For narrow strips, i.e. w/h < 3.3 (2.2.8) (2.2.3) where For wide strips, i.e. w/h > 3.3 (2.2.9) and under a slightly different value of Z > (63 - 2&) S -0.555 (2.2.10) (2.2.4) Equations 2.2.3 to 2.2.10 are accurate up to about 2 GHz. For higher frequencies, the effect of frequency 4 In practice these are almost always calculated using CAD/CAE programs. Wheeler, H.A. Transmission lines properties of parallel wide strips separated by a dielectric sheet, IEEE Trans, MTT-13 No. 3, 1965. CHAPTER 2.2 Transmission lines dependence of Ee has to be taken into account. An ex- pression often used to evaluate e(f) as frequency (f) varies is Transmission line Transmission line (2.2.11) where h is in millimetres, f is in gigahertz, and Ee is the (Z1/4) 81 (Z/4) 81 value calculated by either Equation 2.2.7 or 2.2.10. Example 2.2.3 Two microstrip lines are printed on the same dielectric (Z/4) 81 (Z/4) 81 substrate. One line has a wider centre strip than the other. Which line has the lower characteristic impedance? Assume that there is no coupling between the two lines. Solution If you refer to Equation 2.2.3 and examine the h/w ratio, Fig. 2.2-8 Expanded view of a short section of transmission line. you will see that Z varies as a function of h/w. Therefore, the line with the lower characteristic impedance will have a wider centre conductor. As you can see for yourself, Equations 2.2.3 to 2.2.11 resistance and inductance associated with it. The re- are rather complicated and should be avoided when sistance is associated with the material of the metal possible. To avoid these types of calculations, we have conductors, effective conductor cross-sectional area included with this book a computer software program and length. The inductance is mainly dependent on called PUFF. With this program, it is only necessary to length and type of material. In addition to these, there decide on the characteristic impedance of the microstrip is capacitance between the two conductors. The ca- or stripline which we require and PUFF will do the rest