Dielectric Constant Measurement: Solid and Liquid Materials

This document details the measurement of dielectric constants for both liquid and solid materials. It covers the necessary test equipment and procedures for determining these values.

Theory: Dielectric Constant Measurement

Consider a solid sample of length $l_\epsilon$ loaded in a rectangular waveguide against a short circuit, ensuring good contact. Let $D$ and $D_R$ be the positions of the first voltage minima of the standing wave pattern when the waveguide is unloaded and loaded with the dielectric, respectively. The respective distances from the short circuit will be $(l + l_\epsilon)$ and $(l_R + l_\epsilon)$. The impedances are equal, so $Z_o$ and $Z_\epsilon$ are the characteristic impedances of the empty and dielectric-filled waveguide, respectively. $\beta$ and $\beta_\epsilon$ are the respective propagation constants.

Expanding the tangent sum angle, we get the following equations:

Dielectric constant equation

The dielectric constant calculation is performed using this equation.

Dielectric Constant Measurement Equipments

The following test equipment is needed for the dielectric constant measurement setup:

• Gunn power supply
• Gunn Oscillator
• Frequency meter
• Variable attenuator
• Detector mount
• Isolator
• PIN modulator
• Solid dielectric cell

Solid Dielectric Constant Measurement

Solid dielectric constant measurement setup

Figure 1 depicts the test setup used for solid dielectric constant measurement.

Test Procedure for Solid Dielectric Constant

1. Set up and arrange the test equipment as shown in Figure 1.

2. Energize the microwave power source and obtain a suitable power level on the SWR meter.

3. Ensure the micrometer position of the solid dielectric cell is fully closed.

4. With no sample in the shorted waveguide, measure and record the position of the standing wave minima, starting from an arbitrary plane. Compute the guide wavelength (distance between successive minima being $\lambda_g/2$).

5. Take the position of the first minima as the reference minima, i.e., $D_R$.

6. Using a frequency meter, determine the frequency of the excited wave and compute the free space wavelength ($\lambda_0 = c/F$).

7. Remove the solid dielectric cell and gently insert the dielectric sample into the solid dielectric cell, ensuring it touches the plane of the waveguide.

8. Now, connect the solid dielectric cell without disturbing any settings.

9. Measure and record the shift in minima in a table format.

10. Refer to the calculations for Dielectric Constant to determine the value of the Dielectric Constant.

11. Measure and record the waveguide dimensions. Record the following in a table format and use Equation 3 to calculate the dielectric constant for the solid:

    a.) Waveguide dimension $a =$ cm, $b =$ cm (for x band $a =$, $b =$) b.) Cut-off wavelength $\lambda_c = 2*a/m$ in cm c.) Frequency of operation = GHz d.) Beta $\beta = 2\pi/\lambda_g$, Propagation constant

Dielectric constant calculation

Liquid Dielectric Constant Measurement

Liquid dielectric constant measurement setup

Figure 2 depicts the test setup used for liquid dielectric constant measurement.

Test Procedure for Liquid Dielectric Constant

1. Set up and arrange the test equipment as shown in Figure 2.

2. Energize the microwave power source and obtain a suitable power level on the indicating meter.

3. With no liquid in the cell, read and record the position of the standing wave minima, i.e., $D_R$, starting from any arbitrary plane. Compute the guide wavelength, with the distance between alternate minima being $\lambda_g/2$.

4. Using a frequency meter, determine the frequency of the excited wave and compute the free space wavelength.

5. Carefully fill the cell with a known volume of the liquid sample. Calculate the height of the liquid in the cell (volume/area = V/ab). Read and record in a table the position of voltage minima or the sanding wave pattern with respect to the same reference plane. Measure and record in a table the position of the standing wave voltage minima shifted due to the dielectric constant. The position of the first minima is taken as $D$.

6. Find out SWR as done in the above measurement.

7. Measure the waveguide dimensions.

8. Determine and enter values in a tabular format with the following parameters, and perform calculations as per Equation 3 above:

   a.) Waveguide dimension $a =$ cm, $b =$ cm b.) Cut-off wavelength $\lambda_\epsilon = 2a$ cm c.) Frequency of operation $f =$ GHz d.) Free-space wavelength = $c/f$ = cm e.) $\beta = 2*\pi/\lambda_g$, Propagation constant