Permittivity and Permeability of Materials Obstacle Course

From APL
Jump to: navigation, search

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

  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 (\epsilon) / capacitance and permeability (\mu) / 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). d should be on the order of 1 mm. Measure the capacitances and, from the known surface area A and spacing d, determine the material's relative permittivity. C = \epsilon_r \epsilon_0 \frac{A}{d} (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?

\epsilon_r(air): 1.000536
\epsilon_r(Teflon): 2.1
\epsilon_r(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 G. 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 C and conductance G. C=\epsilon^'\frac{A}{d} and G=\omega \epsilon^{''} \frac{A}{d}, where \epsilon^'\text{/}\epsilon^{''} are, respectively, the real and imaginary parts of the complex permittivity.
    1. Simultaneously measure the voltage and phase across the resistor V_R and capacitor V_C.
    2. The current through the capacitor is given by I_C=V_R/R. The voltage across the capacitor is given by V_C=Z_C I_C, where Z_C is the capacitor's impedance. Solve for the impedance Z_C.
    3. The capacitor's admittance Y_C is given by Y_C=\frac{1}{Z_C}, where the Re(Y_C)=G (the conductance) and the Im(Y_C)=B (the susceptance). Calculate G.
    4. Read section 13.1 (pages 106-107) in this [paper].
    5. Calculate the relative permittivity \epsilon_r as \epsilon'_r=\frac{C}{C_{air}} and \epsilon''_r=\frac{G}{\omega C_{air}}.
    6. Do the above procedure for three frequencies at 0.1 MHz, 1MHz and 10 MHz.
    7. Plot \epsilon'_r and \epsilon''_r 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...