Microwave Engineering 3e Author - D. Pozar

Transcription

1 Microwave Engineering 3e Author - D. Pozar Sections Presented by Alex Higgins 1

2 Outline Section 3.6 Surface Waves on a Grounded Dielectric Slab Section 3.7 Stripline Section 3.8 Microstrip An Investigation of Microstrip Characteristic Impedance Formulae 2

3 Surface Waves on a Grounded Dielectric Slab Surface waves are typified by a field that decays exponentially away from the dielectric surface, with most of the field tightly bound near the surface of the dielectric. Also known as forced surface waves or tightly bound slow surface waves. Geometry of a grounded dielectric slab[4]. 3

4 Transverse Magnetic ( TM ) mode For any nonzero thickness slab, with a permittivity greater than unity, there is at least one propagating TM mode. Dominant mode TM 0 Equation (3.167) Cutoff frequency. Equation (3.168) Field expressions for surface wave in a grounded dielectric slab. 4

5 Transverse Electric ( TE ) mode TE modes can also be supported by the grounded dielectric slab, where the Hz field satisfies the Helmholtz equation. Dominant mode TE 1 Equation (3.174) Cutoff frequency. Equation (3.175) Field expressions for surface wave in a grounded dielectric slab. 5

6 Dominant Mode Comparison Equation (3.167) TM Cutoff frequency. Equation (3.174) TE Cutoff frequency. n TM (GHz) 0 0 TE (GHz)

7 Stripline Supports TEM waves Like the parallel plate waveguide and coaxial lines, can also support higher order TM and TE modes Since TEM mode is dominant an electrostatic analysis sufficiently determines the propagation and characteristic impedance Stripline transmission line (a) geometry. (b) E and H field lines[4]. 7

8 Characteristic Equations for stripline Equation (3.179) Characteristic impedance of a stripline. Equation (3.180) Inverse design formula for a stripline of a given characteristic impedance. (3.179) and (3.180) assume a zero strip thickness, and are quoted as being accurate to about 1% of their exact values. Since the stripline supports TEM mode the attenuation due to dielectric loss is of the same for as that for other TEM lines, i.e. coaxial. The attenuation due to conductor loss can be found by the perturbation method or Wheeler's incremental inductance rule (outlined in Section 2.7). 8

9 Microstrip One of the most popular types of planar transmission lines due to the ease in which they are fabricated and their easy integration with other microwave devices. Exact fields of a microstrip line constitute a hybryid TM-TE wave, however when the dielectric substrate is electrically thin (d >> λ) the fields are quasi-tem. p= c e Cross-sectional geometry for a microstrip transmission line. =k 0 e Where e is the effective dielectric constant of the microstrip line. 9

10 Pozar Characteristic Equations for Microstrip Equation (3.195) Effective dielectric constant Cross-sectional E-field lines for a microstrip transmission line[2]. Equation (3.196) Characteristic impedance of a microstrip line Equation (3.197) Inverse design formula for a microstrip line of a given characteristic impedance. Considering the microstrip as a quasitem line, attenuation is due to both dielectric and conductor losses. 10

11 An Investigation into Microstrip Characteristic Impedance Formulae Motivation Qualitative comparison of three different formulae Large number of papers and books with a wide variety of equations. Which one to use? Pozar From A Designer's Guide to Microstrip Line by Bahl and Trivedi Ulaby From Microstrip Circuit Analysis by Schrader Lee From High Frequency Amplifiers by Carson MATLAB functions written for each formula. Representative physical widths for microstrip lines varied using 1/16 and 1/32 thick FR4 substrate and 1 oz Cu traces. 11

12 Ulaby Lee Cross-sectional geometry for a microstrip transmission line. 12

13 13

14 Conclusions Agreement is seen between Pozar and Ulaby when varying the relative dielectric constant. All three models show agreement in the 1/16 substrate thickness, while they all deviate quite a bit for thicknesses beyond 1/14. Note also that Pozar and Ulaby show agreement in the 1/32 substrate thickness. All three models show agreement for trace widths in the range of in. while, at trace widths less than in. Ulaby and Lee approach infinity. When designing a microstrip transmission line, know the limitations of the formula that you are working with. 14

15 References [1] [2] [3] [4] [5] C. A. Balanis, Advanced Engineering Electromagnetics. Wiley, S. M. Wentworth, Applied Electromagentics - Early Transmission Lines Approach. Wiley, F. Ulaby, E. Michielssen, and U. Ravaioli, Fundamentals of Applied Electromagnetics. Prentice Hall, 6 ed., D. M. Pozar, Microwave Engineering. Wiley, 3 ed., Thomas H. Lee, Planar Microwave Engineering, Cambridge,

16 Questions? 16