Transmission Line Techniques (above 500 MHz)
- 3.8 Waveguide Techniques (above 500MHz)
Permanent Materials
- 6061 3/8" Al rod stock
- Teflon
- Glass microscope slide
- HP Signal Generator (DC-1 GHz)
- Oscilloscope (at least 1GHz bandwidth)
- Miscellaneous electrical components
Materials to Borrow When Necessary
- Milling machine
- Lathe
- RF Lockin
- Active Probes
Activities
Reading
- Read the Wikipedia articles on permittivity and permeability. With the help of the instructor or TA try to achieve a physical understanding of just what the permittivity and permeability mean in a bulk material.
- Read the first three sections of this paper (pages 1-27). Pay particular attention to the permittivity () / capacitance and permeability () / inductance associations.
Capacitance Techniques (Below 10MHz)
* Permittivity of a Lossless Material From a Capacitance Measurement
- Place three samples (air, Teflon, glass) between the aligned and polished ends of two 3/8" diameter, 1/2" lengths of 6061 Al rods (as shown at right). should be on the order of 1 mm. Measure the capacitances and, from the known surface area and spacing , determine the material's relative permittivity. (for a capacitor with no fringing fields).
- How do your measured permittivity values compare to standard reference values?
- Use this web applet to build a capacitor and observe the field lines . Are there fringing fields?
(air): 1.000536
(Teflon): 2.1
(glass): 3.7-10
* A Better Permittivity-Capacitance Measurement of a Lossless Material
- Use this web applet to build a guarded-electrode capacitor (as shown at the right) and observe the field lines . Are there fringing fields?
- Measure the three permittivities (air, Teflon, glass) again using this guarded-electrode setup.
- How do these results compare to your first (unguarded) measurements?
- How do these results compare to the standard values?
The measurements above for a lossless material amounts to requiring the permittivity to be real (as opposed to complex). However, for a lossy material, the permittivity is complex and we need an additional characteristic (beyond simply the capacitance) to characterize the material. This additional characteristic is the conductance . The measurement below will include the conductance of the material.
* Permittivity of a Lossy Material From a Capacitance Measurement (up to 10 MHz)
- Employ the guarded-electrode setup above and measure the lossy material's capacitance and conductance . and , where are, respectively, the real and imaginary parts of the complex permittivity.
- Simultaneously measure the voltage and phase across the resistor and capacitor .
- The current through the capacitor is given by . The voltage across the capacitor is given by , where is the capacitor's impedance. Solve for the impedance .
- The capacitor's admittance is given by , where the (the conductance) and the (the susceptance). Calculate .
- Read section 13.1 (pages 106-107) in this [paper].
- Calculate the relative permittivity as and .
- Do the above procedure for three frequencies at 0.1 MHz, 1MHz and 10 MHz.
- Plot and as a function of frequency.
Beyond 10MHz lumped circuits become non-ideal (resistors start exhibiting capacitive and inductive effects - analogously with capacitors and inductors - even plain wires). So, to go beyond 10MHz, we need to consider how the lumped-component model fails for determining the permittivity. We can put the RC voltage divider circuit on a ground-plane surface-mount PCB for higher frequencies or move to the transmission-line method or the waveguide method (next three sections below).
* Permittivity of a Lossy Material From a Capacitance Measurement (up to ~ 500 MHz)
small surface mount components on a ground-plane PCB...
Transmission Line Techniques (above 500 MHz)
coming soon...
Waveguide Techniques (above 500MHz)
coming soon...