Stray Resistance, Stray Inductance and Stray Capacitance

Stray impedance

There is no perfect or ideal component in the world. Any wire or conductor forming an inductance or capacitor, or its leads will always have some resistance, however low. Further, the leads have their own associated inductance (both self and mutual) due their effect on each other. There will be capacitance between turns of a conductor of an inductor or a resistor. The lead wires running at some distance from each other have some capacitance between them. A high magnitude resistance always exists between terminals of a component over the insulation surface encapsulating them, or between plates of capacitor or turns of inductor. The conductors forming the inductors, as also capacitors, have their own resistance, have a finite resistance, however low. The following diagram explains stray impedance sources in cables and wires.

These unwanted or unintended resistances, capacitances or inductances are ‘stray’ components, and together form ‘Stray Impedances’. They are usually insignificant at power frequencies or up to certain frequency limits, but at high frequencies, they become a nuisance and interfere in normal working of equipment. At high enough voltages, the leakage currents due to stray impedances can seriously affect the performance of both Dc and AC equipment.

For example, parallel equivalent capacitance (stray capacitance) and equivalent series inductance (stray inductance) make a practical resistance appear as a combination of R, L, and C as below.

It is therefore necessary to understand these stray impedance components and handle them in proper manner wherever possible.

Stray Resistance

Stray resistance is an intended resistance in a circuit which is not a design factor, but is present unavoidably. This resistance could be of very low value in milliohms or micro-ohms, or very high in mega ohms. These resistances are normally neglected since they do not matter in the working of equipment. However, these could create serious obstruction in functioning or measurements in some conditions. Stray resistances can arise due to following reasons:

1. Between any two conductors at a separation distance, there is always present a medium of insulation material, which could be even air or vacuum. That means in any given circuit, conductors in different circuit paths will always have some unintended resistance, however large. In measurements of mega Ohms scale measurements, these interfere as parallel resistances between measuring points. High value resistance measurements often needs a shielding device to minimize the effect of these high parallel stray resistances.
2. For very high voltages, these resistances may carry currents of a level as to be dangerous for operating or nearby personnel. When thousands of volts exist between two points on ground, there will be a voltage gradient along ground / floor dangerous enough for a man to walk.
3. Long wires / cables /transmission lines have insulation resistances to earth or nearest ground.
4. All conductors carrying current in a circuit have certain resistance, however low. These become significant at very high current levels, or while dealing with low resistance components. Measurements of milli Ohm range gets affected if connecting wire/ conductor has resistance in milli Ohm range, or even micro Ohm range (which could be comparable to resistance being measured. Hence low resistance measurement is done using four terminal methods to eliminate this influence.
5. Long cables or transmission lines have their own resistance which has to be accounted in any design or calculations.
6. These high and low stray resistances give loss factor in capacitors, and winding resistance to inductors / transformers.

Stray Inductance

From the basics, it is known that all current carrying conductors and leads / wires have inductance. This implies that even resistance with substantial length will have some inductance. Leads of capacitors (or resistors) also have a small inductance. Such unintended inductance exists in most circuits, and these can many time affect functioning of the circuit. Such unintended inductance, which is not designed and is unwanted, is called stray inductance.

One can understand that long wires and cables, or transmission lines have their own inductance. These are often a nuisance and many times have to be taken into account. Capacitor windings can have stray inductance between start and end of a conductor foil. Leads of capacitors (or resistors) always have some inductance. These stray inductances create nuisance in measurements of components, and special measures are needed to mitigate their effect. In conductors / lines running close by, current in one will affect the other nearby conductor by stray mutual inductance.

Stray inductances normally do not pose an issue in most common applications at power frequencies. At high frequencies they become significant and can interfere in functioning of a circuit or equipment. Impedance of an inductor increases with frequency, and even a small inductance becomes significant at high frequencies.

 A capacitor performance is affected as frequency rises, and at some frequency, it becomes resonant with itself due to stray inductance. Beyond this frequency, the capacitor starts functioning as an inductor. Therefore, special design factors are incorporated in capacitors at high frequencies. Construction of capacitor having a coil construction of winding are usually called inductive capacitors, and non-inductive capacitors have features that virtually nullify or minimize the inductive effect as to be insignificant in the operational range.

Most resistors are made by winding resistance wires or by helical shaped etching on ceramic coating on core. In both cases the helical path gives rise to inductance property to resistance. The inductance can be particularly problematic as frequency rises, since the resistance in effect is a resistor with series inductance. When needed, a resistance has to be specially designed to be non-inductive avoiding helical construction.

Sometimes, however, advantage is taken of stray inductance by specifically tailoring it in design. In a design for specific application, capacitor was designed to have a predetermined inductance between start and end of each electrode foil. This inductance was tailored and used by designing four-terminal capacitor for some purpose in very special application. Start and end of each foil each foil was connected to external leads.  The capacitor then had one inductor (few nH) in each of foil, each becoming a part of some circuit design of equipment.

Stray inductance of components decides behaviour of circuits over high frequency range, and designers often make provision for this from known characteristics of components. Manufacturers of components often provide data of their behaviour over large range of frequencies for the benefit of designers. Designers try to keep stray inductance as low as possible by keeping component leads and current paths short, and place conductors at sufficiently long distance from each other.

Stray Capacitance

Capacitance is formed between any two (or more) conductors separated by an insulating material. Shape of conductors may be anything, and distance between them may or may not be uniform. In an instrument, there exists a capacitance between a component and the chassis or casing of instrument. These stray capacitance values can be measured by suitable meter. Such an unwanted capacitance, which is unavoidable, is stray capacitance, also called parasitic capacitance. It is an unintended appearance of electric charge in a circuit or non-capacitive components.

Stray capacitance plays a major part in high frequency disturbance in a circuit or electronic instrument. Often it becomes necessary to overcome or reduce these through means. Stray capacitances often harm safe working of instruments., It has come to notice that in high voltage capacitors (say 100 KV) used for testing, output voltage falls far below the required level because of stray capacitance between the windings and its casing, or transformer and safety net around it. In high frequency circuits, components may act like short-circuit because of these capacitances. They may even create unwanted feedback path in op-amps etc.

In inductance coils or transformer coils, there exists a capacitance between adjacent turns, or between layers of coils, as also between primary and secondary of transformer. On a PCB, a capacitance exists between different conducting tracks. In wiring, wires nearby always have a capacitance.  In transmission lines, capacitance between lines, and between lines and earth are a major nuisance. Underground cables also have capacitance between different conductors, and cables running parallel have capacitance between them, which increase with distance.  The capacitance also exists across a diode or transistor. Any conductor will have stray capacitance to ground.

It is necessary to understand stray capacitance, its sources, and take measures to reduce their effect on working of equipment / installation. Some measures to reduce stray capacitances include:

• Place conductors farther apart.
• Shield the conductor/s
• Decrease conductor / trace width

To summarize

Stray resistance, inductance or capacitance are unavoidable or indispensable part of electrical and electronic circuits. They are not necessarily insignificant, and are a nuisance many times, particularly while dealing with very low resistance, inductance or capacitance values. They are also likewise a source of problem at extremely high values of components. High or very high frequencies can create even a change in nature of components and their behaviour. Therefore, they need a good understanding for their effect and ways to offset their effect in the best possible ways.