MEASUREMENT OF DIELECTRIC CONSTANT OF A SOLID
AIM: To determine the dielectric constant of the given solid.
CONNECTION DIAGRAM:
Tunable
Probe
VSWR Meter
Fixed Short
Optimized Slotted Solid Dielectric
MW Bench Section Cell
PROCEDURE:
1. Arrange the equipment as shown above [place the dielectric slab (shown as hatched rectangle)
only in step-7 below].
2. Energize the microwave power source and obtain suitable power level in the bench and optimize
the same.
3. Find the frequency of the microwave generated using the direct reading type frequency meter.
4. Connect the fixed-short to the solid-dielectric cell as indicated in the figure taking care that no
dielectric slab is placed within the solid dielectric cell.
5. Take some point on the slotted section scale as reference level. Determine the position of the first
and the second consecutive minima D1 and D2 (these are minima determined using an empty
dielectric cell). Determine the guided wavelength using 𝜆𝑔 = 2(𝐷2 − 𝐷1 ).
6. Disconnect the dielectric-cell from the microwave bench; insert the given dielectric slab
(Teflon/nylon/ebonite) into the cell making sure that the slab is placed in such a way that it is in
very good contact with the fixed-short. Reconnect the dielectric-cell to the microwave bench.
7. Determine the first and the second voltage minima using the slotted section considering the same
reference point as was used in step-5. Call these distances D1 and D2, respectively.
8. Determine the guided wavelength once again. Measure the length of the dielectric slab inserted
as 𝑙𝜀 .
9. Calculate 𝛽 = 2𝜋⁄𝜆𝑔 , the phase constant (using the wavelength calculated in step-5)
tan(𝛽𝜀 𝑙𝜀 )
10. Find using the equation:
𝛽𝜀 𝑙𝜀
𝑡𝑎𝑛(𝛽𝜀 𝑙𝜀 ) 𝑡𝑎𝑛[𝛽(𝐷1𝜀 −𝐷1 +𝑙𝜀 )]
= - Eqn. (1)
𝛽𝜀 𝑙𝜀 𝛽𝑙𝜀
Note that all quantities on the RHS have already been determined during the experiment.
11. Now repeat the experiment from step 6-10 by inserting a second dielectric slab into the dielectric
cell (so that the total length of the dielectric now is different, say 𝑙𝜀2 .
12. Solve the transcendental equation Eqn. (1) using the method detailed below for each length of
the dielectric slab.
a) Use the given Tan(X)/X table and find out the possible solutions for the above equation Eqn.
(1).
𝑋
b) For each X determine 𝑙 (using the appropriate length of the dielectric slab,𝑙𝜀 or 𝑙𝜀1 as the case
𝜀
may be)
𝑋
c) The 𝑙 value that comes out as common (or nearly common) in the series of solutions obtained
𝜀
from the two experiments you did (i.e., one with dielectric slab of length 𝑙𝜀 and the second
one with length 𝑙𝜀1 ).
Using each value of X so determined (which are nothing but, 𝛽𝜀 𝑙𝜀 ) calculate the
corresponding dielectric constant using the equation
𝑋
13. Using the correct value of 𝑙 determined in step 12(c) calculate the value of the dielectric constant
𝜀
of the material using the equation :
𝑎 2 𝛽 𝑙 2
(𝜋) ( 𝑙𝜀 𝜀 ) +1
𝜀
𝜀𝑟 = 2
2𝑎
(𝜆 ) +1
𝑔
