Microwave Engineering 3e Author - D....
Transcript of Microwave Engineering 3e Author - D....
February 22, 2011 1
Microwave Engineering 3eAuthor - D. Pozar
Presented by Alex Higgins
Sections 3.6 – 3.8
February 22, 2011 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
February 22, 2011 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].
February 22, 2011 4
Transverse Magnetic ( TM ) mode
For any nonzero thickness slab, with a permittivity greater than unity, there is at least one propagating TM mode.
Equation (3.167) – Cutoff frequency.
Equation (3.168) – Field expressions for surface wave in a grounded dielectric slab.
TM 0Dominant mode
February 22, 2011 5
Transverse Electric ( TE ) mode
TE modes can also be supported by the grounded dielectric slab, where the Hz field satisfies the Helmholtz equation.
Equation (3.174) – Cutoff frequency.
Equation (3.175) – Field expressions for surface wave in a grounded dielectric slab.
TE1Dominant mode
February 22, 2011 6
Dominant Mode Comparison
n TM (GHz) TE (GHz)
0 0 -
1 4.3 2.2
2 8.7 6.5
3 13.0 10.8
Equation (3.174) – TE Cutoff frequency.
Equation (3.167) – TM Cutoff frequency.
February 22, 2011 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].
February 22, 2011 8
Characteristic Equations for stripline
● 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).
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.
February 22, 2011 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=k 0 e
eWhere is the effective dielectric constant of the microstrip line.
Cross-sectional geometry for a microstrip transmission line.
February 22, 2011 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 quasi-TEM line, attenuation is due to both dielectric and conductor losses.
February 22, 2011 11
An Investigation into Microstrip Characteristic Impedance Formulae
● Motivation● Large number of papers and books with a wide variety of
equations. Which one to use?● Qualitative comparison of three different formulae
● 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.
February 22, 2011 12
Ulaby Lee
Cross-sectional geometry for a microstrip transmission line.
February 22, 2011 13
February 22, 2011 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 0.055 … 0.1 in. while, at trace widths less than 0.055 in. Ulaby and Lee approach infinity.
● When designing a microstrip transmission line, know the limitations of the formula that you are working with.
February 22, 2011 15
References
[1] C. A. Balanis, Advanced Engineering Electromagnetics. Wiley, 1989.[2] S. M. Wentworth, Applied Electromagentics - Early Transmission Lines
Approach. Wiley, 2007.[3] F. Ulaby, E. Michielssen, and U. Ravaioli, Fundamentals of Applied
Electromagnetics. Prentice Hall, 6 ed., 2010.[4] D. M. Pozar, Microwave Engineering. Wiley, 3 ed., 2005.[5] Thomas H. Lee, Planar Microwave Engineering, Cambridge, 2004
February 22, 2011 16
Questions ?