Volume
Resistivity
Please
click
on the
section
below
to view
your
area
of interest:
|
|
|
|
|
|
Volume
Resistivity:
The
volume resistivity
of a material is
a parameter that
indicates the electrical
resistance of a
piece of the material.
It is defined in
a manner that allows
the calculation
of the resistance
in Ohms of a piece
of material when
the physical dimensions
are known.
Resistivity is specified
in units of resistance
(ohms) multiplied by units
of length (usually cm).
Resistivity is then expressed
in units of ohm-cm.(  -cm).
Resistivity is usually
represented by the Greek
Letter  ,
(rho).
At first, the units of
resistivity (ohm-cm) may
not seem convenient. To
develop the concept and
improve understanding,
it is essential to relate
the material parameter
resistivity with the actual
resistance in ohms of a
piece of material. The
relationship between them
is:
(Equation #1)
where: is
material resistivity
in ohm-cm,
T is the thickness of the
conductor (chip) (cm)
L is the length of the
conductor (chip) (cm)
W is the width of the conductor
(chip) (cm)
Resistance
is proportional
to thickness (length
of current path)
because for a uniform
cross-sectional
area, increasing
the thickness of
a conductor is
similar to combining
resistors in series.
Likewise, the resistance
is inversely proportional
to the cross-sectional
area as increasing
the cross-sectional
area is similar
to combining resistors
in parallel, which
reduces the overall
resistance.
Resistivity is essentially
an engineering parameter
and it is an extremely
important one. It is useful
because when it is known
for a particular material,
the resistance of a piece
of that material can be
calculated if the dimensions
of the piece are known
also. These calculations
are demonstrated in a numerical
example, but first, the
concept of volume resistivity
of materials is developed
further.
The resistivity of thermistor
material is treated as
a constant for standard
materials. The resistivity
varies with temperature,
so it is specified at particular
temperatures (usually 25°C).
Thermistor manufacturers
produce many different
thermistor materials to
cover an extensive range
of resistance values (100
ohms to 1 Mega-ohm) for
chips of various sizes.
A simple representation
of the manufacturing process
for BetaTHERM thermistors
is shown on the inside
of the front cover of this
catalog.
When the metallization
stage is complete, the
thermistor material is
in the form of a ceramic
sheet or wafer of typical
dimensions 50mm x 50mm
x 0.25mm which is metallized
on both sides. The resistivity
of a piece of the material
can be calculated by dicing
a chip of regular shape
(square or rectangular
faces), measuring the resistance
of that chip at the relevant
temperature (usually 25°C)
and applying the definition
of resistivity as follows:
Volume resistivity
formula:
(Equation
#2)
Where: =
volume resistivity (ohm-cm)
L = length of chip element
(cm)
W = width of chip element
(cm)
T = thickness of chip element
(cm)
R25 = measured resistance
@ 25°C(ohms)
A typical calculation based
on resistivity is illustrated
in the following example.
In such calculations it
is important to observe
consistency of measurement
units and dimensions especially
where some dimensions are
given in inches and others
are in centimetres. For
instance in the thermistor
industry it is common to
express resistivity in
units of ohm-cm, but to
give chip dimensions in
inches.
Example: Calculate
the volume resistivity
for BetaTHERM Curve 3
Material with dimensions
of 0.04" x 0.04" and
thickness 0.01" with
measured resistance value
8120 ohms at 25°C.
When resistivity is specified
in ohm-cm and the other
dimensions are in inches
then the equation can be
written as :
(2.54 is the conversion
factor to relate cm and
inches)
The concept of material
resistivity is extremely
important in the selection
of thermistor material
in relation to chip size
in applications. The equations
indicate that for material
of the same resistivity,
required resistance valuescan
be achieved with different
chip sizes, within the
constraints of the equations
relating resistance and
resistivity. This provides
flexibility for developing
custom solutions in relation
to chip sizes in applications.
Material resistivities
of BetaTHERM thermistors
at 25 °C are listed
in Table #1 below. The
use of resistivity values
in calculating the resistance
of thermistor elements
is of major importance
in the thermistor industry.
These values have been
determined by accurate
measurements.
BetaTHERM Standard
Material Resistivities
at 25°C.
| Material
Curve |
Resistivity
(ohm-cm) |
| 1 |
65 |
| 2 |
50 |
| 3 |
3300 |
| 4 |
3500 |
| 5 |
5500 |
| 6 |
18000 |
| 7LoRo |
300 |
| 7HiRo |
3000 |
| 9 |
325000 |
| Table
# 1: |
|
Since
a thermistor is
a component whose
resistance varies
with temperature,
the variation of
resistivity with
temperature is
a critical material
property. This
relationship is
indicated graphically
below for Betatherm
Material #3 over
a limited temperature
range (-40°C
to +40 °C).
|
