Resistors, Capacitors, Inductors – Passive Components 101
In earlier posts we saw how tubes (valves) and transistors work. Those electronic devices are what makes everything electronic around you work and are referred to as ACTIVE devices because they require power to control or modify electrical signals. However, it takes more than just those active devices to make an amplifier, TV or Radio etc. They need to be interconnected and have electrical voltages and signals applied to them in very particular ways.
This is where PASSIVE electronic components play a major role. They are referred to as passive as they do not require energy to operate and dissipates, stores, and/or releases the energy applied to them.
There are three basic types of PASSIVE electronic component:
- The resistor – R
- The capacitor – C
- The inductor – L
Their basic circuit symbols are:
They would appear in an electronic circuit as seen below:
These passive devices may also be made variable so that their values can be changed while in circuit.
NOTE: Resistors and diodes can be made to change their resistance value using light, E.G. a light dependent resistor (LDR) and a photo diode. Diodes can also be made to vary their depletion layer capacitance by changing their reverse bias voltage (VARICAP).
Before we take a high level look at how these passive components work and their applications, let us very briefly recap what an electrical current and a conductor are.
Electricity & Conduction
An electrical current is nothing more than electrons all moving generally in the same direction at the same time. To achieve this a material must be able to provide “free” electrons to support the current flow and by inference it is therefore known as a conductor E.G. copper. Materials that cannot supply “free” electrons are referred to as insulators E.G. plastic.
Remember that a positive charge is a shortage of electrons that causes a charge imbalance due to the non-moveable positive charges of an atoms protons in its nucleus and that just like magnetic poles, same charges repel while opposite charges attract.
For a more detailed explanation refer to the first part of this post.
Basic Passive Electronic Components
The Resistor – R
Back in 1827 George Ohm showed that the current through a conductor between two points is directly proportional to the voltage between those two points. Applying this to practical measurements creates the Ohms Law equation:
R=V/I (ohms)
Where; I is the circuit current in amps, V is the voltage (potential difference) in volts between the two points and R is the resistance of the conductor between the two points in Ohms.
Electrical Behaviour
The voltage difference produced by a resistor should, in the ideal world, be constant no matter the frequency of the signal, the voltage/current level or temperature. In practice resistors are not perfect and have small levels of inductance and capacitance and may get warm. When resistors warm up or cool down their value rises or falls, respectively changing the voltage drop that they are creating.
Ideal Resistor Response
For most applications, including low frequency RF and particularly at audio frequencies the resistance can normally be considered to be virtually constant no matter the level of the applied voltage or current provided the appropriate power rating is used. Also the voltage and current waveforms are always IN PHASE over the operational frequency range.
For advanced circuit designs, particularly at higher frequencies, the resistor can be considered to have the following equivalent circuit:
At these higher frequencies the electrical behavior of the resistor is strongly dependent upon the manufacturing technique and particularly at RF frequencies they can behave as a complex LCR circuit as shown above.
Resistor Noise
Resistors also create electrical noise from the thermal agitation of their atoms (Johnson noise) and current noise which is caused by random fluctuations of the conductivity of the resistor when it passes a current. The level of resistor noise is important in low level signal applications like phono and MC head amps and RF amplifiers.
Resistor Power
When an electrical current flows through a conductor that has any resistance it creates heat as the energy of the moving electrons is dissipated within the material. This heat energy is measured in watts and may be calculated using the equation:
P=I xV (watts)
Where; P is the power in watts, V is the voltage across the resistor in volts and I is the current through the resistor in amps.
Resistors are therefore manufactured to support a large range of power levels so that the heat created does not change their value or damage them. Their wattage range from less than 1/10 to many hundreds of watts. Generally low power and low noise resistors are made from film resistors where as higher power resistors are often wire wound and can use electrically insulated heat sinks to help dissipate the heat.
Resistor Types
Resistors are manufactured using materials that restrict the availability of electrons. This can be achieved by using:
- Solid carbon – different mixtures of carbon as solid or tube designs
- Wire wound and foil alloys – Nickel-chromium (Nichrome) or a copper-nickel-manganese alloy (Manganin) wire, on ceramic insulators.
- Film – typically carbon or various metal oxides are deposited onto solid or tube ceramic or glass insulators. Their resistive values are adjusted by using different carbon and oxide compositions together with spiral cuts along the length of the insulator body.
Various resistors and powers. L to R. 0.1 watt > 10 watts. Metal oxide>carbon film>wirewound.
Various adjustable pre-set resistors or potentiometers.
Many electronic designs use printed circuit boards (PCB) that require surface mount components. Those resistors have tiny rectangular ceramic bodies coated with various oxide films with silver conductive edges on either end for direct soldering to the PCB copper tracks.
Typical surface mount resistors
Resistive Value & Tolerance
Common commercial resistors are manufactured over a range of many orders of magnitude from as low as 0.1 ohms to as high as 10Meg ohms in a preferred value range with value tolerances from 0.05% to 20%. The resistance and tolerance values are printed on the resistor either as text or using the universal color code with up to 6 color bands. See above image.
Applications
The resistor is widely used to reduce a voltage, to create appropriate bias and operational voltage conditions for valves and semiconductors, to generate voltage signals across, to limit current flow and damp or absorb energy in electrical circuits.
Wire wound and carbon resistors are mainly used where they are required to dissipate high power and handle high temperatures. Often used in power supplies and providing bias voltages for valve and transistor power amplifiers.
Carbon film are general purpose resistors used in more noise tolerant circuits, like power supplies and less sensitive RF, audio and TV circuits.
While the lowest noise levels are observed in resistors using foil and wire wound techniques. Metal oxide film resistors are mostly frequently used for their very low noise performance making them suitable for high quality audio amplifier use and low noise RF circuitry.
The Capacitor – C
A capacitor or condenser stores electrical energy as an electric field by virtue of accumulating electric charges on two close conductive surfaces that are insulated from each other. The electric charge Q in Coulombs stored by a capacitor is directly related to the applied voltage V in Volts and its capacitance C in Farads – named after Michael Faraday, while Q is named after Charles-Augustin de Coulomb. A coulomb is defined as the electric charge delivered by a 1 ampere constant current in 1 second and it can be shown that:
Q=C x V (Coulombs)
Electrical Behaviour
When a DC voltage is applied to a capacitor the voltage or potential difference across the dielectric causes a momentary movement of electrons from one side of the capacitor to the other causing a brief current to flow. The size of the current is proportional to the applied voltage (the amount of push) and the capacitors capacitance (storage size). When the DC supply is removed the electrostatic field created between the capacitor plates holds the electrons in place and the electrical charge remains on the plates. The charge maybe removed by connecting the plates through a wire or resistor and thereby allowing the excess electrons to return to the positively charged plate. Or by reversing the polarity of the DC supply causing the negative stored charge to migrate to the other plate. In this manner a changing or alternating voltage causes a “continuous” current to flow, by continually moving charge between the plates.
A capacitor therefore BLOCKS the flow of DC but allows the flow of AC. The flow of AC is not like a simple wire or resistor in that the capacitors “resistance” to the movement of electrons is dependent upon its capacitance and the applied frequency. It can be shown that the capacitive reactance or impedance Z of a capacitor may be calculated using:
Z = 1/2π F C (ohms)
Where; π = 22/7, F=frequency in Hz, C=capacitance in Farads.
If we plot the impedance Z of a fixed capacitance against frequency F we get the following graph:
We see that at DC the impedance is “infinite” and as the frequency of an applied voltage increases the capacitive reactance/impedance (resistance) falls. Presenting a continually dropping resistance to the “passage” of the AC current.
In the case of a resistor we saw that the voltage a current waveforms are always in phase. For the capacitor the voltage and current waveforms are always <=90 degrees out of phase, with the current leading the voltage.
This phase shift must be taken into account in some circuit designs. If not correctly dealt with it can produce signal distortions and delays.
As with the resistor there is no ideal capacitor, though some designs come very close. They are still subject to dielectric leakage currents, value changes due to heat and in particular aging, especially for electrolytic or polarized capacitors. They also exhibit some inductance and DC leakages giving rise to the following equivalent circuit.
Capacitor Losses
Leakage resistance through the dielectric, and series resistance, also known as ESR (Equivalent series resistance), are two of the more important capacitor losses. ESR is often considered to be the most important loss for capacitors especially for audio. It is influenced by device type, construction, temperature and frequency. The relevance of ESR to capacitor selection is twofold:
- It influences the AC response of the capacitor
- It imposes limits on the amount of AC current that can be permitted to flow through the capacitor due to thermal limitations.
Current flow through a capacitor’s ESR results in I2R losses just like any resistor, causing a temperature increase within the capacitor that contributes to diminished device longevity.
Capacitor Storage and Voltage
The storage capacity of a capacitor is dependent upon:
- The area of the plates
- The space between the plates
- The dielectric used between the plates
With the working voltage depending upon:
- The space between the plates
- The dielectric used between the plates
Capacitor Types
There are numerous physical designs of capacitors that use the following insulating materials (dielectrics):
- Paper
- Glass
- Ceramics
- Plastics
- Oxides (Polarized or Electrolytic capacitors and Tantalum)
Types 1 thru 4 use electrical conducting surfaces that are made from either aluminum foil, aluminum film or a conductive metal oxide film and which are separated by the appropriate dielectric.
For large value capacitors various chemical and metallurgical techniques are used to greatly increase the effective storage of the device for a given physical size. These capacitors are referred to as Electrolytic capacitors, are polarized and must be connected into a circuit with the correct polarity of DC voltage applied in order for them to work correctly and not explode! There are three families of electrolytic capacitor:
- aluminum electrolytic capacitors
- tantalum electrolytic capacitors
- niobium electrolytic capacitors
An electrolytic capacitor has an anode or positive plate made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel electrolyte covers the surface of this oxide layer, serving as the cathode or negative plate of the capacitor. It is the very thin nature of the dielectric oxide layer and the enlarged anode surface that gives electrolytic capacitors a much higher capacitance and working voltage for a given size than ceramic or film capacitors.
Tantalum electrolytic capacitors consist of a pellet of porous tantalum metal as an anode, covered by an insulating oxide layer that forms the dielectric, surrounded by liquid or solid electrolyte as a cathode.
A niobium electrolytic capacitor has an anode made of passivated niobium metal or niobium monoxide, on which an insulating niobium pentoxide layer acts as a dielectric. A solid electrolyte on the surface of the oxide layer provides the capacitor’s cathode.
NOTE: There are electrolytic capacitors composed of a pair of “back-to-back” electrolytic’s. These are referred to as non-polarized (NP) electrolytic’s as they can be used in circuits that have no DC polarizing voltage without damage.
Various low value capacitors. From L>R. Mica, ceramic, polyester, polystyrene, variable.
Various large value capacitors. Polyester and polypropylene.
Surface Mount Capacitors
Various value radial lead and snap-in electrolytic capacitors
Axial lead electrolytic’s. From L>R. Non-polarized, Tantalum, Aluminum
Surface Mount Electrolytic’s
Capacitor Values & Tolerance
Common commercial capacitors are manufactured over a range of many orders of magnitude from a slow as 1pF to many thousands of microfarads in a preferred value range with value tolerances between 1% – 20% or as a +-pF value. The capacitance, tolerance and operating voltage values are printed on the capacitor either as text or using a universal color code with up to 5 color bands. See above images for some typical examples.
Applications
To include: power supply smoothing, DC blocking, AC coupling, audio and RF filters, tuned circuits, RF decoupling. For audiophile use polystyrene and polypropylene capacitors provide the best performance with aluminum for higher value electrolytic’s.
The Inductor – L
An inductor, also called a coil or choke is a two-terminal electrical component that stores energy in a magnetic field when an electric current flows through it. An inductor typically consists of insulated wire wound into a coil, with either an air or solid core made from iron, ferrite or brass.
Electrical Behaviour
When a current flows in an inductor or even a straight wire, it generates a magnetic field around it (Faradays Law). With DC applied that field is static and the resistance of the inductor is just its DC resistance. If the applied voltage now has a varying level (a frequency) the rising and falling magnetic fields will generate an opposite voltage in the wire or coil that opposes the current flow creating the magnetic change, a back EMF (Lenz’s law). This opposite current flow opposes the originating current flow effectively increasing the inductors AC resistance or as it is known its impedance or inductive reactance.
An inductor therefore offers little resistance to the flow of DC but resists the flow of AC. The flow of AC is not like a short wire or resistor in that the coils “resistance” to the movement of electrons is dependent upon its inductance value and the applied frequency. It can be shown that the inductive reactance or impedance Z of an inductor may be calculated using:
Z = 2π F L (ohms)
Where; π = 22/7, F=frequency in Hz, L=inductance in Henries
If we plot the impedance Z of a fixed inductance against frequency F we get the following graph:
We see that the impedance response of an inductor is the opposite to that of a capacitor. At DC the ideal inductor has zero resistance but as the frequency of an applied voltage increases the impedance/inductive reactance (resistance) rises, presenting a continually increasing resistance to the passage of the AC signal.
In the case of a resistor we saw that the voltage a current waveforms are always in phase. For the inductor the voltage and current waveforms are always <=90 degrees out of phase, with the current lagging the voltage.
This phase shift may need to be taken into account in some circuit designs. If not correctly dealt with it can produce signal distortions and delays.
As with the resistor and capacitor there is no ideal inductor. They all exhibit some DC resistance and self capacitance giving rise to the following equivalent circuit that may need to be considered in high frequency and RF designs.
Inductor Losses
For many applications, particularly in passive speaker crossovers, it is the Series resistance that is of most concern as it reduces the amplifiers damping factor. For RF work the series resistance can impact a parameter called Q factor, while the parallel capacitance can be included in RF designs.
Inductor Cores
The more of the magnetic flux that interacts with the coil the greater its inductance value. So there are occasions where helping constrain and concentrate that magnetic flux within the coil can be advantageous, but NOT always. Placing a metallic core inside the inductor runs the risk of magnetically saturating the core material at high coil currents. When this happens the magnetic flux distribution becomes non-linear and it causes various harmonic distortions to the applied signal. So ideally air cored inductors have an advantage here. Large value inductors require lots of wire adding DC resistance and additional capacitance, neither of which are wanted and can cause additional undesirable effects, especially in passive speaker crossover filters.
If cores are used they must be designed to minimize any currents induced into them by the magnetic field (Eddy currents), as these currents are lost energy. This is achieved by segmenting the core into many laminations and using various techniques to electrically insulate each lamination and thereby minimize electrical loops. The two most common materials for AC power and audio inductors are iron/silicon steel and ferrite. Ferrite cores are dense, homogeneous ceramic structures made by mixing iron oxide with oxides or carbonates of one or more metals such as manganese, zinc, nickel or magnesium. They are then pressed into various shapes and Kiln fired to 1300C, after which they can also be machined to into various shapes. For RF use the most common core materials are ferrite and occasionally brass.
Power Transformer Laminated E/I And Toroid Iron/Steel Cores
Ferrite rod radio antenna
Inductor Types
There are numerous designs of inductors from less than 1µH to many Henries and low power to very high power. They may be fixed value air or cored and can be made variable by adjusting the core position within the coil.
Various Inductor styles. From L>R. Axial and Radial with ferrite cores, air cored
and variable with a ferrite core.
Ferrite Cored Surface Mount Inductors
The value of the inductor depends upon:
- The number of coil turns
- The diameter and length of the coil
- The type of core; air, iron, ferrite or brass
Inductor Values & Tolerance
Common commercial inductors are manufactured over a range of many orders of magnitude from a slow as 1µH to many Henries in a preferred value range with value tolerances between 1% – 20%. The inductance and tolerance values are printed on the inductor either as text or using a universal color code with up to 5 color bands.
Applications
Audio frequency tuned circuits like equalizers and speaker crossovers, power supply smoothing, interference suppression and RF tuned circuits and filters.
NOTE:
Skin Effect
Alternating electric currents have a tendency to cause increased current density towards the surface of a conductor. It is caused by opposing eddy currents induced by the changing magnetic field resulting from an alternating current. This effect causes the majority of the current to flow in an area immediately below the conductors surface referred to as the conductors “skin” depth. The “skin” depth is frequency dependent and becomes thinner as the frequency of the signal increases effectively reducing the cross-sectional area of the conductor and increasing its resistance. At 60 Hz in copper, the skin depth is about 8.5 mm (0.33″), at 100KHz it is only about 0.2mm (.008″). At radio frequencies skin depth can be less than 50 μm or 0.0004″.
Red line set at 50Hz.
This increase in resistance can be offset by increasing the conductors surface area, as is achieved by using multiple insulated conductors like Litz wire. Now you know why audiophiles are so concerned about the types of cables they use. Even though they are not dealing with frequencies much above 50KHz, the inductive, resistive, capacitive, and skin effects of cables do impact the cables performance even at audio frequencies.
Transformers
The transformer is an application of the inductor in which the varying magnetic field of one inductor is linked to another inductor. As such transformers ONLY operate on a AC waveform. An AC current in any coil produces a varying magnetic flux which will induce a varying electromotive force (EMF) across any other coils either wound around the same core or in close proximity, thereby transferring electrical energy with no physical/electrical connection. This effect is known as Faraday’s law of induction, it was discovered in 1831 and describes the induced voltage effect in any coil due to a changing magnetic flux encircled by the coil.
Electrical Behaviour
In an ideal transformer with no losses the power that enters the primary winding is all available at the secondary winding. The voltage induced in the transformers secondary winding is directly related to the turns ratio (a) between the primary and secondary windings. Therefore for a given power of transformer and assuming no losses, Primary power in = Secondary power out, so stepping up secondary voltage steps down secondary current and stepping down secondary voltage steps up secondary current.
It can be shown that:
a=Np/Ns (turns ratio)
Where; a=the turns ratio, Np=number of primary turns and Ns=number of secondary turns
It can also be shown that:
a = Ip/Is = Vp/Vs
Where; Ip=primary current, Vp=primary voltage, Is=secondary current and Vs=secondary voltage
Transformer can also be used to match electrical impedances in order to get maximum power transfer using the formula:
Zp=a²Zs
Where; Zp=primary load in ohms and Zs=secondary load in ohms.
The Magnetic Flux Path
Magnetic flux does not easily follow abrupt changes in direction like the right angles of E/I iron core laminated transformer. This causes the flux to leak outside of the cores physical boundaries and drops the efficiency of the transformer. This flux leakage also has the possibility of inducing unwanted voltages in parts of the surrounding electronic circuitry if it is not well magnetically screened. In order to reduce magnetic interference in adjacent circuitry additional steel cheeks and mu-metal screens maybe deployed around the transformer and/or circuitry. Modern techniques can now cost effectively manufacture circular toroidal transformers that exhibit very low external magnetic fields, low flux leakage and low Eddy currents results in high efficiencies.
Transformer Types:
Transformers are designed like inductors to handle specific powers and operate at or over a specific range of frequencies, most commonly 50/60Hz for power transformers, 5Hz-100KHz for audio transformers and up into the many megahertz regions for RF transformers. At AC power and audio frequencies iron laminated E/I cores are very common. However, laminated toroidal power transformers are now often used due to their minimal magnetic flux radiation losses and therefore much higher efficiency, having significantly reduced magnetic interference. At RF frequencies air and ferrite cores are common and in some cases brass cores, with many RF transformers often made to be variable or “tunable”. It is also not uncommon in higher end audio applications to wrap power transformers with copper shields, as shown below. This reduces electrical noise radiation and interference.
The frequency responses of transformers is very varied as they are custom designed for their particular application and frequency. A couple of basic responses are shown below.
Transformer Losses
As with other passive components transformers are not ideal and have various losses, to include:
- Eddy current losses in the magnetic core material
- Flux leakage loss outside the magnetic core material
- The DC resistance loss in the windings
- Magnetic hysteresis losses in the core material
At higher frequencies various self capacitive losses also start to have an impact. All these losses need to be taken into account during a transformers and associated circuitry design.
Typical Construction
E/I and Toroidal AC Power Transformers
Applications
The most common uses for the transformer are to step AC voltages up and down, as in power supplies and provide impedance matching as in valve (and some transistor) power amplifiers for the speaker connection. They are often used to electrically isolate but couple AC circuits and couple RF circuits.
Due to their cost and bulk transformer based power supplies are frequently replaced with electronic switched mode power supplies. However, even with modern techniques these supplies have the ability to produce noise in low level analog and digital video circuits and particularly in low level analog audio circuits. Higher end audiophile equipment will often revert to using analog power supplies using toroids as a well designed toroidal power supply will have extremely low supply noise and radiated interference.
Reading Values and Tolerances
Resistors, capacitors and inductors cannot be manufactured to absolute values and so have a tolerance value measured either as a percentage or +- value of their nominal value. Their nominal values are standardized and are called preferred values. The preferred value of the component falling within the manufacturing tolerance and as seen above is indicated on the component in either text or by a number of colored bands. Transformer voltages and VA ratings are sometimes printed on the device (particularly with toroids) with the full specifications only being available by looking up the model number printed on the transformer with the appropriate manufacture.
Due to the differing physical designs of passive components reading their values is not always obvious. Below are the basic methods for determining R, C and L values plus links for more help and information.
Typical resistor, capacitor and inductor color code markings:
Resistor Color Codes
Image Credit: EEPOWER. Resistor Values
Here is the Digikey resistor color code calculator. For more on determining SMD resistor values go to electricaltechnology.org.
Capacitor Color Codes
Image Credit: EL-PRO-CUS
For more on determining capacitor values visit EL-PRO-CUS or electricaltechnology.org.
Inductor Color Codes
Image Credit: Electricaltechnology.org
For more on determining inductor values visit electricaltechnology.org.
For more on-line electronic calculators check out Digikey.
Want to know more about active electronic devices? Then check out these posts:
