Permittivity and Permeability of Materials Obstacle Course - Revision history

Bsboggs: /* Activities */

2018-05-24T18:00:02Z

‎Activities

Bsboggs: /* Materials to Borrow When Necessary */

2018-05-24T17:46:28Z

‎Materials to Borrow When Necessary

Bsboggs: /* Materials to Borrow When Necessary */

2018-05-24T17:46:01Z

‎Materials to Borrow When Necessary

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

2018-05-24T17:41:48Z

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

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

2018-05-23T23:02:16Z

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

Bsboggs at 19:31, 21 May 2018

2018-05-21T19:31:52Z

Bsboggs: /* * Permittivity of a Lossy Material From a Capacitance Measurement (up to 50 MHz) */

2018-05-21T19:29:54Z

‎* Permittivity of a Lossy Material From a Capacitance Measurement (up to 50 MHz)

Bsboggs: /* Waveguide Techniques (above 50MHz) */

2018-05-21T19:19:56Z

‎Waveguide Techniques (above 50MHz)

Bsboggs: /* * Permittivity of a Lossy Material From a Capacitance Measurement (up to 50 MHz) */

2018-05-21T19:18:11Z

‎* Permittivity of a Lossy Material From a Capacitance Measurement (up to 50 MHz)

Bsboggs: /* * Permittivity of a Lossy Material From a Capacitance Measurement (up to 50 MHz) */

2018-05-21T19:03:57Z

‎* Permittivity of a Lossy Material From a Capacitance Measurement (up to 50 MHz)

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-=== * Permittivity of a ''Lossy'' Material From a Capacitance Measurement (up to 10 MHz)===
+=== * Permittivity of a ''Lossy'' Material From a Capacitance Measurement (up to 10 MHz) ===
 [[File:RCVdivider.png|right|800px |thumb]]
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-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.
+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).
-=== Transmission Line Techniques (above 50MHz) ===
+=== * Permittivity of a ''Lossy'' Material From a Capacitance Measurement (up to ~ 500 MHz) ===
 coming soon...

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 - Lathe<br>
 - RF Lockin<br>
-- Oscilloscope and Active Probes<br>
+- Active Probes<br>
 == Activities ==

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 - Lathe<br>
 - RF Lockin<br>
 == Activities ==

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 === * 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.

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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.
-## 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]].

← Older revision		Revision as of 19:31, 21 May 2018
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−	~~PAGE UNDER CONSTRUCTION~~
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	== Permanent Materials ==		== Permanent Materials ==

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 ## Do the above procedure for at least three frequencies between 10 MHz and 50 MHz.
 ## Plot <math>\epsilon'_r</math> and <math>\epsilon''_r</math> as a function of frequency.
 === Waveguide Techniques (above 50MHz) ===
 coming soon...