Ohmic resistors - effective resistances
In this article, I will explain how to calculate effective resistances of ohmic resistors. In this I have also explained types of resistors along with the neat sketches. In this I also shown how to calculate the resistance by using mathematical expression.
In all electronic circuits you find linear resistors, resistors or ohmic resistances of action here are meant in the strict sense. The resistance value is constant at the same measuring conditions and is calculated from the ratio of voltage to current. Differences are the resistors according to their designs and manufacturing processes.
When a suitable resistance wire resistance wire is wound on a ceramic body. The best-known resistance alloys are constantan, a copper-nickel alloy (CuNi44) and manganin, a copper-manganese-nickel alloy (Ni CuMn12). Both materials have a very low temperature coefficient, making their resistance over a wide temperature range is constant. Through the turns of the resistance wire, the component also receives a coil or inductance characteristics. Using a bifilar winding technique where the current flows in opposite directions in each turn, this prevents any unwanted property can be.
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Resistors are produced in thin film technology with a layer thickness of 50 nm in thick-film technology and with a layer thickness of 30 microns. The coating is applied uniformly to the carrier material in smaller resistance values. Larger values ??are created by screen printing masks in meander through production. Particularly inserted jumpers are partially removed in the subsequent fine-tuning, which can be produced very accurate resistance values.
Film resistors with very high resistance values ??can be produced in the resistive layer by grinding a helical groove. The layer is then similar to a ribbon whose cross section and length is determined by the pitch angle of the groove.
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In a large pitch angle a broad band with a few turns of results. The resistance track then has a large cross sectional area and a short length. The resistance value is less than a small angle of inclination, where the narrow tape and the number of turns is greater. Then the higher resistance value is calculated from the smaller cross section and the greater length of the resistive track. The coil causes an inductive effect, which can be detrimental at very high frequencies.
In all preparative methods, the resistance layer is applied to a heat-resistant insulating glass, ceramic or porcelain. The connecting wires are attached via clips, caps or soldered joints. The resistive layer is usually protected by a glaze, a cement, paint or resin coating.Real resistance
Mostly it to consider the effective ohmic resistance as frequency-independent, and ideal component to be expected with the specified resistance value R is sufficient. As already indicated, other properties can be detected, which may have a negative impact, especially at high and very high frequencies.
The connecting wires to form the actual resistance of a series connection and have a very low inductance L. By the milling of a spiral or meandering path in the resistance material is greater resistance value can be obtained. Many high power resistors are wound like a coil of resistance wire. In helical resistance track, an inductance L is connected in series to the ohmic resistance R. The inductance value is compared to the connecting pins, and is substantially greater in the range of nano-Henry. In high impedance wire resistors few hundred micro Henry are possible.
The resistance track is often contacted by metal caps at the ends. In connection with the voltage measured across the resistor, which can be viewed as a capacitive characteristic. Parallel with the resistor, the capacitor C is connected. The resistance track is not completely homogeneous, so that further added stray capacitances connected in series. The value of the total parasitic capacitance can be assumed to be very small with a few picofarads.
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The sketch shows the equivalent circuit of the real ohmic resistance. However, the undesirable properties of L and C are noticeable only at very high frequencies. With the assumed values ??of R = 1 k, L = 50 nH and C = 5 pF starts the frequency-dependent behavior above 5 MHz. Due to the LC ratio of the ohmic resistance can even get the property of a parallel resonant circuit.Strain gauges - DMS
A special design of the linear resistor is called strain gauges, strain gauge. The resistance value of a resistance wire is directly proportional to the length of wire and inversely proportional to the wire diameter. To a small extent to wire behaves elastically. Is on it within its elastic limits, a tensile force is applied so the material expands. The wire is longer, while reducing its cross section. Eliminates the tension so the wire takes its original length and cross section again. This mechanical change is a change in resistance result. A single wire resistance measurement is called stretching wire. Are known films with embedded meander stretching wires. The connectors are located at the beginning and end, so that the individual sections together form a series connection of many equally long stretch wires. The measurement gratings can be built for one-dimensional and two-dimensional measurements.
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The picture shows DMS films with measuring grids of stretching wire. Most constantan is used, the temperature coefficient is almost 0th The strain gages on the left is a one-dimensional sensor. The meander provides an 8-fold greater stretching wire length. The right design is designed as a two-dimensional sensor. The simple wire length is greater by a factor of 12th
The strain gauge resistance is fixed with a curing adhesive on the measurement object to be monitored. The deformation of the measuring object, such as bridge girders, connecting rod, spring steel is taken as a resistance change, and evaluated. Previously, a calibration curve is recorded by the DMS. It shows the change in resistance as a function of elongation.
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R: resistance of the strain without stretching
DELTA.R: change in resistance [O]
l: length of the measurement object without strain [mm]
DELTA.l: elongation of the test object [mm]
k: k-factor of the data sheet (˜ 2)
The nominal values of the DMS be 120 O, 300 O, 350 O, 600 O. The maximum elongation measured in wire mesh is 1%. Metal foil strain gauge can be up to 5%. Temperature-compensated strain measurement in one direction are very easy to do with two-dimensional strain gauge resistors.