Output impedance
Encyclopedia
The output impedance, source impedance, or internal impedance of an electronic device is the opposition exhibited by its output terminals to an alternating current (AC) of a particular frequency as a result of resistance
, inductance
and capacitance
. It is the Thévenin equivalent impedance
looking back into the output terminals.
In the case of a nonlinear device
, such as a transistor
, the term "output impedance" usually refers to the effect upon a small-amplitude signal, and will vary with the bias point of the transistor, that is, with the direct current (DC) and voltage applied to the device.
The small-signal impedance at DC (frequency of 0) is the same as the resistive component of the impedance and is termed output resistance.
No real device (battery
, generator
, amplifier
) is a perfect source; each has an internal impedance, though this may have little practical effect, depending on the circuit and the load.
Depending on perspective, this impedance can be modeled as being in series with an ideal voltage source
, or in parallel with an ideal current source
(see: Thevenin's theorem
, Norton's theorem
, Series and parallel circuits
). Both models are equivalent, and one may choose whichever model is most convenient for analysis.
For example, having a preamplifier with a 100-ohm output impedance means the output voltage signal appears to be in series with a 100-ohm resistor
.
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
. (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.
The real output impedance (Zsource) of a power amplifier is usually less than 0.1 Ω, but this is rarely specified. Instead it is "hidden" within the damping factor
parameter, which is:
Solving for Zsource,
gives the small source impedance (output impedance) of the power amplifier. This can be calculated from the Zload 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
or voltage bridging.
In this case, Zload>> Zsource, DF > 10
In video, RF, and other systems, impedances of inputs and outputs are the same. This is called impedance matching
or a matched connection.
In this case, Zsource = Zload, 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 simply that impedance into which the amplifier can deliver its maximum amount of power without failing.
. 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:
or
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 wasted by the so-called "internal resistance" of that cell. This wasted energy shows up as lost voltage. Internal resistance is r = (E−V)/I .
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
, inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
and capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
. It is the Thévenin equivalent impedance
Electrical impedance
Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...
looking back into the output terminals.
In the case of a nonlinear device
Nonlinear device
In an electric circuit, a nonlinear element or nonlinear device is an electrical element which does not have a linear relationship between current and voltage. A diode is a simple example...
, such as a transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...
, the term "output impedance" usually refers to the effect upon a small-amplitude signal, and will vary with the bias point of the transistor, that is, with the direct current (DC) and voltage applied to the device.
The small-signal impedance at DC (frequency of 0) is the same as the resistive component of the impedance and is termed output resistance.
No real device (battery
Battery (electricity)
An electrical battery is one or more electrochemical cells that convert stored chemical energy into electrical energy. Since the invention of the first battery in 1800 by Alessandro Volta and especially since the technically improved Daniell cell in 1836, batteries have become a common power...
, generator
Electrical generator
In electricity generation, an electric generator is a device that converts mechanical energy to electrical energy. A generator forces electric charge to flow through an external electrical circuit. It is analogous to a water pump, which causes water to flow...
, amplifier
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...
) is a perfect source; each has an internal impedance, though this may have little practical effect, depending on the circuit and the load.
Depending on perspective, this impedance can be modeled as being in series with an ideal voltage source
Voltage source
In electric circuit theory, an ideal voltage source is a circuit element where the voltage across it is independent of the current through it. A voltage source is the dual of a current source. In analysis, a voltage source supplies a constant DC or AC potential between its terminals for any current...
, or in parallel with an ideal current source
Current source
A current source is an electrical or electronic device that delivers or absorbs electric current. A current source is the dual of a voltage source. The term constant-current sink is sometimes used for sources fed from a negative voltage supply...
(see: Thevenin's theorem
Thévenin's theorem
In circuit theory, Thévenin's theorem for linear electrical networks states that any combination of voltage sources, current sources, and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems the theorem...
, Norton's theorem
Norton's theorem
Norton's theorem for linear electrical networks, known in Europe as the Mayer–Norton theorem, states that any collection of voltage sources, current sources, and resistors with two terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor, R...
, Series and parallel circuits
Series and parallel circuits
Components of an electrical circuit or electronic circuit can be connected in many different ways. The two simplest of these are called series and parallel and occur very frequently. Components connected in series are connected along a single path, so the same current flows through all of the...
). Both models are equivalent, and one may choose whichever model is most convenient for analysis.
For example, having a preamplifier with a 100-ohm output impedance means the output voltage signal appears to be in series with a 100-ohm resistor
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
.
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 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
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
. (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 (Zsource) of a power amplifier is usually less than 0.1 Ω, but this is rarely specified. Instead it is "hidden" within the damping factor
Damping factor
In audio system terminology, the damping factor gives the ratio of the rated impedance of the loudspeaker to the source impedance. Only the resistive part of the loudspeaker impedance is used. The amplifier output impedance is also assumed to be totally resistive...
parameter, which is:
Solving for Zsource,
gives the small source impedance (output impedance) of the power amplifier. This can be calculated from the Zload 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
Impedance bridging
In electronics, especially audio and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one which maximizes transfer of a voltage signal to the load...
or voltage bridging.
In this case, Zload>> Zsource, DF > 10
In video, RF, and other systems, impedances of inputs and outputs are the same. This is called impedance matching
Impedance matching
In electronics, impedance matching is the practice of designing the input impedance of an electrical load to maximize the power transfer and/or minimize reflections from the load....
or a matched connection.
In this case, Zsource = Zload, 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 simply that impedance into which the amplifier can deliver its maximum amount of power without failing.
Batteries
Internal resistance is a concept that helps model the electrical consequences of the complex chemical reactions inside a batteryBattery (electricity)
An electrical battery is one or more electrochemical cells that convert stored chemical energy into electrical energy. Since the invention of the first battery in 1800 by Alessandro Volta and especially since the technically improved Daniell cell in 1836, batteries have become a common power...
. 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:
or
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 batteryInternal 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.
Electromotive force
In physics, electromotive force, emf , or electromotance refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.It is important to note that the electromotive "force" is not a...
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 wasted by the so-called "internal resistance" of that cell. This wasted energy shows up as lost voltage. Internal resistance is r = (E−V)/I .
See also
- ImpedanceElectrical impedanceElectrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...
- Input impedanceInput impedanceThe input impedance of an electrical network is the equivalent impedance "seen" by a power source connected to that network. If the source provides known voltage and current, such impedance can be calculated using Ohm's Law...
- Damping factorDamping factorIn audio system terminology, the damping factor gives the ratio of the rated impedance of the loudspeaker to the source impedance. Only the resistive part of the loudspeaker impedance is used. The amplifier output impedance is also assumed to be totally resistive...
- Voltage divider
- Early effect#Small-signal model