Lossy transmission lines

Lossy Transmission Lines. For lossy transmission lines, the conductor resistance, fl, and dielectric conductance, G, must be considered. The assumption G a)C is usually valid, because the dissipation factor, tan 8 = G/wC, is usually less than 0.01 for most packaging dielectrics (although the dissipation factor may become larger at very high frequencies). For high... 

Figure 11. Idealized input and output signals on a lossless and a lossy transmission line of length 1. Rise time (tr) is defined as the time between the 10 and 90% voltage levels. Other abbreviations are defined in the text.

The MMW region of the electromagnetic spectrum is characterised by quasi-optical electronic components for generation, transmission and detection. MMW sources and detectors are typically semiconductor devices with transmission lines of open tube rectangular waveguide, or coaxial cable at frequencies below 30 GHz. The cables are rather lossy and waveguide is the favoured transmission line for any other than the shortest links or where dielectric loss is less critical than mechanical flexibility, e.g. connecting to a frequency counter. 

In a termination, power is absorbed by a length of lossy material at the end of a shorted piece of transmission Hne (Fig. 4.24(a) and Fig. 4.23(c)). This type of termination is called a matched load as power is absorbed and reflections are very small irrespective of the characteristic impedance of the transmission line. This is generally preferred as the characteristic impedance of transmission lines varies with frequency, particularly so for waveguides. When the characteristic impedance of a hne does not vary much with frequency, as is the case with a coaxial hne, a simpler smaller termination can be reahzed by placing a resistor to ground (Fig. 4.24(b)). 

For a lossy transmission fine due to parasitic resistance of on-chip interconnects, an exponential attenuating transfer function can be applied to the signal transfer at any point on the transmission line. The rate of the attenuation is proportional to the unit resistance of the interconnect. When operating frequency increases beyond a certain level, the on-chip transmission media exhibits the skin effect in which the time-varying currents concentrate near the skin of the conductor. Therefore, the unit resistance of the transmission media increases dramatically. 

Wedepohl, L. M. and A. E. Efth5miiais. 1978. Wave propagation in transmission line over lossy ground—Anew complete field solution. IEEE Proc. 125(6) 505-510. 

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