Input impedance
In electrical engineering, the input impedance of an electrical network is the measure of the opposition to current (impedance), both static (resistance) and dynamic (reactance), into a load network that is external to the electrical source network. The input admittance (the reciprocal of impedance) is a measure of the load network's propensity to draw current. The source network is the portion of the network that transmits power, and the load network is the portion of the network that consumes power.
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Input impedance
If the load network were replaced by a device with an output impedance equal to the input impedance of the load network (equivalent circuit), the characteristics of the source-load network would be the same from the perspective of the connection point. So, the voltage across and the current through the input terminals would be identical to the chosen load network.
Therefore, the input impedance of the load and the output impedance of the source determine how the source current and voltage change.
The Thévenin's equivalent circuit of the electrical network uses the concept of input impedance to determine the impedance of the equivalent circuit.
Calculation
If one were to create a circuit with equivalent properties across the input terminals by placing the input impedance across the load of the circuit and the output impedance in series with the signal source, Ohm's law could be used to calculate the transfer function.
Electrical efficiency
The values of the input and output impedance are often used to evaluate the electrical efficiency of networks by breaking them up into multiple stages and evaluating the efficiency of the interaction between each stage independently. To minimize electrical losses, the output impedance of the signal should be insignificant in comparison to the input impedance of the network being connected, as the gain is equivalent to the ratio of the input impedance to the total impedance (input impedance + output impedance). In this case,
- (or )
- The input impedance of the driven stage (load) is much larger than the output impedance of the drive stage (source).
Power factor
In AC circuits carrying power, the losses of energy in conductors due to the reactive component of the impedance can be significant. These losses manifest themselves in a phenomenon called phase imbalance, where the current is out of phase (lagging behind or ahead) with the voltage. Therefore, the product of the current and the voltage is less than what it would be if the current and voltage were in phase. With DC sources, reactive circuits have no impact, therefore power factor correction is not necessary.
For a circuit to be modelled with an ideal source, output impedance, and input impedance; the circuit's input reactance can be sized to be the negative of the output reactance at the source. In this scenario, the reactive component of the input impedance cancels the reactive component of the output impedance at the source. The resulting equivalent circuit is purely resistive in nature, and there are no losses due to phase imbalance in the source or the load.
Power transfer
The condition of
The formula for complex conjugate matched is
When there is no reactive component this equation simplifies to as the imaginary part of is zero.
Impedance matching
When the characteristic impedance of a transmission line, , does not match the impedance of the load network, , the load network will reflect back some of the source signal. This can create
Applications
Signal processing
In modern
The input impedance for high-impedance amplifiers (such as
Radio frequency power systems
Signal reflections caused by an impedance mismatch at the end of a transmission line can result in distortion and potential damage to the driving circuitry.
In analog video circuits, impedance mismatch can cause "ghosting", where the time-delayed echo of the principal image appears as a weak and displaced image (typically to the right of the principal image). In high-speed digital systems, such as HD video, reflections result in interference and potentially corrupt signal.
The standing waves created by the mismatch are periodic regions of higher than normal voltage. If this voltage exceeds the
In RF systems, typical values for line and termination impedance are
To maximise power transmission[clarification needed] for radio frequency power systems the circuits should be complex conjugate matched throughout the power chain, from the transmitter output, through the transmission line (a balanced pair, a coaxial cable, or a waveguide), to the antenna system, which consists of an impedance matching device and the radiating element(s).
See also
References
- The Art of Electronics, Winfield Hill, Paul Horowitz, Cambridge University Press, ISBN 0-521-37095-7
- "Aortic input impedance in normal man: relationship to pressure wave forms", JP Murgo, N Westerhof, JP Giolma, SA Altobelli pdf
- An excellent introduction to the importance of impedance and impedance matching can be found in A practical introduction to electronic circuits, M H Jones, Cambridge University Press, ISBN 0-521-31312-0