Glossar

Characteristic Impedance

Whoever has seen a picture on their television with double outlines (ghosting), or failed to get a connection on their ISDN telephone or data link because of faulty termination impedance, or stood in front of a damaged microwave in which unsuitable crockery has been placed, has been a witness to a mismatch and indeed mismatches from characteristic impedance which is the result of damaging reflection s. It is not only the so called performance matching between an electrical generator and a consumer load, which is necessary to pass on the maximum performance from the source but also the matching of a running interconnection at the source on one side and at the load on the other side which is responsible for the avoidance of temporally reflections. Since it is scarcely possible to match impedance (the name for a general complex resistance) from one end of a circuit to the other, the designated circuit with its characteristic impedance is given the value of the source and load impedance, which is necessary for reflection free, undisturbed signal transmission. The designation of the characteristic impedance of cable, frequency independent in Ω shows that the model or rather the approximation of a low loss or loss free set-up is the basis. However, it cannot be denied that it is the reactive part of the conductor geometry (inductance and capacitance) which oppose the propagation of current and voltage state (the so called waves) resistance. Their size is intrinsically controlled through the geometry, ohmischer looped resistance and isolation loss and for real audio current generally negligible. Due to the fact that the geometry of RCA connectors, the bodies of which are conductors, have in their base form a feasible resistance of between 15 Ω and 45 Ω in the best case, must the full metal form be designed as a bifilar arrangement, in consideration of the geometric dimensions, so that, with a 75 Ω characteristic impedance, a reflection free operation with a suitable cable can be made. Characteristic Impedance
Surge Impedance
Any signal path should be configured in that way, that source ↔ connection elements ↔ transmission line connection elements ↔ load all have identical (characteristic) impedance (i.e. the commonly complex form of a general resistance). The small signal connections of audio devices for instance are obviously suited for engaged steps in this direction. Such steps are supported by the established technology of broad band transmission and measurement. They offer well proved connection and transmission elements with defined characteristic impedance values (50 Ω, 75 Ω, ., ... )
Fig.1: Phenomenology of transmission line The characteristic impedance of an electrical topology – in our case that of a line element – will be evaluated numerically in 'Ohm' like any other resistance, regardless whether it is purely resistive, reactive, or complex, but that is the only property it has common with the evaluation of discrete electrical components. In all cases of discussing electrical arrangements where the propagation velocity of voltage and current states within the topology is of importance the phenomena of wave propagation have to be considered. This requirement applies for power lines, data highways, microstrip devices, etc. and of course hifi connections. There are two principally different ways to become familiar with the understanding of the time and space depending properties of wave propagation on transmission lines. One approach is offered by the network theory by modelling the line by elements derived from the discrete passive elements R, L, and C. But for our purposes another way, the physically based phenomenological approach will better meet our simpler requirements. Look at Fig.1: When connecting a voltage Ua to the input a-a' of a line (coax, twisted pair …) then a current Ia(t=0) will flow into this port. This current will not depend on the condition defined at the port e-e', it may be short circuit, open-circuit or terminated any way. Only after a certain time tl (1 to 2 ns for 30 cm connection length for instance) the input state reaches the port e-e' (lossless line assumed). If this port is connected to an impedance Ze=Ua/Ia everything is in order. The current Ia may go out as Ie and the voltage Ua may go on to feed Ia into the input. For all other cases, short circuit, open-circuit or line terminated with an impedance Ze ≠ Ua/Ia, at e-e' a correcting state will be generated which corresponds to conditions at e-e'. I.e. for instance that at an open circuit end will generate a state –Ia into direction a-a' because at an open circuit the current has to be zero. This correction state arrives after a time tl at a-a' and superposes the current Ia(2 tl ) going in there at this time. The resistance – commonly impedance - a line opposes states streaming in or surging in is called surge impedance or characteristic impedance (derived from network theory). The phenomenological point of view gives an evident insight to our main problem discussed here: the insertion of plug connections into a transmission line. As result we can state that we have to avoid any mismatch (Zplug ≠ Zline ) of impedances within the chain defined in the first sentence of this section. As shown any mismatch will generate multiple reflections at all points of impedance imparity and cause measurable and hardly measurable but audible distortions. The best way to achieve the necessary impedance matching for a sufficient frequency range is to aim at broadly used impedances (e. g. 75 Ω). The specification of cable impedances, frequency independent in Ω, suggests that the base generally used is the lossless or low loss approach. It is not only the so called power matching between an electrical generator and its load, which is necessary to get the maximum power from the source, but also the matching of a time consuming transmission line to the source at one end and to the load at the other end, which is responsible for the avoidance of temporally resoluted reflections. Since it is scarcely possible to match a transmission line to different impedances (the name for a complex resistance) at each of its ends, the characteristic impedance of the used transmission line will define the source impedance as well as the load impedance to obtain the desired reflection free and undisturbed signal transmission.
The designation of the characteristic impedance of a cable, frequency independent in Ω shows that the model respectively the underlying approximation commonly used is that of a low loss or lossless device. Nevertheless it should not be forgotten that the reactive parts defined by the line or connector geometry (inductance and capacitance) oppose the propagation of current and voltage states (the so called wave) resistance. Their size is intrinsically controlled through the geometry. Loop resistance and isolation loss are, for audio lines, generally negligible. Due to the fact that the given geometry of a RCA connection - which is an essential part of the transmission device discussed here - in its basic form allows characteristic impedances between 15 Ω and 45 Ω the full metal form had to be rearranged as a bifilar design in order to achieve reflection free operation in widely used 75 Ω surroundings.