5.2.1.2. Cable 2This aluminium/mylar-foil cable is a two-wire cable cable that is wrapped in a double layer of aluminium and mylar foil. There is usually also a third, uninsulated, conductor accompanying the other two, because it is difficult to make a good electrical connection to the aluminium foil. we assume here that this drain wire conductor may be treated as part of the foil screen, since it has innumerable points of contact with the aluminium. The transfer impedance shown in Figure 5.6 was measured between the foil sheath and the inner conductors connected in parallel. This impedance fits the model of equation (5.2). The LF value (48 m) is relatively high due to the relatively high resistance of the aluminium foil. The corner frequency is low (225 kHz), because the double layer has relatively large openings between the turns. If we once again assume that Lc2 = 1 H, the k value is found to be 0.966. Compared with k = 0.996 for cable 1, this difference may not seem large. What matters, however, is (1-k); and for cable 2 this value is nine times larger than that for cable 1.With this cable a sheath current causes a common-mode disturbance in the wanted circuit, of which the two inner conductors form a part. The unwanted voltages across components in that circuit now depend on the extent to which the common-mode disturbance is coupled into it. Cable 2 is an example of a screened cable, since the sheath is not one or the signal conductors.5.2.1.3 Cable 3This semi-rigid coax cable has a sheath of solid copper foil. Since the sheath has no openings in it (it is 100% optically closed) the impedance is determined by the common impedance of the sheath, as discussed in Section 5.2. Clearly, the skin effect can greatly reduce the transfer impedance. The influence of skin effect becomes noticeable when the skin depth becomes less than the thickness of the sheath. In Figure 5.6 that ocsurs at 100 kHz. At high frequencies the magnitude of ZT decreases with inereasing frequency, according to (Vance. 1978). 5.2.1.4 Cables 4, 4A And 1A The double-braided coax cable (4 and 4A) has, as the name implies, a second braided sheath over the first one. There is no insulation between these two sheaths. The use of two sheaths causes the optical coverage to approach that of the solid sheath. As a result the cable behaves at first like cable 3, but must at high frequencies admit that there are still tiny openings. The impedance here, however, is about 80 times smaller than that of cable 1. Equation (5.2) would appear also to apply here. That is actually correct for the magnitude of ZT; the phase relationships deviate, however (Demoulin et al., i981). The LF value of ZTG is about half of that for the single-braid cable, as one might expect. In situations where the coax cable with a single-braid sheath does not have to be particularly flexible, the braiding may be woven so tightly that there is noticeable skin effect in a certain frequency range (see cable 1A). The remnant inductance of 1A is about 10 times lower than that of cable 1. The double-braided cable may be optimized in this way (cable 4A).5.2.1.5 Cables 5 The triax-braid cable, triax cable for short. also, has two braided sheaths there is, however, now insulation (dielectric) between these two sheaths. If in Figure 5.6 we follow the dashed line from about 8 MHz, we see the same behaviour as for the coax cable with two braided sheaths. The resonances shown therefore belong to ZTG, and not to ZT! The resonances result from the fact that the transmission line, formed by the two braid sheaths with the dielectric between them, was not characteristically terminated but short-circuited during the measurement, owing to the connectors that were used. The result was resonances in this transnission line of the signal coupled in via the associated transfer impedance, which in turn coupled through to the transmission line formed by the core conductor and the inner sheath. The ZT for this triax cable (valid for an element of infinitesimal length) will not show any resonances. In a practical application of the cable, however, these phenomena may definitely occur if the transmission line formed by the two braided sheaths is not characteristically terminated. A double-braided coax cable does not show these effects, because the two sheaths are woven one atop the other. ln many applications the latter cable is therefore far more reliable, with an almost equally low ZT. 5.2.1.6 Cable 6 And 7 This type of coax cable, often referred to as super screen cable (Martin, 1982), has two or more braid sheaths (cable 6 has two, cable 7 three) with a conductive foil of relative permeability r > 1 (mu-metal) between each pair of braids.One observes that the transter impedance of these cables decreases more rapidly with increasing frequency than does that or semi-rigid coax cable. This is the result of the high r value of the mu-metal, which at low frequencies causes the skin depth to become less than the (total) sheath thickness, so that the skin effect acts to separate the current loops. Cable 6, with two braids and a single layer of mu-metal, leaks slightly above 1 MHz because the braids and the foil none the less have (tiny) openings.The five-layer structure (cable 7) is so well closed that the skin effect remains he winner. At high frequencies, admittedly, the mu-metal loses its high r value; but at these frequencies the skin thickness is already sufficientiy small without the help of a high r.With the exception of cable 2 all the cables discussed are of the coaxial type. That does not mean that the trensfer impedance is only relevant to coax cables. One may alno encounter, transfer impedances with ordinary twin-flex. ribbon cables. twin-axial cables - in short with all cables. It is difficult to measure zr accurately. The first difficulty is a condition that may be derived from equation (5.4). The transfer iepedance Z12 follows, one wili observe, from the voltage across the length element dz and the current I2 for I1 = 0, meaning that the voltage measurement must be 'current free, which is something of an exercise, particularly at high frequencies. Zr is therefore usually derived from a crosstalk measuremeet (I1 0). as for the IEC method (1988). A second difficulty is the fact that the Impedance is not determined exclusively by the cable. The surroundings of the cable are also part of the picture, just as with the calculations of inductance and capacitance in Section 3.2.3. If the starting point for the measurement is weal-defined surroundings, which is sensible, the impedance in the apalication situation is not necessarily the same, so that really a correction is needed. In the case of a Zr measurement om coax ceble the sheath may sometimes form the inner conductor of a coaxial measurement system, which can be characteristically terminated (IEC, l988). The surroundings are now well defined, as is the current I in the length direction or the cabic sheath. In many EMC discussions it is not necessary to know the exact value or Zr, since the uncertainties in the further description of the problem may have a much larger effect on the result (this does not of course imply a Iiccnce to throw all accuracy overboard). Merely giving a good EM description of the surroundings of a cable is already difficult enough: the fact that a cable runs through the air, across a concrete floor, in a metal cable trunk, in a cable harness, etc., has to be translated into EM quantities. Moreover, the surroundings are changed as soon as one moves the cable. It is nevertheless important to make a good estimate for zr, which is possible with the simple setup of Figure 5.7.Figure 5.7(a) shows a photograph of the measuremet setup. 5.7(b) the basic circuit diagram and 5.7(c) the circuit diagram for calculation purposes. The setup is almost the same as that of Figure 4.16. The only difference is that the leads af the connector to which the voltmeter is connected have been interchanged. If, for example, a coax cable is being measured, the inner canductor will normally be connected to the cenrre pin of thnt connector. whereas in Figure 4.16 the inner conductor was connected to the reference. The photograph shows the measurement of a semi-rigid coax cable. At the 50 resistor end the inner and outer conductors are shorted together. A weil-fittiag SMA Figure 5.7 (a) Measurcment setup for simply estimating the transfer impedance (b) basiccircuit diagram; (c) calculation circuit diagram.connector is soldered at the voltmeter end, which keeps the sheath EM wavetight' and which makes good contact with the reterence (the L-shaped netal strip). This way of doing things keeps the influence of the transter impedance of the end terminations (Section 5.2.2) on that of the cable proper negligible. If U0 = Ug/2 and U1 is the voltage measured in the setup of Figure 5.7, then ZTG may be round from

The approximate value applies if the contributions of L1, L2 and M to the loop impedances may be neglected and I1ZTG