Lake Shore 370, Руководство пользователя

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Lake Shore Model 370 AC Resistance Bridge User’s Manual
2.6.3 Resistor Self-Heating and Thermal Resistance
A resistor self heats when the electrical power being put into the measured resistor is large enough to warm the resistor
above the temperature of its surroundings. Electrical power gets into the resistor from both the necessary excitation
current and undesirable noise (Paragraph 2.5). Errors from self-heating are dangerous because they can easily go
undetected. One strategy for detecting these errors is to understand the thermal resistance of the resistor and predict its
reaction to excitation and noise.
Self-heating (
Δ
Tsh) is a product of the resistors thermal resistance (Rt) expressed in kelvin per watt (K/W) and excitation
power (Ps) expressed in watts.
Δ
Tsh = Rt Ps
; Ps can be calculated as excitation current squared times measured
resistance (Ps = I
2
R).
A familiar form of self-heating is sensor self-heating in resistive temperature detectors (RTDs) but the same principles
apply to any resistor being measured. Specifications for the Model 370 include typical sensor characteristics for a
Germanium RTD that estimates the thermal resistance of the sensor. This example demonstrates how excitation current
must be reduced to compensate for the increase in thermal resistance at lower temperature. Otherwise self-heating would
become a significant part of the overall accuracy. Calculations like this are difficult to do for two reasons, first,
manufactures do not always publish specifications on thermal resistance and second, the actual thermal resistance is very
dependent on installation. An explanation of how to calculate thermal resistance of a temperature sensor is given in the
Lake Shore Temperature Measurement and Control Catalog, Appendix A.
With an estimate of thermal resistance, the effect of increased excitation current can be predicted. If self-heating
behavior does not match the prediction, noise power may be high enough to heat the resistor.
2.6.4 Lead Resistance
Measurement leads in cryogenic systems routinely have resistance of tens or even hundreds of ohms. Lead wire is
chosen for its thermal properties first and electrical resistance is a secondary consideration. The Model 370 measurement
circuits can tolerate significant lead resistance without measurement error. A lead resistance specification of 100
Ω
plus
10% of resistance range (for each of the four leads) is given for most excitation currents. This lead resistance will give a
measurement error that is small compared to the specified accuracy on the resistance range and in most cases the error is
not measurable. The lead resistance specification is reduced to 10
Ω
plus 10% of resistance range for the highest current
excitations. At the higher currents, lead resistance of 100
Ω
can create drops of several volts in each lead. These large
voltage swings will measurably affect the millvolt and microvolt resistor measurements. If lead resistance exceeds the
specified values, the instrument will measure with reduced accuracy until the compliance voltage of approximately 7 V
RMS is reached. Keep the resistance in all of the leads similar whenever possible to maintain measurement balance.
2.6.5 Current Leakage
Lead wiring cannot be taken for granted when determining accuracy of cryogenic resistance measurements. Cryostats are
notorious for having bundles of long, thinly insulated leads tightly wrapped around every available heat sink area. Shorts
are inevitable. Lead wires should be “ohmed out” on a regular basis to test for short circuits that develop over time and
thermal cycling.
2.6.6 Cable Capacitance
Cable capacitance and measured resistance act together as a low-pass filter to attenuate the desired measurement signal
and shift its phase. Low excitation frequency was chosen for the Model 370 to minimize this effect but capacitance can
still contribute to measurement error when resistance is high. Driven guards should be used when measuring resistance
above 100 k
Ω but they often cannot be used inside of the cryostat and are not available for scanner input leads.
The effect of cable capacitance on unguarded leads can be estimated by the following equation. This equation is only an
estimate because it models the lead capacitance as a single capacitor across the measured resistor. In a practical
installation there is capacitance from each lead to shield or ground in addition to capacitance across the resistor. Actual
results depend on cable construction and installation techniques. The equation does account for both magnitude
attenuation caused by capacitor impedance in parallel with the resistor and phase attenuation caused by phase sensitive
detection of the input signal.
Theory of Operation 2-11