Crosstalk Between Coaxial Transmission Lines

Abstract

The general theory of coaxial pairs was dealt with in an article on "The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields" by S. A. Schelkunoff (B. S. T. J., Oct., 1934). The present paper considers a specific aspect of the general theory, namely, crosstalk.Formulae for the crosstalk are developed in terms of the distributed mutual impedance, the constants of the transmission lines and the terminal impedances. Some limiting cases are given special consideration. The theory is then applied to a few special types of coaxial structures studied experimentally and a close agreement is shown between the results of calculations and of laboratory measurements.If the outer members of coaxial pairs are complicated structures rather than solid cylindrical shells, the crosstalk formulae still apply· but the mutual impedances and the transmission constants which are involved in these formulae must be determined experimental1y since these quantities cannot always be calculated with sufficient accuracy.The crosstalk between coaxial pairs with solid outer conductors rapidly decreases with increasing frequency while the crosstalk between unshielded balanced pairs increases. In the low frequency range there is less crosstalk between such balanced pairs than between coaxial pairs but at high frequencies the reverse is true. The diminution of crosstalk between coaxial pairs with increasing frequency is caused by an ever increasing shielding action furnished by the outer conductors of the pairs.Finally, crosstalk in long lines using coaxial conductors is discussed and the conclusion is reached that, unlike the case of the balanced structure, the far-end crosstalk imposes a more severe condition than the near-end crosstalk in two-way systems which involve more than two coaxial conductors.

Crosstalk Between Finite Ground Coplanar Waveguides Over Polyimide Layers for 3-D MMICs on Si Substrates

“…This behavior (nonmonotonic increase) observed in the forward coupling for both highand low-silicon wafers is not similar to results presented in literature for coupled transmission lines such as microstrips [15], [21]. In this case, it is believed that the forward and backward coupling when is due to indirect coupling, as described by Schelkunoff and Odarenko [22]. This indirect coupling is a result of a parasitic mode due to the ground planes of each FGC line that create a third transmission line.…”

Coupling between microstrip lines embedded in polyimide layers for 3D-MMICs on Si

“…The magnitude of the forward coupling for shielded microstrip lines with different coupling lengths varies with frequency in a similar manner as shown in Figure 3, which is for unshielded coupled microstrip lines, and to a first order, the forward coupling increases linearly with coupling length. These results agree with the general conclusions for coupling between weakly coupled transmission lines [11], which shows that the shielding structures do not change the basic physics that cause coupling. The effect of shielding structures on the coupling level between parallel microstrip lines fabricated on the same layer, as shown in Figure 1a, is summarized in Figure 5.…”

“…Presented results are backward coupling defined as -20*log|S 41 | and forward coupling defined as -20*log|S 31 |. Note that the definition for forward coupling presented here differs from the definition typically used in the literature which is S 31 /S 21 [11], but if the coupling and attenuation for the lines is very small, |S 21 | is approximately equal to one and the two definitions are equivalent. Also, backward coupling is often called near end coupling and forward coupling is often called far end coupling in the literature [11].…”

Coupling between microstrip lines with finite width ground plane embedded in thin-film circuits

“…4, IS4d has a periodic frequency dependence and a component that increases monotonically with frequency. Both of these characteristics is an indication that there are two components of coupling, direct coupling and indirect coupling through phantom circuits or, as they are now commonly called, parasitic modes [28]. This is not surprising because the coupled, finite width ground plane microstrip lines shown in Fig.…”

“…4, it is noted that IS3d increases monotonically with frequency, but it does not increase smoothly as is typical of coupling between two TEM transmission lines [28] and coupled microstrip lines [17]. Backward coup ling, IS4d, of two TEM transmission lines should have a series of maxima of the same magnitude and a periodicity dependent on the coupling length, L.…”