Transmission lines are important elements in radio-frequency integrated circuits (RFICs). The design of RFICs, especially at extremely high frequencies such as those in the upper end of the millimeter-wave range, would not be complete, or even optimum, without considering transmission lines. While the use of transmission lines in RFICs is, in general, not appealing due to their relatively large size as compared to on-chip lumped elements, they are inevitable at extremely high frequencies where lumped elements do not behave properly and/or have quality (Q) factors so low that render their effectiveness. Even at low radio-frequency (RF) ranges, where on-chip elements are preferred and used, RFIC designers should make use of the theory of transmission lines to properly implement lumped elements in circuits to achieve certain features. Therefore, it is crucial that RFIC engineers have sufficient knowledge in transmission lines and consider their possible use in RFICs. The basics of transmission lines can be found in various textbooks in electromagnetics, for example, Reference [1]. In this chapter, we will address the fundamentals of transmission lines for both single and multiconductor transmission lines including transmission-line equations and important transmission-line parameters such as characteristic impedance, propagation constant, phase velocity, effective relative dielectric constant, dispersion, loss, distortion, impedance, reflection coefficient, etc. This chapter also discusses synthetic transmission lines and commonly used printed-circuit transmission lines, particularly their use for RFICs.
ESSENTIALS OF TRANSMISSION LINESTo illustrate the possible need of considering transmission lines in RFICs, we consider a very simple interconnect consisting of two conductors, or one conductor and a ground plane, with the input and output of the two conductors connected to a voltage source and a load, respectively, as shown in Figure 4.1. We assume the source produces a sinusoidal signal v S (t) = V S cos(2 ft) at f = 200 MHz, the substrate supporting the interconnect has a relative dielectric constant r = 4.7, and the length of the interconnect is = 0.1 m. As Radio-Frequency Integrated-Circuit Engineering, First Edition. Cam Nguyen.