CHAPTER 3 THEORY AND METHODS - INFLIBNETshodhganga.inflibnet.ac.in/bitstream/10603/39222/9/09_chapter 3.pdf · Theory and Methods 44 I = V jωC 0 k* (3.6) where k* = k'− jk" The

Theory and Methods 42

CHAPTER 3

THEORY AND METHODS

3.1 Elementary Discussion About Dielectric Material

In electromagnetism, materials are classified into two categories:

1) Conductors and 2) insulators or dielectrics. The dividing line between the two

categories is sharp and some media (eg. the earth) are considered as conductors in

one part of radio frequency range but as dielectrics (with losses) in other part of

frequency range. A material is categorized as a “dielectric” if it has the capacity to

store energy when external electric field is applied. The theory of dielectrics was

proposed by Faraday and then later on it was modified by Maxwell. In 1837,

Michael Faraday performed experiments to investigate the effect of filling dielectric

material in the space between the plates of capacitor. If a DC voltage is applied

across a parallel plate capacitor as shown in Fig. 3.1, it is observed that more charge

is stored in the case when a dielectric material is placed between the plates than the

case when no material (a vacuum) is placed between the plates. The dielectric

material enhances the storage capacity of the capacitor by neutralizing the charges at

the electrodes which ordinarily would contribute to the external field. This

phenomenon is dependent on the dielectric properties such as breakdown voltage.

The capacitance of the capacitor filled with the dielectric material depends on the

dielectric constant of the material.

Fig. 3.1: Application of DC voltage across the plates of a parallel plate

capacitor (Agilent, 2005)


From the Figure 3.1,

C0 = A / t (3.1)

C = C0 k' (3.2)

k' = ε'r = C /C0 (3.3)

where k' = ε'r is the real dielectric constant of the material

C0 = Capacitance without material (vacuum) =A / t

C = Capacitance with dielectric material = qd /V

A= area of capacitor plates

t = distance between the capacitor plates

qd = magnitude of charge stored on each plate

V = voltage applied to the plates

If an ac sinusoidal voltage Ve jωt

is applied across the same capacitor as

shown in Fig. (3.2), the resulting current is made up of a charging current Icharge and

a loss current Iloss that is related to the dielectric constant. The losses in the material

can be represented as a sum of conductance (G) in parallel with a capacitance (C).

Fig. 3.2: Application of AC voltage across the plates of a parallel plate capacitor

For the applied voltage across the capacitor, the current

I = Icharge+ Iloss (3.4)

= jωVC0k' + VG

If G =ωC0 k'' then

I = jωVC0k' +VωC0k'' (3.5)

I = jωVC0 k '+ (− j)2 VωC0k''


I = V jωC0 k* (3.6)

where k* = k'− jk"

The complex dielectric constant k* consists of a real part k' which represents

the storage of energy and an imaginary part k'' which represents the loss.

The complex dielectric constant k* of a material is equivalent to relative or

normalized complex permittivity given by

εr* = k* = ε'/ε0 - j ε''/ ε0 = ε'r - εr'' (3.7)

where εr*, i.e. the permittivity ε* relative to free space ε0,is called complex relative

permittivity, and ε0 = Permittivity in free space = 8.854 x 10-12

Farad/m

The real part of permittivity ε'r is a measure of the ability of dielectric

material to store electric energy from an external electric field. The imaginary part

of permittivity ε"r is called the loss factor and is a measure of how dissipative or

lossy a material is, to an external electric field. The imaginary part of permittivity ε"r

is always greater than zero. The loss factor includes the effects of both dielectric loss

and conductivity. Fig. 3.3 shows complex permittivity in the form of a simple vector

diagram .The real and imaginary components (ε'r, ε"r) are 90° out of phase. The

vector sum ε*r forms an angle δ with the real axis ε'r. The relative “lossiness” of a

material is the ratio of the energy lost to the energy stored.

Fig. 3.3: Loss factor vector diagram


tan δ = = (3. 8)

The product of angular frequency and loss factor is equivalent to a dielectric

conductivity.

ζ = ωε0ε''

3.2 Polarization of Dielectric Materials

The dielectrics contain bound charges which are tightly bound together in

atoms and molecules. They differ from plasma and conducting media, in as much as

they do not contain free charges like the other two states of matter. The application

of a steady external electric field causes a small but significant separation of the

bound charges so that each infinitesimal element of volume behaves as if it were an

electrostatic dipole. The induced dipole field tends to oppose the applied field. A

dielectric material which exhibits this separation of bound charges is said to be

polarized. On a microscope scale, the type of polarization is determined by the

nature of material. In most of the materials, polarization occurs only in the presence

of an applied field, although a few materials exhibit permanent polarization;

ferromagnetic crystals exhibit permanent polarization while certain other materials

called electrets become permanently polarized if allowed to solidify in a strong

electric field. On an atomic scale, charge separation can occur due to the

displacement of the negatively charged electron cloud relative to the positively

charged nucleus; this is called electronic polarization. On a molecular scale, ionic

and orientational polarization are important. Ionic polarization results from the

separation of positive and negative ions in molecules which are held together by

ionic bonds. Orientational polarization arises in materials whose molecules are

permanently polarized but randomly oriented; the application of an external electric

field causes the molecules to align themselves parallel to the applied field, thus

producing a net polarization in the material. On a still larger scale, one encounters

space charge polarization which arises when free conduction electrons are present

but are prevented from moving through large distances by the barriers such as grain

boundaries; when a field is applied,the electrons „pile up‟ against these barriers

producing the separation of charges required to polarize the material. The four types


of polarization described above are indistinguishable in a steady field, but in a time

varying field each type exhibits a different characteristic response time. A molecule

develops a dipole moment proportional to applied electric field for small field

magnitude. This proportionality is expressed as

p = αT Eav (3.9)

In which the total polarizability αT is the sum of polarization arising from

each of the different types of polarization viz electronic, ionic etc. Eav is the average

rms field acting on a molecule (which in general is different from the applied field).

If we multiply the equation by n0 the number of molecules per cubic meter, the

result is the dipole moment per unit volume or the polarization. P.

P = n0 p = n0αTEav (3.10)

When a material having non-polar atoms is subjected to an electric field it

gets polarized due to the displacement of the center of charge of electrons relative to

the nucleus in each atom, causing electronic polarization (Pe).and the displacement

of atoms of different polarity relative to one other induces dipole moments in the

molecules called atomic polarization (Pa). These two polarizations together

constitute a distortion polarization (Pd).

In a polar molecule, a third process also contributes to the polarizability

(provided the dipoles are free to orient /reorient) in which when an electric field is

applied there is a tendency for the permanent dipoles to align themselves parallel to

it, although, because of the thermal motion the departure from a random arrangement

is very small in the fields of the strength normally used for measurement and at

ordinary temperatures. In polar molecules, the orientation polarization is in addition

to the distortion polarization observed in non polar materials, so that polar materials

have higher permittivity than non polar ones. The relationship between permittivity

and the various types of polarization can be expressed in the following way:

ε = 1 + (3.11)

where P is the polarization produced by the applied field E in an isotropic material.

Substituting the value of P from equation (3.9), we get


ε = 1 + (n0αTEav) (3.12)

Each of the three types of polarizability is a function of the frequency of the

applied field. As the field alters and reverses, both the distortion of the molecules

and their average orientation must change. When the frequency is sufficiently low,

all types of polarization attain the value they would have had in a steady field equal

to the instantaneous value of alternating field, but as the frequency is raised the

polarization no longer has time to reach its steady value. The orientation polarization

is the first to be affected. This type of polarization takes a time of the order 10-12

to

10-10

seconds to reach its equilibrium value in liquids and solids with moderately

small molecules and at normal temperatures; consequently when the applied field

has a frequency in the range 1010

to 1012

cycles/sec, the orientational polarization

fails to reach its equilibrium value and contributes less and less to the polarization as

the frequency rises.

It is this fall of polarizability from αT = αe + αa + αo to αT = αe + αa, which has

associated with it related fall of permittivity and occurrence of absorption that

constitutes dielectric dispersion. In the frequency range in which the dielectric

dispersion occurs, αe and αa remain unchanged, since the distortion polarization of a

molecule takes much less time to reach equilibrium state with an applied field than

the orientational polarization does .At frequencies comparable with the natural

frequencies of vibration of the atoms in the molecules, however, αa will fail to attain

its equilibrium value and as a result of it further dispersion regions will occur. These

usually lie in the infrared region of the spectrum. The fall-off of the electronic

polarization occurs at frequencies corresponding to the electronic transitions

between different energy levels in the atom, that is, mostly at visible, ultraviolet and

X-ray frequencies. In electronic and atomic polarization, quantum effects are

predominant in all phases, but the dielectric dispersion in the liquid phase, and to

some extent also in solid phase, can be explained by classical theory.


3.3 Determination of Dielectric Parameters at Microwave Frequencies

Electromagnetic waves are in general observed in bounded space, confined

by various types of boundaries. The reflection and refraction of fields by matter

provide an essential mean for directing and modifying such fields, which are useful

in measurements of the dielectric properties of materials.

When the electromagnetic waves travel through a dielectric medium, its

amplitude and phase change with the distance in the medium. These changes are

governed by the complex propagation factor

γ d = αd + j βd (3.13)

where αd is the attenuation constant and βd is the phase constant, such that

βd = 2 π / λd (3.14)

λd being the wavelength of electromagnetic wave in the dielectric medium.

For rectangular wave guides, γ d for TEmn and TMmn modes is given by the relation

γ d = j √ω2 μ ε – {( ) )} (3.15)

Here ε and μ are the absolute permittivity and permeability of dielectric

medium respectively. Wavelength in free space (λ0) of the electromagnetic wave is

given by

λ0 = 2π / ω√μ0ε0 (3.16)

The absolute permittivity ε and the complex permittivity ε* of the dielectric

material are related as

ε = ε0ε* (3.17)

Since μ = μ0 (for non magnetic materials), substituting the equations (3.14)

and (3.15) in equation (3.13),we obtain

γ d = j √( )2 ε*

– {( ) } (3.18)

γ d = j ( ) √ ε* – {( ) ) } (3.19)

Cutoff wavelength (λc ) for rectangular waveguide in TEmn and TMmn modes

is given by


λc = (3.20)

Substituting (3.20) in equation (3.19) we obtain

γ d = j ( ) √ ε* – ( ) (3.21)

Since ε* = ε' - jε'' (3.22)

Substituting the value from equation (3.12) and (3.22) in equation (3.21) and

separating the real and imaginary parts we have

2 2 2

0 0 d

c d d

' 1

(3.23)

2

0 d

d d

" 2

(3.24)

Where βd = ( 2π / λ d),

Equations (3.23) and (3.24) may be used for determining dielectric constant

and dielectric loss factor for both low loss and high loss dielectric materials.

3.4 Methods Suitable for Investigation of The Dielectric

Properties of Food Materials at Microwave Frequencies

The dielectric properties of food materials at the microwave frequencies can

be determined by several methods using different microwave measuring sensors

(Kraszewski, 1980). According to Kraszewski (1980), measurement techniques can

be categorized as reflection or transmission types, using resonant or anti-resonant

systems, with open or closed structures for sensing of the properties of material

samples. Waveguide and coaxial line transmission measurements represent closed

structures while the free-space transmission measurements and open-ended coaxial-

line systems represent open-structure techniques, respectively. These techniques

include wave guide measurements, resistivity cell, lumped circuit, coaxial probe,

transmission line, resonant cavity, free space transmission, parallel plate capacitor,

cavity resonator, and time domain spectroscopy, each having unique advantages and


disadvantages (Icier and Baysal, 2004; Nyfors and Vainikainen, 1989). The use of

lumped circuit techniques is limited to low frequencies and high loss materials.

Open-ended coaxial probe method is one of the most commonly used method to

determine the dielectric properties of high loss liquid and semi-solid foods (Nelson

et al., 1994; Herve et al., 1998), and fresh fruits and vegetables (Nelson and Bartley,

2000). The measurement technique relevant for any specific application depend on

the nature of the dielectric material, physical state of the material (liquid or solid),

shape (thickness, flatness), desired range of frequency and the degree of accuracy

(Agilent,2005; Nelson 1999). The sample holder design also depends upon the

physical state of the dielectric materials to be measured. The measurement methods

that have been used to determine the dielectric properties of agri-food materials are

described here.

3.4.1. Cavity Perturbation Technique

The dielectric properties of homogeneous food materials can be measured by

cavity perturbation technique which is a preferred technique because of its simplicity,

easy data reduction, accuracy, and high temperature capability (Bengtsson and

Risman 1971; de Loor and Meijboom, 1966). This technique is well suited for

dielectric measurements of low loss materials and is also sensitive to low loss

tangents (Hewlett-Packard 1992; Kent and Kress-Rogers 1986). In the resonant

cavities, the mode of oscillation of the electromagnetic fields is the standard TM

(transverse magnetic) or TE (transverse electric) mode. This method of determination

of dielectric properties is based on the shift in resonant frequency and the change in

absorption characteristics of a tuned resonant cavity, due to insertion of a sample of

target material. The sample is placed completely inside the cavity through the centre

of the waveguide and the measurements are made by noting the changes in the

resonant frequency and the width of resonance maxima due to insertion of the

sample. The arrangement is shown in Fig. 3.4.


Fig. 3.4: Schematic representation of a resonant cavity method (R = reflected

power, T=transmitted power (adapted from Venkatesh and Raghvan,

2005)

The use of vector network analyzer (VNA) makes the measurement easy

since it automatically displays changes in frequency and width of resonant maxima

which can be used to compute the values of ε' and ε'' (Engelder and Buffler,1991).

The measurement details and the perturbation equations adapted for determination

of dielectric constant( ') and loss factor ( '') along with accuracy information for

network Analyzer were reported by Liao et al. (2001). With the help of the resonant

cavity systems, the dielectric measurements are limited to a single frequency.

Calibration is required to be done for each cavity but once the calibration curves are

obtained, calculations can be done rapidly. Preparation of sample is relatively easy

and measurements can be made on a large number of samples in a short span of

time. This method can be used at temperatures as high as 140°C and as low as

−20°C according to Ohlsson and Bengtsson (1975) and Risman and Bengtsson

(1971). Sharma and Prasad (2002) have used the cavity perturbation method to

measure the dielectric properties of garlic at selected levels of moisture content and

at 35°C to 75°C.

3.4.2 Transmission Line Technique

The transmission line is an ordinary method to determine the complex

permittivity for solid, particulate and liquid material. In transmission line methods, a

sample of the substance is put inside an enclosed transmission line energized by an


electromagnetic source and both reflection and transmission are measured. This

method is more accurate and sensitive as compared to coaxial probe method but it

has a narrower range of frequencies over which dielectric measurements can be

made. The measurements are restricted to the dominant mode and frequency range.

Preparation of the sample is difficult and time consuming since the material has to

be filled in the cross-section of the transmission line (coaxial or rectangular),

(Engelder and Buffler 1991; Hewlett-Packard 1992). Kraszewski (1996) reported

that when such methods are used for moisture content determination, the frequency

employed should be above 5 GHz to avoid the effect of ionic conductivity and

bound water relaxation. Dielectric properties of liquids and viscous-fluid type foods

can be measured by this method by using a sample holder connected through E

plane bend at the end of a transmission line. According to Nelson et al.(1974), the

dielectric properties can be easily and inexpensively obtained by this technique by

utilizing a slotted line and standing wave indicator. A more sophisticated version of

this technique uses a swept-frequency network analyzer, which measures the

impedance automatically as a function of frequency. This technique is cumbersome

when it is used for solid samples because the sample must be made into a slab or

annular geometry for being used in a waveguide or coaxial transmission line. At

2,450 MHz, the sample size is somewhat large, particularly for fats and oils

(Venkatesh and Raghavan, 2005).

3.4.3 Network Analyzers

A measurement of the reflection from and transmission through a material

along with knowledge of its physical dimensions provides the information to

characterize the permittivity and permeability of the material. Vector network

analyzers such as the PNA, PNA-L, ENA, and ENA-L make swept high frequency

stimulus-response measurements from 300 kHz to 110 GHz. A vector network

analyzer consists of a signal source, a receiver and a display as shown in Fig. 3.2.

The source generates a signal at a single frequency and make them incident on the

material under test. The receiver is tuned to that frequency to detect the reflected and

transmitted signals from the material. The measured response gives information

about that the magnitude and phase data at that frequency. The source is then


stepped to the next value of frequency and the measurement is repeated to display

the reflection and transmission measurement response as a function of frequency on

the screen of the detector. (Agilent, 2005)

Fig.: 3.5. Network analyzer system (Agilent,2005)

3.4.4 Open Ended Coaxial Probe Technique

The coaxial probe method is basically a improvised form of the transmission

line method. It uses a coaxial line, which has a special tip that senses the signal

reflected from the material. The tip of the probe is brought into contact with the

substance by touching the probe to a flat surface of a solid or by immersing it in a

liquid. This probe acts as the receiver of the signal reflected by the sample. The

reflected signal gives information about the dielectric properties of the substance by

measuring the phase and magnitude. The method is quite easy to use and it is

possible to measure the dielectric properties over a wide range of frequencies viz. 50

MHz to 50 GHz,500 MHz to 110 GHz by using different models of probe with

different types of Network Analyzer. It provides limited accuracy in the case of

materials with low values of absolute permittivity i.e. dielectric constant and loss

factor (Engelder and Buffler, 1991; Hewlett-Packard, 1992). According to Sheen

and Woodhead (1999); Hewlett-Packard (1992),this technique yields good results

for materials with loss factors greater than one when used for 915 and 2,450 MHz.

Typical open ended probes utilize 3.5 mm diameter coaxial line. For measurement of


solid samples, probes with flat flanges may be utilized (Hewlett-Packard,1992). An

open-ended coaxial probe technique was used to measure the dielectric properties in

thermal treatment for controlling insects in fruits at temperatures 20°C to 60°C over

a frequency range from 1MHz to 1,800 MHz (Wang et al., 2003). For liquid and

semi-solid materials including biological and food materials, open-ended coaxial-

line probes have been used for broadband permittivity measurements (Blackham and

Pollard,1997; Grant et al.,1989). A similar technique was used by Nelson et al.

(1994) and Ohlsson et al. (1974a) for permittivity measurements on fresh fruits and

vegetables. This technique is not free from errors because of the probability of air

gaps or air bubbles between the end of the coaxial probe and the sample. This method

has advantages that include ease of sample preparation and small size of sample. It

is non destructive and provides broadband information (Komarov et al.,2005).

3.4.5 Time Domain Spectroscopy /Reflectometry (TDR) Method

Time domain spectroscopy/reflectometry methods for determination of

dielectric properties were developed in the 1980s. The frequency range covered by

this technique from 10 MHz to 10 GHz. This method also employs the reflection

characteristic of the material under test to compute the dielectric properties. The

measurement is very rapid and accuracy is high with error within a few percent only

(Afsar et al., 1986). The material under test should be homogeneous and the size of

the sample used is very small .Although these methods are expensive, they can be

employed for advanced research on the interaction of the electromagnetic energy

with materials over a wide range of frequency (Mashimo et al., 1987; Ohlsson et al.,

1974b). The dielectric properties of honey-water mixture have been investigated by

Puranik et al. (1991) using this technique in the frequency range of 10 MHz to 10

GHz at 25°C. This technique has been used by Lahane et al. (2003) to study

dielectric relaxation of ayurvedic medicines with varying volume fractions in

ethanol.


3.4.6 Free Space Transmission Techniques

Fig. 3.6: Schematic of a free space transmission technique for measuring

reflection and transmission (Port 1 and 2 are connected to Vector

Network Analyzer) (Venkatesh and Raghvan, 2005)

In this method, sample is placed between a transmitting antenna and

receiving antenna and the attenuation and phase shift of the signal are measured. The

dielectric sample holders with rectangular cross-section were placed between the

horn antennas or similar radiating elements by Trabelsi et al. (1997). It is assumed

that a uniform plane wave is normally incident on the flat surface of a homogenous

material, and that the planar sample has infinite extent laterally (Venkatesh and

Raghavan,2005). This method does not require special sample preparation.

Kraszewski (1980) reported that this method can be easily implemented in industrial

applications for continuous monitoring and control, e.g., moisture content

determination and density measurement. Broadband and accurate measurement of

the permittivity can be achieved by this technique.

3.4.7 Micro Strip Transmission Line

Micro strips have long been used as microwave components, making it

suitable for use in dielectric permittivity measurement and show such properties

which overcome some of the limitations faced in other methods. It is well known

that the effective permittivity of the combination of the substrate and the material

above the line taken in form of a layer, i.e. for a micro strip transmission line with at

least thin width to height ratio is strongly dependent on the permittivity of the region

above the line (Venkatesh and Raghavan, 2005). This effect has been utilized in


implementing microwave circuits and to a lesser extent for investigation of dielectric

permittivity. Furthermore, the measurement of effective permittivity by this method

is relatively straightforward and well suited for testing of permittivity in industrial

equipments. Keam and Holmes (1995) suggested that permittivity of the material

can be derived by determining the effective permittivity of a micro strip line covered

with and without an unknown dielectric substance.

3.4.8 Six-Port Reflectometer (SPR) Using An Open-Ended Coaxial Probe

SPR can provide non-destructive broadband permittivity measurements with

accuracy comparable to commercial instruments as per review presented by Venkatesh

and Raghavan (2005). Non destructive broadband permittivity measurements, using

open-ended coaxial lines as impedance sensors, are of great interest in a wide variety

of biomedical applications (Ghannouchi and Bosisio 1989). The test device used in

this method is an open-ended coaxial test probe immersed in the test liquid, kept at a

constant temperature and data acquisition and reduction are fully automatic. This

effective transmission line method, used to represent the fringing fields in the test

medium, provides a good model to interpret microwave permittivity measurements

in dielectric liquids. Using such a model, the precision on relatively high-loss

dielectric liquid measurements is expected to be good. However, this method

involves a more complex mathematical procedure in order to translate the signal

characteristics into useful permittivity data (Venkatesh and Raghavan 2005).

3.5 Determination of ε' and ε'' Using Transmission Line Techniques

The transmission line methods of measurement of complex permittivity are

based on the use of a slotted line and a variable short circuit. Slotted line techniques

are well suited to complex permittivity measurements (except for very low loss

samples) at microwave frequencies. The accuracy of measurement depends to a

large extent on the accuracy with which the VSWR and the position of the voltage

minimum can be found.

3.5.1 Von Hippel’s Method:- This method is also known as shorted waveguide

method. This method essentially involves reflection of microwaves propagating

in TE10 mode, incident normally on a dielectric sample placed against a

perfectly reflecting surface.


When an electromagnetic wave traveling through medium 1 strikes normally

on medium 2, a part of it is reflected and the rest is either absorbed or gets

transmitted. A standing wave pattern is thus produced in medium 1. The transverse

electric field component in this partial reflection case is given by

Ey = 1 12

0 0. 1j x x

E e r e (3.25)

where γ1 is the propagation constant in medium 1.

Fig . 3.7: Standing waves in a waveguide (a) without dielectric (b) loaded with

dielectric of any length represented by ‘d’ (c) loaded with dielectric of

length λd/2


The reflection coefficient r0 is given by

ro = | r0 | e-2jψ

(3.26)

Where | r0 | is the magnitude and 2ψ is the phase angle of reflection

coefficient. The input impedance Z(0) at the boundary x = 0 is given by

Z(0) = 0

1

0

1

1

rZ

r (3.27)

where Z1 is the impedance of medium 1.

As attenuation in medium 1 is negligible, inverse voltage standing wave ratio

(IVSWR) in medium 1 may be written as

1 0

max min

0

1/

1

rE E

r (3.28)

Putting ro = e-2u

(3.29)

where u = θ + jψ (3.30)

We may write equation (3.27) as

00 1 1

0

1coth

1

rZ Z Z u

r (3.31)

and

2

min

2max

1tanh

1

eE

E e (3.32)

On expanding coth u in equation (3.31), we get

1

tanh cot0

1 tanh cot

jZ Z

j (3.33)

If x0 be the position of the first minimum (from the surface of the dielectric)

where the incident and reflected waves combine out of phase, i.e. at a phase

difference of π, we obtain

4 / 2o gx (3.34)


Thus the phase angle is obtained as

12 4

4

o

g

x (3.35)

Substituting the value of ψ from equation (3.33) in equation (3.31), we

obtain the expression for Z(0) as

1

2tan

(0)2

1 tan

o

g

o

g

xj

Z Zx

j

(3.36)

If medium (2) is terminated in a short circuit, the input impedance at the

interface x = 0 is given by

2 2tanho scZ Z d

(3.37)

Where Z2, γ2 and d are respectively the characteristic impedance,

propagation constant and the length of the medium (2). If the shorting metal plate is

placed at a distance λg /4 from medium 2 (Fig.3.6), it corresponds to an open-

circuited termination and the input impedance at the interface is

2 2cotho ocZ Z d (3.38)

For rectangular waveguides, the propagation constant (γ2) for TEmn and

TMmn modes is given by

Fig. 3.8: Standing waves in a waveguide in which short circuiting plunger is

placed at a distance λg / 4 for medium 2


1/22 2

2

2

m nj

a b (3.39)

Where ε and μ are the absolute permittivity and permeability of the dielectric

medium respectively. If εo and μo are the values of these quantities for free space,

then these can be related as

* o r (3.40)

and μ = μo (for non-magnetic materials) (3.41)

Where ε* is the complex permittivity of the dielectric medium given by

ε* = ' - j '' (3.42)

On using equations (3.40),(3.41) and (3.42), equation (3.39) can be expressed as

2 2 2

02 2 2

0

2*

2

m nj

a b (3.43)

or2

/ / / 0 .2 2

0

2

c

j j

(3.44)

where λo is the free space wavelength and λc is the cut-off wavelength

12 2 2

2 2

2c

m n

a b

(3.45)

If αd and βd are the attenuation constant and phase factor for the dielectric

medium, then

2 d dj

(3.46)

Separating real and imaginary parts of equation (3.44) and (3.46), we get

2 2 2

/ 12

o o d d

c d

(3.47 )

2

/ / /od d

d

(3.48)


Equations (3.47) & (3.48) may be used for determining dielectric constant

and loss factor for both low loss and high loss dielectric materials.

3.5.2 Yadav Gandhi Method

3.5.2.i Theory

This method is used for the samples in powder form. This method is a

combination of the method of Dube and Natrajan (1974) and the method employed

for polar liquids in dilute solutions of non – polar solvents, employing a slotted

waveguide and a short circuiting plunger used by Heston et al (1950). This method

has been successfully Srivastava and Vishwakarma(2004) for study of dielectric

properties of Bauxite, by Gupta and Jangid (2008) for dielectric properties of soil

and by Sharma et al.(2010) for determination of dielectric properties of wheat in

powder form.

When a rectangular waveguide filled with a dielectric material of complex

permittivity ε* is excited in TEmn or TMmn mode, the propagation constant γd of the

electromagnetic waves through the dielectric can be written as (Yadav and

Gandhi,1992)

1/ 22

0d d d

0 c

2j j * (3.49)

Here αd and βd are the attenuation and phase shift introduced by unit length

of the material, measured respectively in Nepers/m and radians/m; λ0 represents the

wavelength of electromagnetic waves in free space and λc is the cut off wavelength

of the waveguide.

Substituting ε* = ε ' – j ε" in Eq.(3.49) and separating real and imaginary

parts, we obtain

2 2 2

0 0 d

c d d

' 1 (3.50)

2

0 d

d d

" 2 (3.51)


The food grains are known to appreciably absorb electromagnetic radiation

at microwave frequencies, as evidenced from the fact that the domestic microwave

ovens operate at 2.45 GHz (Dibben, 2001). In the present investigations equations

(3.48) and (3.49) are used for finding out dielectric properties of the powder of

foodstuff. The main quantities to be measured experimentally are αd and βd for the

samples for which ε' and ε" values are to be determined.

Fig. 3.9: Experimental set up for measurement of dielectric properties of

powders by Yadav and Gandhi method

Symbolic meanings of numerals used in the Figure are as given below:

1 Power supply 9 Mica window

2 Microwave oscillator 10 Sample holder

3 Isolator 11 Movable plunger

4 Frequency meter 12 Water circulating jacket

5 E-H tuner 13 Screw gauge for plunger movement

6 Variable attenuator 14 Tuning probe

7 Slotted waveguide section 15 Crystal detector

8 E-band 16 Indicating meter


3.5.2.ii Measurement of λd

The experimental arrangement is shown schematically in Fig.3.6. Microwave

power obtained from a microwave source, viz. Klystron tube or Gunn Oscillator, is

allowed to form standing waves in the slotted waveguide section after being reflected

from the short circuiting plunger in the dielectric cell, which is initially kept at its

lowest position in the cell. The probe in the slotted waveguide section is accurately

adjusted at the node of the standing waves, as adjudged by the position of the minima

in the indicating meter. Now a small quantity of food grain powder is introduced in

the dielectric cell and the plunger is brought over it by moving the micrometer screw

till a proper contact is established. The height h of the powder in the dielectric cell is

determined from the difference of readings on the scale of micrometer screw taken

with and without food powder in the cell. The position of minima in the slotted

section shifts either towards the receiver or towards the generator on introducing the

powder in the cell. The shift is towards the receiver when h < (λd/4) and towards the

generator when (λd/4) < h < (λd/2). If h1 and h2 are two heights of the powder

column in the cell for which equal shift of minima position is obtained towards the

receiver and the generator respectively, then

1

d g

2 2h x (3.52)

2

d g

2 2h x (3.53)

where λg is the guide wavelength.

Combining equations (4) and (5) we obtain

1 2

d

2(h h ) (3.54)

or

d 1 22(h h ) (3.55)


Alternatively, we may go on adding slowly the powder in the dielectric cell

till for a height h of the powder in the cell, the position of minima in the slotted

section is the same as for the empty cell. For this position

dh2

Or d 2h (3.56)

Eq. (3.56 ) permits us to directly determine the value of λd..

3.5.2.iii Measurement of αd

Let Ei and Er be the amplitudes of the incident and reflected fields respectively

forming standing waves in the slotted guide carrying the probe. Assuming no loss in

reflection, Er = Ei with no sample in the sample holder, if the movable probe is

located at maximum position and the indicating meter gives a deflection of x1 units,

we may write

E i + E r α √x1 (3.57)

On introducing the sample of length L in the sample holder and locating the

movable probe at the resulting maximum position, the output shown by the

indicating meter will change to x2 units due to partial absorption of the e.m. waves.

The absorption takes place twice, once when the incident wave travels through the

sample and again when the reflected wave travels through it. Therefore, Er becomes

Er = Ei e-2αL

(3.58)

Again at the maximum, we have

Ei + E r = (Ei + Ei e-2αL

) α √x2 (3.59)

From equations (3.58 ) and (3.59 )

1

d

2 1

x2.303log

2h ' 2 x x (3.60)

For measuring αd we start with the empty cell, the plunger being kept at the

bottom of the cell. The probe is located at one of the maximas, i.e., at the position of

a voltage antinode in the waveguide slotted section, and reading x1 of the indicating


meter is noted. The powder (flour of the food stuff in the present case) is now added

slowly in the dielectric cell and position of the maxima in the slotted section is noted

every time from the indicating meter. The height of the powder column in the

dielectric cell (h') is accurately adjusted so that the probe position locating the

maxima in the slotted section is again the same as with the empty cell. The deflection

x2 of the indicating meter in this state, for such height h' of the powder column, is

noted. In this experiment the electromagnetic waves travel twice through the powder

column in the cell before they form stationary waves in the slotted waveguide

section, after being reflected from the plunger of the dielectric cell. For obtaining

appreciable absorption of the wave, height of the powder column in the cell is taken

equivalent to several λd. The value of the αd is then calculated using equation (3.60) .

3.5.3 Two Point Method Using Solid Dielectric Cell

A most widely used and simple microwave measurement technique to measure

the complex permittivity of solid materials, which could be shaped in the size of the

waveguide for preparation of samples, is the two point method which involves the

solution of a transcendental equation. The input impedance of a short circuited

waveguide is measured with and without the sample placed in the waveguide, shift

in minima position is noted for the sample and a transcendental equation is solved to

obtain dielectric properties of the material. A proper solution out of many is chosen

on the basis of approximate value of dielectric constant of the material. If the

approximate dielectric constant is not known, then two such measurements are

carried out with samples of different lengths.

Two point method (Sucher and Fox, 1963; Behari, 2005) is a technique

involving measurement of reflection coefficient of a solid material in a wave guide,

backed by a short circuiting conducting plate. This method is suitable for low and

medium loss dielectrics and can be adopted for measurement of dielectric properties

of food stuff in powder form.

3.5.3.i Theory

Figure (3.7 a) shows an empty short-circuited waveguide dielectric cell with

a probe located at a voltage minimum DR. Figure (3.7 b) shows the same waveguide,


containing a sample of length lε with the probe located at a new voltage minimum D.

The sample is kept adjacent to the short circuit. At the open boundary of the sample

as shown in Fig. 3.7 (b), impedance equation can be written as

Z0 tan βl = −Zε tan βε lε (3.61)

(a) (b)

Fig. 3.10: (a) Wave guide with a short circuit ;(b) wave guide loaded with a

sample and short circuit

Similarly in figure (3.7a), looking toward the left, one can write

Z0 tan β (lR + lε) = 0 (3.62)

Now, consider

tan β (DR – D + lε ) = tan β [(lR + lε) – (l + lε)+ lε ]

= tan β[(lR + lε) –l ]

=–

= - tan βl (3.63)

Since, tan β (lR + lε) = 0 from equation (3.60)

From equation (3.59), tan βl = [- tan βεlε (3.64)

tan β (DR – D + lε ) = - [- tan βεlε (3.65)

But, = which gives

Zε


tan β (DR – D + lε ) = tan βεlε (3.66)

Dividing both sides of this equation by βεlε, we get

Rtan (D D l tan l

l l (3.67)

In equation (3.67) all the quantities on the left hand side are measurable,

where as the right hand side term is of the form tan Z /Z,with Z = βε lε, so that once

the measurements have been carried out, the complex number, Z = βε l ε, can be

found by solving the transcendental equation, and from it, βε can be determined.

There exist infinite number of solutions of the transcendental equation for εr. To

obtain proper solution, the measurements are carried out on two samples of different

sample length lε and lε'. A solution common to the two sets of solutions will be the

proper solution for εr . The solution is given by the “intersection point” of the two

curves shown in the Fig. 3.8.

Fig. 3.11: Two sets of solutions for two samples of different lengths, point of

intersection represents the proper solution

It should be noted that the accuracy of the experimental results of complex

permittivity y using this method depends to a large extent on the smoothness of the

sample, the fitting of the sample in the waveguide, the care which should be taken to

ensure that its surfaces are made flat and properly shaped as „rectangular‟ fitting

with the dimensions of the waveguide, the accuracy of measurement of length lε of


the sample, the positions of minima DR and D and the accuracy in the measurement

of VSWR.

3.5.3.ii Experimental Set Up for Estimation of Complex Permittivity of Powders

Employing Two Point Method

For using this method for powders, the waveguide is bent through 90° by

means of a E-plane bend and terminated by a specially designed dielectric cell in

which powder sample is filled up. In this method, the experimental set – up for

measurement of dielectric properties of powders is shown in figure 3.9, where the

details of components used in the microwave bench are self explanatory. First with

no sample in the dielectric cell, the position of the first minimum DR in the slotted

section is noted. Now the powder sample is filled up in the dielectric cell and

compressed by using the hydraulic press and applying pressure which the dielectric

cell can withstand. The height of the compressed sample in the cell is noted, say it is

lε. Then the position of the first minimum D on the slotted line and coressponding

VSWR are measured. The VSWR is measured by a micrometer or VSWR meter.

For the measurement of VSWR using micrometer no amplitude modulation is

applied to the microwave signal but when the VSWR meter is connected, the

amplitude modulation is applied to the microwave signal, by using internal

modulation in Klystron power supply or by using a pin diode if a Gunn diode is used

as microwave source. The accuracy of measurements of dielectric constant of

powders by this method has been estimated to be of the order of 5% whereas the

accuracy for the measurement of dielectric loss is within 10%.

Fig. 3.12: Experimental setup for determination of dielectric properties of

powders by two point method


The transcendental equation obtained by impedance matching at the

boundary of flat surface of powder and air can be written as

Rtan (D D l tan l

l l (3.68)

Where β = ( 2π / λ g), λ g being the waveguide wavelength;

and βε = ( 2π / λ0) { εr μr – (λ0 / λ c)2}

1/2, λ0 being free space wavelength and λ c

is the cut off wavelength of the waveguide.

The propagation constant β in powder is calculated, by using

β = ( 2π / λ g) (3.69)

where, λg =2 x (distance between successive minima with empty short

circuited waveguide sample holder)

The phase difference in the waves traveling in the guide with and without

dielectric is given by

θ = 2 β (∆ x – lε) (3.70)

where ∆ x is the shift in minima position

We determine voltage standing wave ratio for the load (food powder in this

case) and compute magnitude of the reflection coefficient (│Г│ ) by employing the

following relation:

│Г│ = (S- 1) / (S+1) (3.71)

where S is the VSWR for the sample.

In two point method, the complex dielectric constant is given by

j

j

1 e1 tan XC

j l 1 e X (3.72)

The transcendental equation provides several solutions for X θ, which can

be found by employing graphs and tables provided for solution of such equations by

Hippel (1954) or alternatively the problem may be solved by using a mathematical

tool like MATLAB. The experiment is repeated with a different length ( lε') of the


sample compressed to the same pressure as used in the first case. The common root

of solutions obtained for the two cases, on using samples of different lengths, is

chosen for evaluation of the admittance. Alternatively we may perform the experiment

for a given sample at two different frequencies to obtain the correct root X θ.

The admittance (Yε ) of the material of the sample is given by

XY 2( 90 ) G jS

l (3.73)

where Gε and Sε are respectively the normalized conductance and normalized

susceptance of the sample.

The values of Gε and Sε are obtained by separating Equation (3.71) in to real

and imaginary parts, from which the values of ε' and ε'' can be calculated in the

following form:

2

g

2

g

G ( / 2a)'

1 ( / 2a) (3.74)

2

g

S''

1 ( / 2a) (3.75)

A computer program in Matlab may be used to solve the transcendental

equation and obtain the values of dielectric constant (ε') and loss factor (ε''), by

using equations (3.74) and (3.75).

3.6 Dielectric Mixture Equations

Dielectric mixture equations can be used to estimate the dielectric properties

of the solid material from the properties of an air-particle mixture, made up of air

and the pulverized particles of the solid. To use such equations, one needs to know

the complex permittivity (ε*) of the pulverized sample at its bulk density, i.e., the

air- particle mixture density (ρ). If the density of solid material is ρ2, the fractional

part of the total volume of the air-particle mixture occupied by the particles (i.e., the

volume fraction occupied by the solid in the mixture), v2 is then given by ρ / ρ2.

In the present work two component dielectric mixture equations are proposed

to be used, in which ε represents the complex permittivity of the mixture, ε1 is the


complex permittivity of the medium (air in the present case, for which ε1 = 1 _

j0), in

which particles of the solid material having complex permittivity ε2 are dispersed, v1

and v2 being the volume fractions of the medium (i.e., the air in this case) and the

solid material (i.e. the bulk solid material of food powder) respectively, such that v1

+ v2 = 1.

The formulation of the dielectric mixture equations to be used in the present

work are as given below (Nelson,1991):

i) Complex refractive index mixture equation:

1/ 2 1/ 2 1/ 2

1 1 2 2( ) v ( ) v ( ) (3.76)

ii) Landau and Lifshitz, Looyenga equation:

1/3 1/3 1/3

1 1 2 2( ) v ( ) v ( ) (3.77)

iii) Böttcher‟s equation :

1 2 1

2

2

v3 2

(3.78)

iv) Bruggeman – Hanai equation:

1/3

2 12

1 2

1 v (3.79)

v) Rayleigh‟s equation:

1 2 1

2

1 1 2

v2 2

(3.80)

3.7 Estimation of Nutrients

The basic aim of estimation is to evaluate the nutrients in the food grains by

using the standard methods available for estimation of nutrients, viz., moisture,

protein, fat, ash, crude fiber and carbohydrate. The estimation of nutrients was carried


out using standard reagents and glasswares. All the analytical instruments used were

standardized and calibrated before use, as per their respective specified methods.

The nutrients analyzed, for the present study, in food grains are moisture by

oven drying, protein by Micro Kjheldal Method, fats by ether extraction method, ash

and crude fiber by acid alkali method. The carbohydrate is estimated by the

difference method. Proximate analysis for estimation of different nutrients is done as

per procedure given below:

3.8.1.i. Moisture (AOAC,2005)

Procedure – About 5 g of the prepared sample is weighed accurately in a tarred

aluminium dish with a cover, having a diameter of at least 50 mm and a depth of

about 40 mm. The dish is shaken until the content is evenly distributed. With cover

removed, the dish is placed in an air oven maintained at102 2°C and heated for

about 3-4 hours . After cooling it to the room temperature, it is weighed.The process

of heating, cooling and weighing is repeated until the difference in weight between

two successive weighing is less than one milligram.

Calculation –

Moisture, percent by mass = 1 2

1

100( )W W

W W

where,

W1 = weight in g of the dish with the material before drying,

W2 = weight in g of the dish with the material after drying, and

W = weight in gram of empty dish

3.8.1.ii Crude Protein (AOAC,2005)

Principle – The percentage of crude protein is ascertained by multiplying the

percentage of nitrogen other than ammoniacal nitrogen by a factor. The factor used

in the present case is 6.25

Apparatus – Kjeldahl flask distillation assembly: The assembly consists of a

round bottom flask of a 1000 ml capacity fitted with a rubber stopper through which


passes one end of the connect in bulb tube. The other end of the bulb tube is

connected to the condenser, which is attached by means of a rubber tube to a dip

tube, which dips into a known quantity of the solution of standard sulphuric acid and

boric acid, contained in a conical flask of 500 ml capacity, to which 3 to 4 drops of

methyl red indicator solution are added.

Reagents-

1. Potassium Sulphate or Anhydrous Sodium Sulphate

2. Copper Sulphate

3. Concentrated Sulphuric Acid – sp gr. 1.84( IS:266-1961)

4. Sodium Hydroxide Solution – About 450 g of sodium hydroxide is dissolved

in 1000 ml of water.

5. Standard Sulphuric Acid – 0.1 N

6. Standard Sodium Hydroxide Solution – 0.1 N

7. Methyl Red Indicator Solution – 1 g of methyl red is dissolved in 200 ml of

rectified spirit (95 percent by volume)

8. 60 g of boric acid is dissolved in 2 litre of hot water; cooled to room

temperature and allow maturing for 3 days before decanting the clear liquid.

9. Magnesium Oxide – carbonate free freshly ignited.

Procedure

Total Nitrogen - About 2 g of the prepared sample is accurately weighed and

carefully transferred to the Kjeldhal flask. About 10 g of potassium sulphate or

anhydrous sodium sulphate, about 0.5 g of copper sulphate and 25 ml or more, if

necessary, of concentrated sulphuric acid is added. The flask is placed in an inclined

position, and heated to a temperature below the boiling point of the acid, until

frothing ceases. Heating is continued until the acid boils vigorously and digested for

a time after the mixture is clear or until oxidation is completed ( about 2 hours). The

contents of the flask are cooled and transferred quantitatively to the round bottom

flask with water, the quantity of water used being about 200 ml. Few pieces of

pumice stone are added to prevent bumping. Sodium hydroxide solution is then

added carefully in quantity which is sufficient to make the solution alkaline,by the

side of the flask so that it does not mix at once with the acid solution but forms a


layer below the acid layer. The apparatus is assembled taking care that the tip of the

dip – tube extends below the surface of the standard sulphuric acid solution in the

receiver. The contents of the standard sulphuric acid solution is then thoroughly

mixed. Titration with standard sodium hydroxide solution is done and a blank

determination is carried out using all reagents in the same quantities but without the

material to be tested.

Alternatively, the ammonia evolved by distillation is absorbed in boric

acid.The digestion is carried out as prescribed earlier. The contents of the digestion

flask are transferred completely through the separating funnel. The separating funnel

is rinsed with water. The total volume of the liquid in the distillation flask should not

exceed half the capacity of flask otherwise frothing may occur. Excess of sodium

hydroxide solution is then added to make the solution alkaline. The round- bottom

flask is then connected immediately to steam trap and condenser. The condenser is

arranged to dip the dip-tube in 50 ml of boric acid which is kept cool in the conical

flask. 2 or 3 drops of the mixed indicator are added to the flask. About one third of

total volume of the solution is distilled in the flask. The distillation assembly is

cooled and dismantled. The tip of the condenser and the dip – tube are rinsed with

water. The washings are collected in the receiver. The ammonia present in the

distillate is titrated with sulphuric acid until the grass – green colour changes to steel

grey, an addition of one drop of acid giving the purple colour.

Calculation –

Total nitrogen ( on moisture- free basis) = –

Percent by mass

where

B = Volume in ml of the standard sodium hydroxide solution used to

neutralize the acid in blank determination.

A = Volume in ml of the standard sodium hydroxide solution used to

neutralize the excess acid in the test with the material.

N = normality of the standard sodium hydroxide solution.

m = mass in g of the material for the test.


M = moisture percentage.

When boric acid has been used for absorption, calculation of total nitrogen

are given below:

Total nitrogen (on moisture - free basis) =

percent by mass

where,

V = volume in ml of standard sulphuric acid used in titration.

N = normality of the standard sulphuric acid.

m = mass in g of the material taken for test and

M = moisture percentage.

3.8.1.iii.Crude Fat (AOAC,2005)

Reagents-

Petroleum ether of boiling range 40 °C to 60 °C

Hexane, food grade-conforming to IS : 3470-1966.

Procedure – About 2.5 g of the dried material is taken and weighed accurately as

described earlier and then it is extracted extracted with petroleum ether or hexane,

food grade, in a Soxhlet or other suitable extractor. The extraction period may vary

from 4 hours to 6 hours. The extract is dried on a steam – bath for 30 minutes,

cooled in a dessicator and weighed. The process of alternate drying and weighing is

repeated at intervals of 30 minutes until the difference between two successive

weighing is less than one mg. The lowest mass of the sample is noted.

Calculation –

Crude fat (on moisture free basis), Percent by mass = –

Where,

M1 = mass in g of the extraction flask with dried extract

M2 = mass in g of the extraction flask, and

M = mass in g of the dried sample taken for the test.


3.8.1.iv Crude Fiber (AOAC,2005)

Reagents –

Sulphuric acid – 0.255 N [1.25 per cent (m/v)], accurately prepared.

Sodium hydroxide solution – 0.313 N [1.25 percent (m/v)], accurately prepared.

Procedure – About 2 g of the dried material is taken and weighed accurately and

the fat is extracted for about 8 hours with petroleum ether or hexane, food grade,

using a Soxhlet or other suitable extractor or the residue from the crude fat

determination. The fat free dry residue is transferred to a one liter conical flask.

200 ml of dilute sulphuric acid is taken in another flask and was heated to

boil. The whole of the boiled acid is transferred to the flask containing the fat free

material and the flask is immediately connected with a reflux water condenser and

heated, so that the contents of the flask begin to boil within one minute. The flask is

rotated frequently, not permitting the material to be deposited on the sides of the

flask, out of contact with the acid. Boiling is continued for 30 minutes and then the

flask is removed and the content of the flask is filtered through fine linen (about 18

threads in the centimeter) held in a funnel and washed with boiling water until the

washings are no longer acidic to litmus. Now the filterate is mixed with some

quantity of boiled sodium hydroxide solution under a reflux condenser and boiled

again for 30 minutes. The flask is then removed and its contents are immediately

filtered through the filter cloth. The residue is thoroughly washed with boiled water

and transferred to a Gooch crucible prepared with a thin but compact layer of ignited

asbestos. The residue is washed thoroughly first with hot water and then with about

15 ml of 95 % (by volume) ethyl alcohol. The Gooch crucible and contents are dried

at 105±1ºC in the air oven till it attains constant mass. It is then cooled and weighed.

The contents of the Gooch crucible is incinerated at 600±20 ºC in a muffle furnace

until all the carbonaceous matter is burnt. The Gooch crucible containing the ash is

cooled in a dessicator and weighed.

Calculation –

Crude fiber (on moisture free basis), Percent by mass = –

where,

M1 = mass in g of Gooch crucible and contents before ashing


M2 = mass in g of Gooch crucible containing asbestos and ash, and

m = mass in g of the dried material taken for the test

When the residue from fat determination is used.

Crude fiber (on moisture free basis) = (M1 – M2) (100-f ) percent by mass

Where,

M1 = mass in g of Gooch crucible and contents before ashing

M2 = mass in g of Gooch crucible containing asbestos and ash

f = crude fat ( on moisture free basis),percent by mass, and

m = mass in g of the fat free material taken for the test.

3.8.1.iv Ash (AOAC, 2005)

Procedure - About 2 g of the dried material is taken and weighed accurately in a

tarred porcelain, silica or platinum dish. It is then ignited with the flame of a Meker

burner for about one hour. The ignition is completed by keeping it in a muffle

furnace at 550± 20 ºC until grey ash results. It is then cooled in a dessicator and

weighed. The dish is ignited again in the muffle furnace for 30 minutes, cooled and

weighed. This process is repeated until difference in mass between two successive

weighings is less than 1 mg. The lowest mass of the dish and its contents is noted.

Calculation -

Total ash (on moisture free basis) percent by mass = –

M2 = the lowest mass in g of the dish with the ash.

M = mass in g of the dish, and

M1= mass in g of the dish with the dried material taken for the test.

3.8.1.v. Carbohydrate (AOAC 2005)

Principle – The carbohydrate estimation method used in the present study is based

on the principle that total carbohydrates can be estimated by the difference between

total weight of the sample and sum of the estimated values of moisture, protein, fat,

ash and crude fiber present in the sample.


Procedure – A sum of values (g /100g) of moisture, protein, fat, ash and crude fiber

is subtracted from 100 g to get the carbohydrate content (g / 100g) of sample.

Formula –

Carbohydrate (g /100g) = 100 - [Moisture + Protein + Fat + Ash + Fiber] (g

/100g of sample)

3.8.2. Correlation Between Dielectric Properties and Food Nutrients

After practical determination of the dielectric properties and nutrients of the

food samples, attempts are made to establish a correlation between the two types of

properties by employing the SPSS software and linear and curvilinear regression

techniques.

Documents

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