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

Latest revision as of 10:00, 24 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
- 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 ( $\epsilon$ ) / capacitance and permeability ( $\mu$ ) / 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). $d$ 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).
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?

$\epsilon _{r}$ (air): 1.000536
$\epsilon _{r}$ (Teflon): 2.1
$\epsilon _{r}$ (glass): 3.7-10

* A Better Permittivity-Capacitance Measurement of a Lossless Material

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 $G$ . 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 $C$ $C$ and conductance $G$ $G$ . $C=\epsilon ^{'}{\frac {A}{d}}$ $C=\epsilon ^{'}{\frac {A}{d}}$ and $G=\omega \epsilon ^{''}{\frac {A}{d}}$ $G=\omega \epsilon ^{''}{\frac {A}{d}}$ , where $\epsilon ^{'}{\text{/}}$ $\epsilon ^{'}{\text{/}}$ $\epsilon ^{''}$ $\epsilon ^{''}$ 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...

@@ Line 1: / Line 1: @@
-PAGE UNDER CONSTRUCTION
 == Permanent Materials ==
@@ Line 16: / Line 13: @@
 - Lathe<br>
 - RF Lockin<br>
+- Active Probes<br>
 == Activities ==
@@ Line 49: / Line 47: @@
 <br><br><br><br><br><br><br>
-=== * Permittivity of a ''Lossy'' Material From a Capacitance Measurement (up to 50 MHz)===
+=== * Permittivity of a ''Lossy'' Material From a Capacitance Measurement (up to 10 MHz) ===
-[[File:RCVdivider.png|right|350px]]
+[[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 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>
+## 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_{out}=Z_C I_C</math>, where <math>Z_C</math> is the capacitor's impedance. Solve for the impedance <math>Z_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 at least three frequencies between 10 MHz and 50 MHz.
+## 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>
-=== Waveguide Techniques (above 50MHz) ===
+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...

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

Latest revision as of 10:00, 24 May 2018

Contents

Permanent Materials

Materials to Borrow When Necessary

Activities

Reading

Capacitance Techniques (Below 10MHz)

* Permittivity of a Lossless Material From a Capacitance Measurement

* A Better Permittivity-Capacitance Measurement of a Lossless Material

* Permittivity of a Lossy Material From a Capacitance Measurement (up to 10 MHz)

* Permittivity of a Lossy Material From a Capacitance Measurement (up to ~ 500 MHz)

Transmission Line Techniques (above 500 MHz)

Waveguide Techniques (above 500MHz)

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