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2.11 Transmission lines – Design and Practical Realisation 109 This means that the signal propagates at different speeds above ( ) and below ( √ ⁄ ) the signal line and this influences the direction of the fields also. Nevertheless, if the cross-section geometrical size of the microstrip line is much smaller than the wavelength of the signal 22 , we may assume that the signal propagates approximately in a TEM mode. This type of propagation is called quasi-TEM. Figure 2.11-8 Electric and Magnetic Fields in a microstrip line This assumption allows us to analyse the microstrip line as if it comprised of a homogenous medium supported by 2 conductors, just as in the case of TEM. The dielectric constant of this fictitious homogenous medium is assigned an effective dielectric constant which is typically 50- 85% of the substrate dielectric constant . Equation (2.11-5) shows how may be calculated 23 . √ ⁄ The characteristic impedance of the line may then be calculated by means of equation (2.11-6). { √ ( ) ⁄ √ [ ( ⁄ ) ⁄ ] ⁄ Also, the velocity of propagation along the line and effective wavelength become √ ( ) √ ( ) With microstrip you usually start with a specific characteristic impedance that you aim to achieve, then pick a substrate with dielectric constant and height and calculate the width that the line needs to be to achieve the desired impedance. A more useful formula than (2.11-6) would therefore be one which allows us to calculate given , and . This formula does exist but it is quite complex! An easier way to design a microstrip line is to use the TXLine tool included in Microwave Office shown in figure 2.11-9. 22 As a rule of thumb, in order to prevent higher-order transmission modes affecting the wave propagation, you should limit the thickness of your microstrip substrate to 10% of a wavelength. 23 In some textbooks two different expressions are given for , when ⁄ and ⁄ however the difference is usually very small and, due to the empirical nature of the equations, often negligible. We follow the Pozar approach which only uses one formula for (2.11-6) (2.11-5) (2.11-7) Conquer Radio Frequency 109 www.cadence.com/go/awr