Output impedance

From Academic Kids

The output impedance, source impedance, or internal impedance of an electronic device is the opposition exhibited by its output terminals to the flow of an alternating current (AC) of a particular frequency as a result of resistance, induction and capacitance.

The impedance at DC (frequency of 0) is the same as the resistance component of the impedance.

It is important to realize that no real device (battery, generator, amplifier) is a perfect source; all have an internal impedance, though this may have negligible effect, depending on the load.

Depending on perspective, this impedance appears in series with a perfect voltage source, or in parallel with a perfect current source (see: Thevenin's theorem, Norton's theorem).

For example, a preamplifier with 100 ohms output impedance means the output voltage signal appears to be in series with a 100 ohm resistor.

Contents

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 1/2 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 versus 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, 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

Missing image
Source_and_load_circuit_Z.png
Image:Source and load circuit Z.png

The real output impedance of a power amplifier is usually less than 0.1 ohm, but this is rarely specified. Instead the value is "hidden" within the damping factor parameter, which is:

<math>

DF = \frac{Z_\mathrm{load}}{Z_\mathrm{source}} <math>

Solving for Zsource,

<math>

Z_\mathrm{source} = \frac{Z_\mathrm{load}}{DF} <math>

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 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 output impedance is not the same as the rated output impedance. A power amplifier may have a rated impedance of 8 ohms, but this does not mean the output impedance is of that value. 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 us model the complex chemical reactions that occur inside a battery. 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:

<math>R_B=\left( \frac{Vs}{I} \right)-R_L<math>

or

<math>R_B=\left( \frac{V_S-V}{I} \right)<math>

where

<math>R_B<math> is the internal resistance of the battery

<math>V_S<math> is the battery voltage without a load

<math>V<math> is the battery voltage with a load

<math>R_L<math> is the total resistance of the circuit

<math>I<math> is the total current supplied by the battery

See also

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