## Solid and Liquid dielectric constant measurement equipments

This page mentions dielectric constant measurement of liquid and solid. It cover liquid dielectric and solid dielectric test equipments and test procedure for the measurement of dielectric constant.

Consider a solid sample or length l_{ε} loaded in rectangular waveguide
against short circuit that touches it well.

D & D_{R} are the positions or first voltage minima of the sanding wave
pattern when waveguide is unloaded & loaded with the dielectric.
The respective distance from the short circuit will be ( l + l_{ε} ) &
( l_{R} + l_{ε} ).

The impedance are equal so

Zo & Z_{ε} are respectively the characteristic impedance of empty & dielectric filled
waveguide β & β_{ε} are respective propagation constant.
Expanding tangent sum angel we get following equations.

The dielectric constant calculation is done with this equation.

### Dielectric constant measurement equipments

Following test equipments are 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

The figure-1 depicts test setup used for solid dielectric constant measurement.

### Test Procedure for Solid dielectric constant

➨Do the setup and arrange test equipments as shown in the figure-1.

➨Energize the microwave power source & obtain suitable power level in the SWR meter.

➨Micrometer position of solid dielectric should be fully closed.

➨With no sample in the shorted waveguide, measure & record in table position of
standing wave minima, starting from an arbitrary plane. Compute guide
wavelength (distance between successive minima being λg/2).

➨Take position of first minima as reference minima i.e.D_{R}.

➨Using frequency meter determine the frequency of the excited wave & compute
free space wavelength (λ_{0} = c/F).

➨Remove the solid dielectric cell & insert gently the dielectric sample into the solid
dielectric cell such that it should touch the plane of waveguide.

➨Now connect solid dielectric cell without disturbing any setting.

➨Measure and record shift in minima in the table format.

➨Refer the calculations Dielectric constant for finding the value of Dielectric
Constant.

➨Measure and record waveguide dimension.

Record following in table format and use equation-3 to calculate dielectric constant for solid.

a.) Waveguide dimension a = ----- cm, b = ----- cm

(for x band a = , b = )

b.) Cut-off wavelength λ_{c} = 2*a/m in cm

c.) Frequency of operation = ------ in GHz

d.) Beta β = 2π/λg , Propagation constant

### Liquid dielectric constant measurement

The figure-2 depicts test setup used for liquid dielectric constant measurement.

### Test Procedure for Liquid dielectric constant

➨Do the setup and arrange test equipments as shown in the figure-2.

➨Energize the microwave power source & obtain the suitable power level in the
indicating meter.

➨With no liquid in the cell, read & record in table position or standing wave
minima i.e. D_{R} starting from any arbitrary plane. Compute guide wavelength the
distance with alternate minima being λg/2.

➨Using frequency meter determine the frequency of the excited wave & compute
free space wavelength.

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

➨Find out SWR as done in the above measurement.

➨Measure waveguide dimension.

➨Determine and enter values in tabular format with following parameters and
do calculation as per equation-3 above.

a.) Waveguide dimension a = ---- cm, b = ---- cm

b.) Cut-off wavelength λ_{ε} = 2a ----- cm

c.) Frequency of operation f = ---- GHz

d.) Free-space wavelength = c/f = ---- cm

e.) β = 2*π/λg, Propagation constant

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