Ohmmeter

An ohmmeter is a measuring device used to measure electrical resistance . The colloquial term ohmmeter is misleading because of the unit of the same name, ohmmeter . In addition, the unit of measurement is referred to as the ohm and not the physical quantity that is actually measured.

The resistance of an electrically conductive component to direct voltage results essentially from its geometric shape and a material property ( specific electrical resistance ) and leads to ohmic resistance or direct current resistance , in some cases also to a differential resistance.

When operating on AC voltage , the inductance and capacitance of the component also contribute an AC component ( reactance ) to the resistance. Direct current and alternating current components are combined to form impedance or complex electrical resistance.

An ohmmeter is usually designed to measure the ohmic resistance, for example of an unknown component or an electrical consumer. Simplified devices for detecting an electrical connection are called continuity testers. Reference is made below to devices for advanced resistance measurement tasks.

Preferred measurement method

Current and voltage measurement

Digital measuring devices

A constant current source is built into a digital multimeter to measure resistance , adjusted to a smooth power of ten in mA or μA, so that the numerical value of the measured voltage immediately gives the numerical value of the resistance without measuring the current intensity. Only the comma position and the unit symbol (Ω, kΩ) are switched to match the measuring range in the device. Depending on the manufacturer's specifications, the error limits are ≤ 1% of the measured value + 1 ‰ of the final value.

Digital multimeters usually have an automatic range selection and automatically switch the current intensity of the constant current source to the appropriate measuring range. For use as a continuity tester , they often have a switchable acoustic signal.

Analog measuring devices

The lowest scale from ∞ to 0 is used to measure resistance

Analog resistance measuring devices consist of a pointer measuring device with moving coil measuring mechanism , an adjustable series resistor and an auxiliary voltage source (battery); they have a strongly non-linear scale on which the resistance value can be read directly in ohms or kilo-ohms.

Due to the large measuring range 0… ∞, which covers all conceivable measured values, a reasonably accurate reading is only possible in the middle area of the scale. Some ohmmeters have a switchable measuring range in order to be able to read different values in the middle of the scale.

Due to the supply from a non-stabilized voltage source (battery with age-related decreasing voltage), the device must be adjusted before the measurement. In the event of a short circuit between the measuring terminals, an externally accessible potentiometer (part of the series resistor) is set so that = 0 is displayed. However, this also changes the scaling due to the principle involved. In the middle part of the scale, the typical error limits are therefore around 10% of the measured value. ${\ displaystyle R}$

Due to the disadvantages such as the more complicated application, the larger measurement errors, and higher mechanical sensitivity, analog resistance measuring devices have been almost completely replaced in practical laboratory use by digital multimeters for resistance measurement.

Measuring circuit with current and voltage measuring device

Via current and voltage measuring devices

In many cases, the voltage drop and the current strength are measured on the measurement object . The resistance is calculated from these two values according to Ohm's law . In principle, this method is not free from systematic measurement errors . The feedback deviations (circuit influence errors) due to the internal resistance of the ammeter or the voltmeter can be excluded by a more complex approach: ${\ displaystyle U}$ ${\ displaystyle I}$ ${\ displaystyle R}$ ${\ displaystyle R_ {I}}$ ${\ displaystyle R_ {U}}$

In the upper circuit ( current-correct circuit ) the measured voltage is greater than the voltage across the resistor by the voltage drop at the ammeter,

{\ displaystyle R = (U-U_ {I}) / I}

with .

{\ displaystyle U_ {I} = I \ cdot R_ {I}}

In the lower circuit (voltage-correct circuit) the measured current strength by the current consumption of the voltmeter is greater than the current strength through the resistor,

{\ displaystyle R = U / (I-I_ {U})}

with .

{\ displaystyle I_ {U} = U / R_ {U}}

Bridge circuit

This is a process with voltage compensation , in which the voltage dropping across the target is compared with another voltage dropping across a known resistor. For the measurement, one of the voltages is matched to the other; see Wheatstone measuring bridge .

Measurement of small resistances

Resistance measurement with constant current source and voltmeter,
top connection in two-wire circuit ,
bottom connection in four-wire circuit

When measuring small resistances (guide value <1 Ω), contact resistances in the connection terminals become noticeable as measurement errors; see measuring resistor . This influence can be avoided by connecting in four-wire technology ( Kelvin connection ) with terminals for the current feed and separately connected terminals for voltage measurement. Systematic measurement errors are excluded under the following conditions: ${\ displaystyle R_ {x}}$ ${\ displaystyle R_ {x}}$ ${\ displaystyle R_ {Kl}}$

When the current through the voltmeter is negligibly small

{\ displaystyle I_ {U} \ ll I_ {0}}

and the voltage loss in the terminals for the measuring lines is negligibly small,

{\ displaystyle I_ {U} \ R_ {Kl} \ ll I_ {0} \ R_ {x}}

the resistance value results from

{\ displaystyle R_ {x} = U_ {m} / I_ {0} \.}

When feeding from a constant current source, the voltage drop at the current terminals has no effect and does not appear as the cause of a measurement error . ${\ displaystyle I_ {0}}$

For an older analog measuring method see under Thomson Bridge .

A digital measuring method for measuring small resistances works as follows:

Digital voltmeters provide a display by comparing the voltage being measured with a built-in reference voltage ; see digital measurement technology . For example, with the two-ramp method, a voltage to be measured is displayed according to ${\ displaystyle U_ {ref}}$ ${\ displaystyle U_ {m}}$ ${\ displaystyle N_ {m}}$

Circuit for digital measurement of small resistances; ADU: voltage measuring device

{\ displaystyle U_ {m} = - U_ {ref} {\ frac {N_ {m}} {N_ {i}}}}

There is a device constant in it. ${\ displaystyle N_ {i}}$

Exact knowledge of can be dispensed with if the reference voltage is also formed with a reference resistor built in using four-wire technology, see circuit. ${\ displaystyle I_ {0}}$ ${\ displaystyle I_ {0}}$

{\ displaystyle U_ {ref} = - I_ {0} R_ {ref}}

{\ displaystyle U_ {m} = V \, U_ {x}}

{\ displaystyle U_ {m} = - U_ {ref} {\ frac {N_ {m}} {N_ {i}}} = I_ {0} R_ {ref} {\ frac {N_ {m}} {N_ { i}}}}

{\ displaystyle R_ {x} = {\ frac {U_ {x}} {I_ {0}}} = {\ frac {U_ {m}} {VI_ {0}}} = R_ {ref} {\ frac { N_ {m}} {VN_ {i}}}}

The display is proportional to . The method is implemented with a measuring range of 200 μΩ with a smallest step size of 1 nΩ. ${\ displaystyle N_ {m}}$ ${\ displaystyle R_ {x}}$

Measurement of large resistances

When measuring large resistances (guide value > 20 MΩ), the small size of the current still flowing becomes a problem with the usual small measuring voltages. The measuring voltage must be increased, which is often only possible with insulation measuring devices. These offer switchable measuring voltages from around 100 V. The voltage is limited by the dielectric strength or specified by test regulations. ${\ displaystyle R_ {x}}$ ${\ displaystyle R_ {x}}$

The main requirement for measuring very high resistances (giga to teraohm range) is when measuring insulating materials (plastics, cables, foils, etc.). A distinction must be made between these bodies

the surface resistance with current flowing along the surface and
the volume resistivity or resistance to current flow across the surface, that is through the body.

Because of the very small current strengths (up to <1 pA), which can easily be falsified by external interference and leakage currents, protective shielding technology (guard technology) is required, which requires a third connection between the measuring object and the measuring device. This additional connection has ground or earth potential and creates a continuous reference potential for the shielding (e.g. the guard rings) without being included in the current measurement. Such guard rings surround, for example, the connection sockets for the device under test or the connection legs of the operational amplifier used for current amplification on the circuit board of the measuring device.

Resistance measuring cell with three electrodes

Measuring arrangement with voltage, current and guard connection for measuring a volume resistance

To measure the insulation resistance of a flat measuring object one works with

a circular inner electrode,
a ring electrode surrounding it and
an opposing counter electrode.

To measure the volume resistance (→ figure), the current intensity flowing through the body via the internal electrode to the reference potential is measured. The counter electrode is connected to the test voltage. In this example, the ring electrode is connected to reference potential (guard); therefore, there is no voltage to the internal electrode and no surface current can flow. In this context, one speaks of a guard ring capacitor .

To measure the surface resistance, the current intensity flowing along the surface from the ring to the inner electrode is measured. The ring electrode is connected to the test voltage. The counter electrode is connected to reference potential or ground; therefore there is no voltage to the inner electrode and no current can flow through the volume.

The protective resistor makes the arrangement short-circuit proof.

The method is suitable up to a measuring range of 100 GΩ with a relative error limit of 1% and a measuring range of 100 TΩ with an error limit of 10%.

Measurement of differential resistances

In a right-angled diagram with linearly divided axes, which is plotted against , a straight line through the zero point results for a component with ohmic behavior; whose rise is clearly the resistance. Some components, in particular semiconductor components, but also incandescent lamps , have a non-linear behavior: Instead of a straight line, a curved characteristic is produced . The ratio is different for each current or voltage; it is no longer a component identifier. The voltage change that results from a small change in current intensity is considered and its ratio is called the differential resistance : ${\ displaystyle U}$ ${\ displaystyle I}$ ${\ displaystyle U / I}$ ${\ displaystyle r}$

{\ displaystyle r = {\ frac {\ mathrm {d} U} {\ mathrm {d} I}}}

In the diagram mentioned, it is the rise in the characteristic curve (tangent to the characteristic curve) at a certain point (the operating point of the component or another current intensity to be specified).

The differential resistance is an important parameter of semiconductor diodes ( rectifiers , Zener diodes , light emitting diodes , laser diodes ).

Measuring arrangement for measuring a differential resistance by means of an oscilloscope;
A Zener diode is shown as the measurement object

The circuit shown on the right works together with an oscilloscope in XY mode and is suitable for direct determination of the differential resistance without first having to record a characteristic curve:
A constant current source is used to set an operating point on the object to be measured. A small alternating current is superimposed on this direct current from an alternating voltage source. The capacitor blocks direct current, but allows alternating current through. The coil blocks alternating current, but has only about the wire resistance for direct current. The AC voltage over the measurement object is used for the Y deflection of the oscilloscope, the AC voltage over as a measure for the alternating current for the X deflection. You can see an almost straight, small section of the characteristic curve around the operating point on the screen. The differential resistance is determined from the increase . ${\ displaystyle R_ {M}}$ ${\ displaystyle \ mathrm {d} Y / \ mathrm {d} X}$ ${\ displaystyle \ mathrm {d} U / \ mathrm {d} I}$

Other measuring devices

For measuring additional inductive or capacitive components in the resistance: AC voltage bridge
For measuring small ohmic resistance changes : Wheatstone bridge

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