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Electromagnetic Field Theory

by: Mr. Chelsie Bergstrom

Electromagnetic Field Theory EEL 6486C

Mr. Chelsie Bergstrom
GPA 3.57

Stephen Saddow

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Stephen Saddow
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This 26 page Class Notes was uploaded by Mr. Chelsie Bergstrom on Wednesday September 23, 2015. The Class Notes belongs to EEL 6486C at University of South Florida taught by Stephen Saddow in Fall. Since its upload, it has received 31 views. For similar materials see /class/212713/eel-6486c-university-of-south-florida in Electrical Engineering at University of South Florida.


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Date Created: 09/23/15
Planar Transmission Lines EEL 6486 EM Theory I Lecture 17 S E Saddow November 5 2002 Don t forget to VOTE Reviewing The Basics Of Microstrip Lines An understanding of the fundamentals of microstrip transmission lines can guide highfrequency designers in the proper application of this venerable circuit technology By Leo G Maloratsky Principal Engineer see course website for link Why Planar TX Lines PRINTED transmission lines are widely used and for good reason They are broadband in frequency They provide circuits that are compact and light in weight They are generally economical to produce since they are readily adaptable to hybrid and monolithic integrated circuit IC fabrication technologies at RF and microwave frequencies To better appreciate printed transmission lines and microstrip in particular some of the basic principles of microstrip lines will be reviewed here HES lines Modi cations W a Hewi E t E 1 11quot a39 E 39 Im wrza 3 H w a H 3 m L W E Micrustrip Iina mm g m micw p m Sh idldedmicmsari p line a L 5 5 1r 1 1 2quotfWI E 13 1h w E Str ipling Unuhlecundumm stripline 2 quotan 11 F39h i H WzizmI HWt11b u i 7 7 7 i a mi lta 51 3 5 1 a r I b Shielded du hum Shielded suspended an spanned gimme Shielded suspended slnplme dwhlemhmale Winn g r H W gt armS la IWH jr 3 Edgy1quot H a ai39af in 3mmquot dutipnda slumMina Bilateral linllnn Lu wags quot4 a Sm i wt quot1 am A 53 J3 quot h D I my U m S mmalnnal 3 7539 r coplanar line Shiedded cuplanar waveguide r 141 h t quot a In I l E H a H 39at a H H a rI 5 3quot Finline Ei ateral sledding Antipodanl linline mm m 39nmee am39n In a microstrip line the guide wavelength A is given by A XEEFFV S where 8 EFF the effective dielectric constant which depends on the dielectric constant of the substrate material and the physical dimensions of the microstrip line and 7 the freespace wavelength In a microstrip line the electromagnetic EM elds exist partly in the air above the dielectric substrate and partly Within the substrate itself Intuitively 8 EFF of the line is expected to be greater than the dielectric constant of air 1 and less than that of the dielectric substrate 169 1 lt 8 EFF lt 3 SUBSTRATE remit5 1 I11 III M IIMI M L 2J1 LEI WWI Various curves for effective dielectric constant are shown in Fig 2 as a function of physical dimensions and relative dielectric constant Referring again to Fig 1 it should be apparent that a basic unshielded microstrip line is not really a practical structure It is open to the air and in reality it is desirable to have circuits that are covered to protect them from the environment as well as to prevent radiation and EM interference EMI Covering the basic microstrip con guration with metal top plates on the top and on the sides leads to a more realistic circuit con guration a shielded microstrip line with a housing Fig 1 20mm 250 Low m w Isa Hugh Medium High so a 200 20 a 250 The main purposes of the housing or package are to provide mechanical strength EM shielding hermetization and heat sinking in the case of highpower applications 9 An MIC mounted into a housing may be looked on as a dielectrically loaded cavity resonator Fig 3 left with the following inner dimensions a is the width 1 is the length and H is the height of the enclosure These dimensions should be selected in a way so that the waveguide modes are below cutoff Can you think of why this should be so Wannergm m mm Fig 3 Housing dimensions are selected for microstrip circuim left to minimize losses The effects of unfavorable housing height versus wavelength and different parasitic modes is shown right The parasitic niodes appear in this resonator if H NH q HsHRMR H L where R an i swigw l 1 N inquot I ran and M and N positive integers From eq 2 it is possible to obtain the condition of absence of parasitic modes R 1 lt 0 R lt1 1 or Af e Mint1quot r t N m3 H or it lt grimm1 3 us myquot 3 m Equation 4 is known as the condition for wave propagation in a waveguide with dimensions 1 X a In the case of this article it can also be considered the condition for the absence of parasitic modes in a waveguide of crosssection a X H or 1 X H If eq 4 is not satis ed parasitic modes can arise and the height H must be chosen to suppress these modes Figure 3 right illustrates the resulting graphs of unfavorable H versus k0 for housing dimensions of a 24 mm 1 30 mm and dielectric substrate with a dielectric constant of 98 and THK of 05 mm The top and side covers essentially redistribute the eld of the more theoretical microstrip and understandably have an in uence on the effective dielectric constant Figure 4 shows the relationship between the effective dielectric constant and the physical dimensions of the shielded microstrip line for different values of the relative dielectric constant of the substrate material IiMm In these curves its assumed that the side walls are suf ciently spaced so they only see weak fringing elds Therefore they have a negligible effect on 8 EFF Top cover tends to lower 8 EFF which is consistent with intuition The top wall enables electric elds in the air above the strip conductor thereby giving air more in uence in determining prop characterlisstics The characteristic impedance of a microstrip line may be approximately calculated by assuming that the EM eld in the line has a quasi transverseEM TEM nature The characteristic impedance of a microstrip line can be calculated using the Wheeler equations n E Fig 5 The characteristic line impedance has been plotted for substrates with high a and law b dielectric constanm Figure 5 shows the characteristic impedance of microstrip lines for various geometries and substrates of different relative dielectric constants Fig 6 illustrates the relationships between characteristic impedance and the physical dimensions of shielded microstrip lines for two examples substrates with low 2 and high 96 relative dielectric constants C m a 1m l g g 15a 3 a E E1131 E E E g 111m 13 2 2 a E E TI U m W l39ll 39l th Fig 6 These plots show the relationship between the characteristic impedance and the physical dimensions of microstrip lines using substrates With high 96 left and low 20 right 8 1 3 1 5th 3114 Jquot l Th l lz v 1 The top cover tends to reduce the impedance When the ratio of the distance from the top cover to the dielectric substrate and the substrate thickness H hh is greater than 10 enclosure effects can be considered negligible The characteristic impedance range of a microstrip line is 20 to 120 The upper limit is set by production tolerances While the lower limit is set by the appearance of higherorder modes 20 Three types of losses that occur in microstrip lines conductor ohmic losses 06C dielectric losses ocd and radiation losses OCR Microstrip line being open to a semiin nite air space acts like an antenna and tends to radiate energy Substrate materials with low 8 5 used when cost reduction is priority Similar materials used at MMW frequencies to avoid excessively tight mechanical tolerances Lower e gt lower concentration of energy in substrate region hence OCR T OCR depends on 8 the substrate thickness and the circuit geometry 21 The use of highdielectricconstant substrate materials reduces radiation losses because most of the EM eld is concentrated in the dielectric between the conductive strip and the ground plane The real bene t in having a higher dielectric constant is that the package size decreases by approximately the square root of the dielectric constant can you tell me WHY This is an advantage at lower frequencies but may be a problem at higher frequencies If tan is high then OCR low but ocd high one of many tradeoffs 22 To minimize 06C tMETAL 35 X skin depth 5 In a microstrip line ocC increases with increasing ZO due to the greater resistance of narrow strips 06C follows trend which is opposite to OCR with respect to Wh The fabrication process of real microstrip devices creates scratches and bumps on the metal surfaces The current concentrated metal surface next to substrate follows uneven surface of substrate and encounters greater resistance compared to case of smooth substrate As roughness of surface increases current path length increases 06C increases 23 The rapid development of highdensity modules requires the design of interconnects and transitions especially for multilayer circuits Consider useful transitions from microstrip to other printed transition lines A transition between two microstrip lines Fig 9a can be realized through a slot in the ground plane 24 Fig 9 Various transitions between microstrip and other circuit structures are possible microstrip to microstrip a microstrip to suspended stripline b microstrip to slotted line c and microstrip to coplanar waveguide d 5 Lets look at some sample hardware Then some interesting work done by yours truly over 10 years ago that shows an interesting merger of EM theory and techniques with modern optoelectronics and solidstate devices can be bene cial 26


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