Ajaya Kumar Kavala Research Scholar Department of Physics IIT Patna Technique for measuring the Dielectric constant using open ended coaxial cable in the microwave frequency region Tuesday, June 14, 20161

Introduction of Dielectrics Dielectric is an entity,in which equal positive and negative charges separated by equal small distance. In which each molecule has permanent dipole moment P This type of materials are known as polar materials Different molecules has different different directions of the dipole moment. In Non polar materials,The centre of the positive charge distributution in an atom or molecules coincides with the centre of the negative charge distribution. The atoms or molecules do not have permanant dipole moment Dielectric constant = capacitence without dielectric over capacitence with dielectric Tuesday, June 14, 20162

Types of polarizations Definition: Dipole moment per unit volume is called Polarisation 3 types of polarisation 1.Dipole polarisation 2.Ionic polarisation 3.electronic polarisation Tuesday, June 14, 20163

Principle  An electromagnetic wave of particular frequency passed through a coaxial probe to the sample, some part of the wave is transmitted and some part of the wave reflected.  From the reflected signal we can get the reflection coefficient of that sample, from that we can get the corresponding impedance of that sample at that particular frequency  From that impedance we can obtain the complex dielectric constant at that frequency Tuesday, June 14, 20164

 Accurate determination of the frequency-dependent probe-end impedance in vacuum.  Elimination of spurious impedances such as those due to connector mismatch  Indeterminacy of probe parameters  Accurate modeling of the probe-liquid interface impedance after the above problems are eliminated. Tuesday, June 14, 20165

 Open With the coax terminated by free space, the measurement plane of the ANA was moved to the coax end using the electrical delay provided. The delay, which corresponds to the length of the coax (typically 6-12 in), was adjusted to give a cluster of points near the real and imaginary parts. Experimental data collection is described below step by step A short at the coax end was created by raising a small vessel (about 6 cc) filled with mercury, until the coax end was well within the liquid. This resulted in a cluster of points around the position [Re and Img parts.  Standard Liquid At this point, the display was checked to ensure that the date returned to the configuration for an open. A cell (of volume typically <10 cc) with a standard liquid, usually acetone, was now inserted so that the coax end was well immersed in the liquid. The data ρc were again read into the computer.  Short Tuesday, June 14, 20166

Z1Z1 Z2Z2 ZέZέ Z3Z3 ZmZm Z[ε,ω] Cf[ω] C[ε,ω] Zm Z3 Z1 Co[ω] Lumped parameter circuit model Tuesday, June 14, 20167

 The value of Zm is calculated from the reflection coefficient,  as Zm = Z 0 [(1+  )/(1-  )] ………… (1) Zm also can be expressed from the equivalent circuit as Zm= Z1 + Z2[ Z3+ Z(  )] / [Z2+Z3+ Z(  )]  It can be written as  +  12 Z(ε)-  23 ZM(ε) = ZM(ε) Z(ε) …… (2) where  = Z1 Z2 +Z2 Z3 +Z3 Z1  12 = Z1 + Z2  23 = Z2 +Z3  The coax terminated by a medium filling the other half space can be described the equivalent circuit,which represents the  and ω dependent complex capacitance due to fringing field Z (ω,ε) = [jB(ω,ε) + G(ω,ε) ] -1 = [j ωcf(ω) + jωc(ω,ε)] -1 ε = Zm -  12 /  + Zm  23 Tuesday, June 14, 20168

 Error analysis Analysis shows that the instrument accuracies contribute negligibly (less than 0.1%) to the accuracy of measurement. he principal source of error is caused by the termination modeling. The calibration procedure eliminated the error in determining the capacitance parameters Cj(ω) and Co(ω). Residual errors are due to ignoring higher orders of ωε in B(ω,ε) and the radiation conductance G(ω, ε). We estimate the error introduced by these higher order corrections as Δε/ε ≈ [B(ω,ε) √(ωεC)-jG(ω,ε)] / √ (ωεC) (C is a constant.) Tuesday, June 14, 20169

Variation of real part of dielectric permittivity with respective frequency Tuesday, June 14,

Tuesday, June 14,

Sample AM1 PM3 MNDO Glycine Variation of relaxation time with weight percentage level of Bovine serum albumin aqueous solution medium Optimized geometrical structure from the Hamiltonian quantum mechanical calculations Dipole moment values from the theoretical Hamiltonian quantum mechanical calculation Tuesday, June 14,