Millimeter Wave Sensor: An OverviewMillimeter Wave Sensor: An Overview

SURYA K PATHAKINSTITUTE FOR PLASMA RESEARCH

BHAT, Gandhinagar – 382428 , GUJARAT, INDIAsurya@ipr.res.in

Interaction of Electromagnetic Waves with Material MediumInteraction of Electromagnetic Waves with Material Medium

Interaction produces following Physical Phenomenon which are basis of Material characterization •Reflection•Refraction•Attenuation•Scattering •Diffraction

Techniques for Material measurements

Time delay measurementsPhase measurementsInverse Scattering methods

Interferometry and Reflectometry systemsInterferometry and Reflectometry systems

Measurement MirrorDisplacement

Light Source

Beam Splitter

Reference Mirror

Screen/ Detector

Interferometry and Reflectometry is a scientific technique, to interfere or correlate two, or more than two, signals to from a physically observable measure, from which any useful information can be inferred.

- Fringe pattern in optical Interferometry- Electrical signals of power/ voltage in Radio measurement

Plasma or Dielectric

Quadrature Mixer

Frequency Source

Power Divider

Measurement Path

Antenna

Reference Path

I Q

Quadrature Mixer

Frequency Source

Power Divider

Measurement Path

Reference Path

I Q

Circulator Antenna

Plasma or Dielectric

Interferometer system Reflectometer system

Michelson Interferometer

Interaction of Electromagnetic wave dielectrics (1)Interaction of Electromagnetic wave dielectrics (1)

The electromagnetic wave incident normally on the dielectric and traveling in z-direction is given by:

(1)

Where is the propagation constant. On applying boundary conditions across the individual boundaries. Following expressions are obtained in terms of reflected Ei and transmitted Er wave:

(2)

Where 0, and T0 are reflection and transmission coefficient.Z is the impedance of the mediumSubscript corresponds to respective medium

( )0( , ) j t z

iE z t E e

Dielectric

0 d

2

2

1

1

0

0

Ei

Er

Etz

y

1 1

1 1

0 1 1

0 10 1

0 1

1 1 0 0

011 0

1 2

(1 ) (1 )

(1 ) (1 )

( )

( )

o

d d

d d

E E

E E

Z Z

E e e T E

EEe e T

Z Z

Interaction of Electromagnetic wave dielectrics (2)Interaction of Electromagnetic wave dielectrics (2)

Solving above equations we can calculate the components of reflected and transmitted wave:

The reflected wave is obtained by

(3)

where,

And the transmitted wave is expressed by

(4)where,

Wave equations (3) and (4) constructs the measurement path wave in an interferometry

0 0

1 1 21 1

0 0 10

1 1 21 1

0 0 1

1 cosh( ) sinh( )

.

1 cosh( ) sinh( )

rE E

Z Z Zd d

Z Z Z

Z Z Zd d

Z Z Z

0 0

1

0 010 1 1

2 2 1

11 cosh( ) sinh( )

2

tE T E

Z ZZT d d

Z Z Z

Determination of Relative Dielectric constant and Thickness (1)Determination of Relative Dielectric constant and Thickness (1)

Complex Permittivity or Dielectric Constant

The relative permittivity or dielectric constant (r) as well as relative permeability (r) characterize the relationship between electromagnetic waves and material properties. For a lossy material, the relative dielectric constant can be expressed as:

(5)

where r is the relative dielectric constant, 0 is the dielectric constant of free space, is the conductivity of the material, and is angular frequency of EM waves. Above equation can be represented in terms of loss tangent (which is ratio of imaginary to real component of the complex dielectric constant) :

(6)

Reflection Measurement

In reflection measurement method, the dielectric is typically conductor-backed to increase the reflected power. In this case, Z2 is equal to zero and reflection coefficient in equation (3) is:

(7)

0 0

r r j

(1 tan )r r j

1 1

1 1

0 1 0 10

0 1 0 1

( ) ( )

( ) ( )

d d

d d

e e

e e

Determination of Relative Dielectric constant and Thickness (2)Determination of Relative Dielectric constant and Thickness (2)

Impedance Z1 in terms of free space impedance is given by:

(8)

Transmission Measurement

In this method, the dielectric is located in free space between two antennas. Therefore, Z2 = Z0 and 2 = 0 are satisfied, and transmission coefficient is given as:

(9)

1 1

1 00 2 2

0 1 0 1

4

( ) ( )d dT

e e

0 01 0

11r

ZZ Z

Fig: Phase of reflection coefficient depending on (a) relative dielectric constant(b) dielectric thickness

Determination of Relative Dielectric constant and Thickness (3)Determination of Relative Dielectric constant and Thickness (3)

Determination of Relative Dielectric constant and Thickness (4)Determination of Relative Dielectric constant and Thickness (4)

Fig: Phase of transmission coefficient depending on (a) relative dielectricconstant (b) dielectric thickness.

Displacement MeasurementDisplacement Measurement

The phase difference between the reference and measured paths, produced by displacement of the target location, is determined from in-phase (I) and quadrature (Q):

Where, (t) represents phase difference and can be determined by for an ideal quadrature mixer:

Practically, quadrature mixers, however, have a nonlinear phase response due to their phase and amplitude imbalances as well as DC offset. A more realistic from of the phase including the nonlinearity effect can be expressed as:

( ) ( )

( ) ( )I I

Q Q

v t A sin t

v t A cos t

1 ( )( ) tan

( )I Q

Q I

v t At

v t A

1 ( )1( ) tan tan

cos ( ) ( )I OSI

Q OSQ

v t VAt

A A v t V

Displacement MeasurementDisplacement Measurement

The detected phase is generated by the time delay, , due to round trip-trip traveling of electromagnetic wave for the distance between antenna aperture and target. Therefore, it has relationship with range, r as:

where, f0 and c are operating frequency and speed in free space of electromagnetic waves. The range as a function of time variable can be defined as :

Range variation is produced by changes in target location and can be expressed in the time domain as:

where, T is the sampling interval. The displacement for the entire target measurement sequence can be described as a summation of consecutive range variations:

00

4( ) 2

f rf

c

0

( )( )

4

tr t

( ) [ ] [( 1) ], 1, 2,3,.....r nT r nT r n T n

1

( ) ( ), 1, 2,3,.......,k

n

d nT r nT n k

Fig: Measurement set-up for water level gauging

Heterodyne Interferometric sensor. The target sits either on the XYZ axis (for displacement sensing) or on the conveyor (for velocity measurement). The Reference channel is not needed for velocity measurement.* Courtesy: Kim and Nguyen, IEEE Trans on Microwave Theory and Techniques, vol.52, p2503, Nov 2004

An Interferometric Sensor* An Interferometric Sensor*

The block diagram of a Ka-band heterodyne measuring setup for lossy dielectric materials.

ConclusionsConclusions

Reflectometry is a non destructive sensorsWith little modifications it is used in different applications