This document summarizes a method for retrieving the electrical and physical properties of dielectric samples using time domain multiple reflection analysis. It presents the theoretical models for computing reflection coefficients and extracting relative permittivity, thickness, conductivity, and loss tangent of samples. Experimental results applying the technique to measure a 2.3 cm thick red granite sample and 2.8 cm thick unknown material at normal and 30 degree oblique incidence are also presented, with low errors between reconstructed and actual properties.

1. Electrical and Physical Properties
Retrieval
Aman, V. Singh, and S. Bhattacharyya, “Retrieval of Electrical and Physical Properties of Dielectric Samples Using Time
Domain Multiple Reflection Method,” IET Microwaves, Antennas and Propagation, vol. 14, issue 8, pp. 701-706, 2020.
2
1 1
r t
P L P
 
2 2 2
2 2 (1 - ) exp(-4 d)
r t
P L P

  
6 2 2
3 3 (1 - ) exp(-8 d)
r t
P L P

  

2. • Computation of reflection coefficient (equal loss in all conditions):
• Retrieval of relative permittivity and thickness of the sample [2]:
• Retrieval of other parameters [3]:
Time domain multiple
reflection model
[2] L. F. Chen, C. K. Ong, C. P. Neo, V. V. Varadan, and V. K. Varadan, Microwave Electronics:
Measurement and Materials Characterization, West Sussex, U.K.: Wiley, 2004.
[3] Muqaibel, A. H., Jazi, A. S.-, “A new formulation for characterization of materials based on measured
insertion transfer function,” IEEE Transactions on Microwave Theory & Techniques, 2003, 51, (8), pp.
1946-1951.
 
2
2
1
2
1
ln 1
4
r
r
P
d P

 
  
 
 
 
2
2
1
0 2
1
ln 1
2
r r
t
r
P
d P



 
  
 
 
1/2
2
tan
( )
r
c


 


3. • Location of the second peak:
• Location of the third peak:
• Range resolution limited by the bandwidth:
Time domain multiple
reflection model (contd.)
2
c
R
BW
 

4. 2.3 mm thick Red Granite
Marble (εr = 6.5)
2.8 mm thick unknown
MUT

5. Material
Reconstructed Results
Epsilon Thickness Conductivity loss tangent
Red Granite of
Thickness 2.3 cm
6.587 2.233 8.40E-05 0.023
Unknown MUT of
Thickness 2.8 cm
8.748 2.744 6.13E-05 0.013
2.3 mm thick Red Granite
Marble (εr = 6.5)
2.8 mm thick unknown MUT

6. Electromagnetic and Physical
Properties Retrieval
PNA
Horn
Antenna
d
Pr1
Pr2
Pr3
MUT
A
B C
D
Medium 1 Medium 2 Medium 3
Horn
Antenna
i
t
Aman, Vineet Singh, Nilotpal, and Somak Bhattacharyya, “A Free Space Frequency-Time-Domain Technique for
Electromagnetic Characterization of Materials Using Reflection-Based Measurement,” International Journal of RF and
Microwave Computer-Aided Engineering, vol. 31, issue 1, Article No. e22490, January 2021.

7. Theoretical Analysis for retrieval
.
r x y
 
r
y
x
 
[4] V. Degli-Esposti, M. Zoli, E.M. Vitucci, F. Fuschini, M. Barbiroli, and J. Chen, “A Method for the Electromagnetic
Characterization of Construction Materials Based on Fabry–Pérot Resonance,” IEEE Access, 5, pp. 24938-24943, 2017
 
2
2
1 3
2 2
2 1-
r r
r
P P
P
 

  

 
 
2
1
1-
r
r
x


 
 
   
 

 
1
.
2 .
r r
c t
d
 


Normal
Incidence
Oblique
Incidence
[4]
2
.
.cos
2 .
t
r r
c t
d 
 


2
. i
r r
t
Sin
y
Sin

 

 
   
 
2
.
.2 .cos
r r
t
c
f d
 

 
  

 

8. Experimental Setup
Samples under test
Normal Incidence Oblique Incidence

9. Experimental Results
Material
Reconstructed Results Error (%)
ɛr r d (cm) σ (S/m) tanδ d
Red Granite of 2.3
cm thickness
6.6501 1.0218 2.170 5.434e-2 0.015 5.65
Unknown MUT of
2.8 cm thickness
8.5161 1.0037 2.786 6.602e-2 0.014 0.5
Normal Incidence Oblique Incidence (30˚)