The output
impedance of an
electrical network
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources ...
is the measure of the opposition to current flow (impedance), both static (
resistance) and dynamic (
reactance), into the load network being connected that is ''internal'' to the electrical source. The output impedance is a measure of the source's propensity to drop in voltage when the load draws current, the source network being the portion of the network that transmits and the load network being the portion of the network that consumes.
Because of this the output impedance is sometimes referred to as the source impedance or internal impedance.
Description
All devices and connections have non-zero resistance and reactance, and therefore no device can be a perfect source. The output impedance is often used to model the source's response to current flow. Some portion of the device's measured output impedance may not physically exist within the device; some are artifacts that are due to the chemical, thermodynamic, or mechanical properties of the source. This impedance can be imagined as an impedance in series with an ideal
voltage source
A voltage source is a two-terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output current. However, a real-world voltage source cannot supply unl ...
, or in parallel with an ideal
current source
A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it.
A current source is the dual of a voltage source. The term ''current sink'' is sometimes used for sources fed ...
(''see'':
Series and parallel circuits
Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an ...
).
Sources are modeled as ideal sources (ideal meaning sources that always keep the desired value) combined with their output impedance. The output impedance is defined as this modeled and/or real impedance in series with an ideal voltage source. Mathematically, current and voltage sources can be converted to each other using
Thévenin's theorem
As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that ''"For any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A–B ...
and
Norton's theorem
In direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of ...
.
In the case of a
nonlinear device
Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be analyzed as multiple electric ...
, such as a
transistor
upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink).
A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
, the term "output impedance" usually refers to the effect upon a small-amplitude signal, and will vary with the
bias point
In electronics, biasing is the setting of DC (direct current) operating conditions (current and voltage) of an active device in an amplifier. Many electronic devices, such as diodes, transistors and vacuum tubes, whose function is processing ...
of the transistor, that is, with the direct current (DC) and voltage applied to the device.
Measurement
The source resistance of a purely resistive device can be experimentally determined by increasingly loading the device until the voltage across the load (AC or DC) is one half of the open circuit voltage. At this point, the load resistance and
internal resistance
A practical electrical power source which is a linear electric circuit may, according to Thévenin's theorem, be represented as an ideal voltage source in series with an impedance. This impedance is termed the internal resistance of the source. ...
are equal.
It can more accurately be described by keeping track of the voltage vs current curves for various loads, and calculating the resistance from
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
. (The internal resistance may not be the same for different types of loading or at different frequencies, especially in devices like chemical batteries.)
The generalized source impedance for a reactive (inductive or capacitive) source device is more complicated to determine, and is usually measured with specialized instruments, rather than taking many measurements by hand.
Audio amplifiers
The real output impedance (Z
S) of a
power amplifier
An audio power amplifier (or power amp) is an electronic amplifier that amplifies low-power electronic audio signals, such as the signal from a radio receiver or an electric guitar pickup, to a level that is high enough for driving loudspea ...
is usually less than 0.1 Ω, but this is rarely specified. Instead it is "hidden" within the
damping factor
Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples inc ...
parameter, which is:
:
Solving for ''Z''
S,
:
gives the small source impedance (output impedance) of the power amplifier. This can be calculated from the ''Z''
L of the loudspeaker (typically 2, 4, or 8 ohms) and the given value of the damping factor.
Generally in audio and
hifi, the input impedance of components is several times (technically, more than 10) the output impedance of the device connected to them. This is called
impedance bridging
In audio engineering and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one in which the load impedance is much larger than the source impedance. The load measures the source's voltage while minima ...
or voltage bridging.
In this case, ''Z''
L>> ''Z''
S, (in practice:) ''DF'' > 10
In video, RF, and other systems, impedances of inputs and outputs are the same. This is called
impedance matching
In electronics, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or minimize signal ...
or a matched connection.
In this case, ''Z''
S = ''Z''
L, ''DF'' = 1/1 = 1 .
The actual output impedance for most devices is not the same as the rated output impedance. A power amplifier may have a rated impedance of 8 ohms, but the actual output impedance will vary depending on circuit conditions. The rated output impedance is the impedance into which the amplifier can deliver its maximum amount of power without failing.
Batteries
Internal resistance
A practical electrical power source which is a linear electric circuit may, according to Thévenin's theorem, be represented as an ideal voltage source in series with an impedance. This impedance is termed the internal resistance of the source. ...
is a concept that helps model the electrical consequences of the complex chemical reactions inside a
battery
Battery most often refers to:
* Electric battery, a device that provides electrical power
* Battery (crime), a crime involving unlawful physical contact
Battery may also refer to:
Energy source
*Automotive battery, a device to provide power t ...
. It is impossible to directly measure the internal resistance of a battery, but it can be calculated from current and voltage data measured from a circuit. When a load is applied to a battery, the internal resistance can be calculated from the following equations:
:
where
:
is the internal resistance of the battery
:
is the battery voltage without a load
:
is the battery voltage with a load
:
is the total resistance of the circuit
:
is the total current supplied by the battery
Internal resistance varies with the age of a battery, but for most commercial batteries the internal resistance is on the order of 1 ohm.
When there is a current through a cell, the measured
e.m.f. is lower than when there is no current delivered by the cell. The reason for this is that part of the available energy of the cell is used up to drive charges through the cell. This energy is wasted by the so-called "internal resistance" of that cell. This wasted energy shows up as lost voltage. Internal resistance is r = (E −
)/I .
See also
*
Impedance
*
Input impedance The input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (the ...
*
Nominal impedance
Nominal impedance in electrical engineering and audio engineering refers to the approximate designed impedance of an electrical circuit or device. The term is applied in a number of different fields, most often being encountered in respect of:
...
*
Damping factor
Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples inc ...
*
Voltage divider
In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (''V''out) that is a fraction of its input voltage (''V''in). Voltage division is the result of distributing the inp ...
*
Early effect small-signal model
*
Equivalent series resistance
Practical capacitors and inductors as used in electric circuits are not ideal components with only capacitance or inductance. However, they can be treated, to a very good degree of approximation, as being ideal capacitors and inductors in series w ...
*
Power gain The power gain of an electrical network is the ratio of an output power to an input power. Unlike other signal gains, such as voltage and current gain, "power gain" may be ambiguous as the meaning of terms "input power" and "output power" is not alw ...
References
*{{cite book, last=Tocci, first=Ronald J., author-link=Ronald J. Tocci, title=Fundamentals of electronic devices, url=https://books.google.com/books?id=dpFYAAAAYAAJ, access-date=27 October 2011, edition=2nd, year=1975, publisher=Merrill, isbn=978-0-675-08771-1, pages=243–246, chapter=11
External links
Calculation of the damping factor and the damping of impedance bridging
Electrical parameters
Audio amplifier specifications