Difference between revisions of "Permittivity and Permeability of Materials Obstacle Course"

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(→‎* Permittivity of a Lossy Material From a Capacitance Measurement (up to 10 MHz))
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# 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.
 
# 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.
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## Simultaneously measure the voltage across the resistor <math>V_R</math> and [https://en.wikipedia.org/wiki/Lock-in_amplifier Lock-in] (both in-phase <math>X</math>and in-quadrature<math>Y</math>) voltages <math>V_{Lock-in}</math> at <math>V_{out}</math>. Employ a lock-in time constant that is much longer than the period of the AC driving voltage. The lock-in voltage <math>V_{Lock-in}</math> is given by <math>V_{Lock-in}(X)=\frac{1}{2}V_{out} \,\, cos(\theta)</math> and <math>V_{Lock-in}(Y)=\frac{1}{2}V_{out} \,\, sin(\theta)</math>, where <math>V_{out}</math> is the voltage across the capacitor and <math>\theta</math> is the phase difference between the AC driving voltage and <math>V_{out}</math>
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## Simultaneously measure the voltage and phase across the resistor <math>V_R</math> and capacitor <math>V_C</math>.
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## 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_{out}=Z_C I_C</math>, where <math>Z_C</math> is the capacitor's impedance. Solve for the impedance <math>Z_C</math>.
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## 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>.
 
## 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]].
 
## 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]].

Revision as of 15:02, 23 May 2018

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

Activities

Reading

  1. 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.
  2. 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

Epsiloncap1.png
  1. 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).
  2. How do your measured permittivity values compare to standard reference values?
  3. 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

Epsiloncap2.png
  1. Use this web applet to build a guarded-electrode capacitor (as shown at the right) and observe the field lines . Are there fringing fields?
  2. Measure the three permittivities (air, Teflon, glass) again using this guarded-electrode setup.
  3. How do these results compare to your first (unguarded) measurements?
  4. 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)

RCVdivider.png
  1. 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.
    1. Simultaneously measure the voltage and phase across the resistor and capacitor .
    2. 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 .
    3. The capacitor's admittance is given by , where the (the conductance) and the (the susceptance). Calculate .
    4. Read section 13.1 (pages 106-107) in this [paper].
    5. Calculate the relative permittivity as and .
    6. Do the above procedure for three frequencies at 0.1 MHz, 1MHz and 10 MHz.
    7. 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 abandon the lumped capacitance model for determining the permittivity. There are a few techniques for doing this. And the transmission-line technique is one of them.

Transmission Line Techniques (above 50MHz)

coming soon...

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