VOLTAGE COEFFICIENT OF RESISTANCE
Application Note #1
The purpose of this application note is to describe some important
positive voltage coefficient. This voltage dependent change of
resistance happens instantaneously and can be observed to occur in
less than 1 nanosecond. If the period of voltage application is too
long, the temperature may rise and cause large resistance changes
that can mask voltage coefficient effects.
considerations in high voltage pulse measurements with resistors
as dividing elements. The term "Voltage Coefficient of
Resistance" has been around for a long timeP1P; but is seldom
used or well understood. As high voltage pulse measurements
improve, and higher accuracy becomes available, voltage
coefficient errors that could once be ignored now must be
considered.
Short pulses applied to many resistors will show voltage
coefficient effects during the time the voltage is applied. Although
a resistor may not burn out during extensive pulsing, or have a
permanent resistance change, it can have significant voltage
coefficient changes during the time of the pulse.
It is well known that the resistance increases with temperature
rise of nearly all resistors, including the commonly encountered
carbon composition resistor. The temperature coefficient of
resistance (of a resistor) may be expressed as the ratio of the
resistance change to the temperature rise. Such a temperature
coefficient classification is useful if the resistance changes
uniformly with temperature rise and fall.
The voltage coefficient varies with different resistive
materials, and seems to be greatest for materials that are composed
of a granular conglomeration of resistive material held together
with an insulating binder. Carbon composition and cermet film
resistors use these types of resistive materials.
Resistors undergo temperature variations not only due to
changes in ambient temperature, but also due to dissipation of
electrical energy when current is passed through them. It is
desirable in measurements using resistors, that their temperature
coefficient be small to minimize errors. One can see, for example,
that when a measurement apparatus involving resistors is
calibrated at low signal levels, the calibration may be invalid at
higher signal levels if the resistance values change.
Nonlinear resistivity can easily be displayed by placing a
small amount of finely powdered conducting or semiconducting
material between two skewed small diameter wires. Graphite,
shaved from a pencil or from a carbon composition resistor
displays this effect nicely. The effect can be observed using as
little as 1 volt between the two wires. The nonlinear voltage versus
current ratio can easily be seen on a simple transistor/ diode curve
tracer as a nonlinear slope. This nonlinear resistance occurs for
both positive and negative voltages and is symmetrical if there is
no rectifying contact. Of course, resistors of a few thousandths of
an inch in length are not used in high voltage applications; but if
you put 1,000 of these small resistors mentioned above, that are
three thousandths of an inch long, in series, you would have a
resistor three inches long. This resistor, assembled from many low
voltage nonlinear junctions, would have a nonlinear resistance
when used at 1,000 volts.
It has also been known for a long time1 that the resistance of
a resistor can change due to a change in the voltage applied to it,
even though the temperature may be held constant. The voltage
coefficient of resistance may be expressed as the ratio of the
resistance change in ohms to the corresponding increase in applied
voltage in volts when the temperature is held constant. Such
voltage coefficient of resistance definition is useful to characterize
the resistance change with an increase in applied voltage. Of
course, for any useful resistor material, the resistance returns to its
original value when the applied voltage is removed.
The voltage coefficient of resistance of the resistor depends
not only upon the length of the resistor, but also upon the
conductive interfaces between the resistive particles that make up
the resistor. These interfaces result in emission current (tunneling)
across microscopic gaps between conductive particles such as
graphite. It is complicated by many factors such as size of
particles, their size distribution, and electron emission coefficients.
If resistance can be obtained without resorting to high resistance
contacts between granular low resistivity materials, then low
voltage coefficients can be achieved.
When a steady voltage is applied to a resistor, it normally
undergoes resistance changes due to both applied voltage and
temperature increase. The temperature increase is caused by the
dissipation of electrical energy in the resistor due to current flow.
At low voltages the temperature coefficient is usually larger than
the voltage coefficient. This change in resistance is almost entirely
due to a temperature change in the resistor.
When a short pulse is applied to a resistor, and very little
average power is dissipated in the resistor, its temperature will not
rise appreciably. Most of the resistance change of a low
temperature coefficient resistor will be due mainly to the
application of voltage, and limited to the time when the voltage is
applied. When high voltage pulses are applied to low value
resistors, the change in resistance can be appreciable, and can be
very important in measurement applications.
Bulk metal resistors have almost unmeasurable voltage
coefficients. However, due to the low resistivity of metals, wire
wound resistors must be used to achieve reasonable resistance
values. The combined inductance and capacitance effects of wire
wound resistors prevent their use either at high frequencies or with
fast pulses.
Measurement of short high voltage pulses are made in
investigations of the effects of lightning strikes, EMP testing on
electrical equipment, instrumenting underground nuclear tests, and
the pulse power industry.
Thin metal film can also be used to achieve reasonable
resistance values, but these resistors have a high voltage
coefficient. This may result from the extremely thin metal film
deposited on a very rough ceramic substrate, that allows tunneling
or current flow across the ceramic valleys.
Most resistors have a negative voltage coefficient, which
means that at higher voltages, the resistance decreases during the
pulse. If the resistance increases with voltage, the resistor has a
Carbon composition resistors are made with powdered or granular
graphite material, which has a relatively low bulk resistivity.
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