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Swetha Sharma - NDSU Libraries

1. A O S21 in dB nm al 0 2 4 6 8 10 12 14 16 18 20 Frequency in GHz Fig 5 25 MATLAB response of the lumped element and distributed element low pass filter example This example was fabricated on a copperclad board see Fig 5 26 The fabrication produced a very thin 217 5 Q line of width 0 064 mm This example is very hard to implement practically The thin line that was generated had a tendency to break and was almost invisible This example problem is practically realizable but the implementation is difficult and has a lot of disadvantages because of the thin line that was generated The measured performance of the device is shown in Fig 5 27 The response has many small ripples in it One reason for the ripples might be because the filter is a Chebyshev filter which has ripples in the passband Another reason might be the errors caused by the milling machine in the fabrication of the 217 5 Q line The cutoff frequency was greater than 4 GHz 42 Fig 5 27 ADS display of S21 in dB vs frequency in GHz using the network analyzer 43 Many difficulties were faced while implementing this filter The thin line tended to break even if only a little pressure was put on the fabricated device This device is physically realizable but the fabricated device must be handled carefully The same problem was implemented using CAMDS to check its functionality The detailed procedure to solve the abov
2. Fig 5 10 So in dB vs frequency in GHz for stepped impedance filter using network analyzer The CAMDS software was verified by solving the same example from Pozar as considered above To review the user intends to design a stepped impedance low pass filter having a maximally flat response with a cutoff frequency of 2 5 GHz and a 20 dB insertion loss at 4 GHz The impedance is given as 50 Q the highest line impedance is given as 120 Q and lowest line impedance is 20 Q A microstrip substrate having d 0 158 cm and e 4 2 was to The steps to solve the above problem using CAMDS are as follows 1 Select Stepped Impedance Low Pass Filter from StartHere fig and then press Go 32 2 Enter the order of the filter In the above problem the order of the filter is 6 as shown in Fig 5 11 order ox Please give the order of Filter omen Fig 5 11 Box to input the order of the filter 3 Enter the filter impedance as shown in Fig 5 12 ls Please enter the filter impedance ba cra Fig 5 12 Box to input the filter impedance 4 Enter the highest practical line impedance In the above problem it is given as 120 Q as shown in Fig 5 13 CE lola Please enter the highest Impedance of line Zh h 20 con Fig 5 13 Box to input the highest practical line impedance 5 Enter the lowest practical line impedance In the above problem it is given as 20 Q as given in Fig 5 14 33 BER ox Please enter
3. Q Do you want to see a plot for reflection co efficient Ys frequency E Fig 6 14 Question box 5 Once the user clicks Yes a box will pop up asking for the frequency range As per the example problem from Pozar the frequency range should be 1 GHz to 3 GHz as shown in the Fig 6 15 gt Frequency REGA ETE Frequency from fies Frequency to bes caren Fig 6 15 Box to enter frequency range 6 Enter a frequency of 2 GHz at which the load is to be matched and then press OK as shown in Fig 6 16 ioii Please enter the frequency at which the load is to be matched Pes carca Fig 6 16 Box to input the matching frequency 58 7 A question box asking for the stub type will appear Select the stub type that is required for the design Fig 6 17 shows the stub type as short as given in Pozar stubtype io The shunt stub is Open Fig 6 17 Question box asking for the stub type 8 The command window will generate two solutions for the problem It will calculate the distance of the stub from the load the open circuited stub length and the short circuited stub length in terms of wavelength The output that was generated in the command window is as follows SOLUTION 1 The distance of stub from load in terms of wavelength is 1 104232e 001 The open circuited stub length in terms of wavelength is 3 449746e 001 The short circuited stub length in terms of wavelength is 9 497462e 002
4. 5 32 Question box for the filter configurations ee AE REEL SE et 45 61 A matebhing NETWORK EE 48 6 2 Circuit for Z inside the 1 Ke E 48 6 3 Circuit for Z outside the lrmemcle cnc ncnanaonos 49 6 4 UA e Oe en an 50 6 5 Box to input characteristic mpedance 6 cece cece cece eee ne eee ene e ea eneeenaees 51 6 6 Input box for the deent ge dE A 51 6 7 Question DI aba 51 6 8 Input box asking frequency range 6 cece cece eee ence e eee nee e eens e nee ee aee 52 6 9 Plot of the reflection coefficient vs frequency for the L match using CAMDS 53 6 10 Plot obtained using MATLAB for S31 in dB versus frequency A 6 11 Single stub tuning a shunt stub and b series stb 0 eceeee eee eeeenne eee 56 6 12 Box to enter the value of load mmpedance ccc cece cence ence nese ee eneeeaeens 57 6 13 Box to enter the characteristic impedance iia dt 57 6 14 Question EE 58 6 15 Box to enter the frequency TES lle 58 6 16 Box to input the matching equi di si ada dE 58 6 17 Question box asking for the stub tpe 00 c cece cee ce eee e eee e eee eee ene ena tenets 59 6 18 Plot obtained for the reflection coefficient vs Dreguencx eee e cence 60 6 19 Plot obtained using MATLAB for S31 in dB versus frequency ocoocononccccconccnos 61 7 1 CAMDS start window using Kuroda s Low Pass Filter selected 00000na00ue 64 7 2 Box to input the order of the EE 64 7 3 Box to enter the Ee ET 65 7 e toselectth Tiller EE 65 7 5
5. If Z is outside the 1 jx circle then the circuit in Fig 6 3 is used The 1 jx resistance circle 48 Fig 6 3 Circuit for Z outside the 1 jx circle on the Smith chart is the circle for which r 1 In both configurations the reactive element may be an inductor or a capacitor 1 The value of X and B can be either positive or negative Thus there are four L match circuits for each configuration Consider the Fig 6 2 The impedance seen looking into the matching circuit should be Zo jX 6 1 RL jXL Solving the above equation for X and B gives the following equations A x EL R2 X2 ZoR 62 a R2 X and 1 XiZo Zo X B Ro BR 6 3 Similarly for Fig 6 3 when Z is outside the 1 jx circle the admittance seen looking into the matching network should be equal to Thus 0 1 EE S 6 4 Solving 6 4 for X and B gives the following equations 49 X HyRi Zo Ry Xi and Zo Ry RL B zw Zo The sign of X and B determines if it is a capacitance or an inductance The value of the capacitor or inductor is calculated as follows AL L Se henry and C farad 2TfXc 6 5 6 6 6 7 6 8 To verify CAMDS an example problem from Pozar 1 is solved In this section a user is asked to design an L section matching network to match a series RC load with an impedance ZL 200 j 100 Q to a 100 Q line at a frequency of 500 MHz The steps u
6. lution eS e pe Ze pesas CL Solution S21 in dB ER t i t i t i t t t t 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 Frequency in GHz Fig 6 10 Plot obtained using MATLAB for S34 in dB versus frequency 6 2 Single Stub Tuner In a single stub tuner a transmission line a stub is connected either in parallel or in series with the transmission feed line at a certain distance d from the load It uses a single open circuited or short circuited stub There are two design parameters for the single stub tuner The first one is the location of the stub with reference to the load The second one is the length of the stub line In single stub tuning the distance d from the load and susceptance or the reactance provided by the series or shunt stub are the only two adjustable parameters There are two types of single stub tuning They are as follows 1 single stub shunt tuning and 2 single stub series tuning Fig 6 11 shows the single stub shunt and single stub series tuners The stub is connected in parallel for the single stub shunt tuner and the stub is connected in series for the single stub 55 series tuner The stub can be short circuited or open circuited The open circuited stub length and short circuited stub lengths are as follows 1 lb 4 18 SE tan SCH 6 9 US toe 12 and 7 gt tan ta 6 10 SEI where Yo and B E lo is the length of the open circuited stub and 0 Oort L 0 l is the length of th
7. the stepped impedance performance starts to differ from the lumped element ideal Study of its performance beyond 6 MHz indicates that the microstrip elements no longer provide a satisfactory approximation of the lumped element filter for that higher frequency range If suppressing frequency components in this range were necessary additional filtering would have to be employed The stepped impedance filter that was fabricated is shown in Fig 5 7 29 Fig 5 7 Fabricated stepped impedance filter The actual performance of the filter was obtained using an Agilent E5071C network analyzer as is shown in Fig 5 8 Figs 5 9 and 5 10 show the experimental response obtained using the network analyzer The response that was generated produced a graph that had a cutoff frequency of 2 5 GHz and had more than a 20 dB insertion loss at 4 GHz The response obtained with the fabricated device is consistent with that specified in Pozar Thus this proves that the example problem given in Pozar is realizable in practice The section that follows presents the verification of this same example problem using CAMDS to check its functionality It also explains the complete steps necessary to study such a filter problems using the CAMDS software 30 Fig 5 9 Clear view of the response obtained from the network analyzer 31 S21 dB S21 Responce of Stepped Impedance Filter a l a T 0 5 1 15 2 25 Frequency GHz
8. 3 Box to enter relative permittivity 4 The characteristic impedance is given as 50 Q in the given problem as shown below in Fig 4 4 Characteristic LAJA xi Please enter Z0 Ohms cs Fig 4 4 Box to input the characteristic impedance 5 The given problem has an operating frequency of 2 5 GHz Fig 4 5 gt operating Frequency P T Please enter the operating frequency in Hz h seq omen Fig 4 5 Box to enter the operating frequency 6 A question box will appear asking if the user wants to calculate the loss The user may choose Yes as shown in Fig 4 6 There are two types of loss dielectric and conductor A box will appear asking the user to select the type of loss There are three options dielectric conductor or both as shown in the Fig 4 7 Here the user chooses dielectric Do you want to calculate loss No Fig 4 6 Question box Loss E15 m xj d Do you want to calculate loss Dielectric Conductor P Fig 4 7 Box to select the type of loss for the microstrip 7 The user enters the value of the loss tangent as 0 001 This value is selected to demonstrate the CAMDS software but was not given in the problem ioii Please enter the loss tangent Don con Fig 4 8 Box to enter the loss tangent value 8 The output is displayed in the command window The values that were displayed in the command window are different from the values stated in Bais 4 This difference
9. Aided Microwave Design System CAMDS Department of Electrical and Computer Engineering North Dakota State University 2008 D Bais Computer Aided Microwave Design System CAMDS M S thesis North Dakota State University Fargo ND 2008 TH Lee Planar Microwave Engineering Cambridge University Press 2004 Z Hussain Design of High Frequency and Microwave Amplifiers M S paper North Dakota State University Fargo ND 2007 R G Brown R A Sharpe W L Hughes and R E Post Lines Waves and Antennas The Transmission of Electric Energy John Wiley and Sons Inc New York 1973 K C Gupta Teaching CAD to Microwave Students JEEE Trans Educ vol 33 pp 140 144 Feb 1990 A Azemi and C Stook Utilizing MATLAB in Undergraduate Electric Circuits Courses Proc ASEE Frontiers Educ Conf pp 599 601 1996 10 A Azemi and C Stook Utilizing MATLAB in Graduate Electrical Engineering Courses Proc ASEE Annual Conf session 1532 paper no 01637 1996 11 D Bais and D A Rogers Developing a CAD Tool for Radio Frequency and Microwave Engineering Education Proc ASEE North Midwest Sectional Conf Session 1B paper no 3 2008 12 D Bais User Manual for CAMDS A MATLAB Based Computer Aided Microwave Design System Department of Electrical and Computer Engineering North Dakota State 73 University Fargo ND 2008 13 R E Collin Foundations for Microwave Enginee
10. SOLUTION 2 The distance of stub from load in terms of wavelength is 2 594445e 001 The open circuited stub length in terms of wavelength is 1 550254e 001 The short circuited stub length in terms of wavelength is 4 050254e 001 9 The response obtained for the reflection coefficient vs frequency is as shown in Fig 6 18 It shows the responses for both of the solutions The results obtained using CAMDS are the same as those of Pozar 59 note new toolbar buttons data brushing amp linked plots ep a Play video x 1 Soalution 1 0 3 5 Solution 2 0 8 0 7 0 6 0 5 0 4 0 3 Absolute Reflection Coefficient r 0 2 0 1 1 12 14 16 18 22 24 26 28 3 Frequency Hz 10 Fig 6 18 Plot obtained for the reflection coefficient vs frequency In the above example CAMDS correctly produced the design for a single stub impedance matching network given the source impedance the load impedance and the design frequency As another example consider a source impedance of 50 Q a load impedance of 100 Q and an operating frequency of 1 5 GHz As with the L match this is of educational interest since the 100 Q load impedance can be provided in the laboratory by a 50 Q load as seen through an appropriately designed quarter wavelength impedance transformer The single stub routine in CAMDS returns SOLUTION 1 The distance of stub from load in terms of wavelength is 1 520434e 001 The open circuited stub length in te
11. in the output is due to the significant improvement in the microstrip code introduced in the present work The improvement in the code changed the values 18 of phase velocity guide wavelength the propagation constant beta the filling factor the capacitance per unit length of the line and the dielectric loss The output obtained using the improved code is as given below The Relative Permitivity 1s 2 2 The characteristic impedance is 50 The effective dielectric constant is 1 8712 W d ratio is 3 08117 Operating Frequency in Hz is 2 5e 009 kO per meter is 52 3599 The angular velocity in rad sec is 1 5708e 010 Phase velocity vp in m s is 2 19311e 008 Guide wavelength Lambda_g in meters is 0 0877245 beta in per meter is 71 6241 Filling Factor in Hz is 0 853571 Capacitance per unit length of the line in farads is 9 11946e 011 Dielectric loss in Np m is 0 0672498 The values that were obtained prior to this improvement as stated in 4 in the code are as follows the phase velocity was obtained as 2 30268e 008 the guide wavelength lambda in meters was 0 0921072 B was obtained as 88 8739 the filling factor in Hz was 0 7353228 the capacitance of the line was 8 68553e 011 and the dielectric loss in Np m was 0 0565205 Thus due to the improvements in the code CAMDS generates results that are consistent with those stated in Pozar Note that the user must consider the available number of significant 19 figures in the input da
12. order lumped element prototype through b transmission line equivalent circuit to c microstrip implementation of a stepped impedance filter Table 5 1 Values computed using the substrate described in Table 5 2 Section Characteristic Electrical Microstrip Microstrip Impedance Z Length fl Width W in Length Li in in ohms mm mm L 20 11 80 11 3 2 05 L2 120 33 8 0 428 6 63 L 20 44 3 11 3 7 69 La 120 46 1 0 428 9 04 L 20 32 4 11 3 5 63 Le 120 12 3 0 428 2 41 24 Table 5 2 Electrical and physical properties of the substrate described in Table 5 1 Substrate Conductor Dielectric Substrate Loss Copper Conductivity Constant Thickness Tangent Thickness 4 2 0 158 cm 0 02 1 mil 5 8 x 10 S m The values given in Table 5 1 were confirmed independently using CAMDS ADS and MATLAB The design was simulated using ADS This yielded the results described below The schematic Fig 5 3 which was generated using ADS uses a function var function which is a tuning function used in the ADS software When we simulated the schematic without the var function the response which we obtained was different from that of Pozar 1 and from the MATLAB result Example 8 6 in Pozar specifies that there be more than a 20 dB insertion loss at 4 GHz ADS did not obtain this result Thus the var function was used to tune the values of the lengths and the widths to obtain t
13. to acknowledge my family for all their support iv TABLE OF CONTENTS E Eeer iii ACKNOWLEDGMENTS 1 AA iv EISTOETADLES A AAA vii SKI Vili CHAPTER Ls INTRODUCTION Eed EEEIEE ERA 1 IR RE 2 1 2 Advanced Design System ADS did 2 1 3 Computer Aided Microwave Design System CAMDS cceeeee cence eee ees 3 CHAPTER 2 THE SCATTERING DARAMPIERS 5 CHAPTER 3 NEE 10 3 1 Advantages and Disadvantages of CAM 10 3 2 MISES O CAMS a EE 11 EREECHEN E E EE R tat 11 34 Capabilliesor CAMDS EE 11 3 5 A Brief User Guide for CAMDS dees dE AEN Ee 12 CHAPTER4A MICROSTRIP EE 13 CHAPTERS MICROWAVE FILTERS ceciren oeeaaeaii 21 5 1 Stepped Impedance EE 21 5 2 Filter Design Using Zeg ics eeh dE Sek 37 CHAPTER 6 IMPEDANCE MATCHING ege ege deeg se Eder 47 Sl The b Matehrrsee reren era a Otc wt tual amacyow a OSC orn art ren cync gett ay 48 G22 Sie lest ET EE EE 55 CHAPTER 7 IMPROVEMENTS AND SUGGESTIONS FOR CAM CHAPTER 3 CONCEUSIO Niusccinirii a a diia di REFERENCES vi LIST OF TABLES Table Page 5 1 Values computed using the substrate described in Table 37 24 5 2 Electrical and physical properties of the substrate described in Table 5 1 25 5 3 Filter dimensions as determined by AIDS 26 70 7 1 Improved project results obtained using CAMDS vii LIST OF FIGURES Figure Page Lele ne CAMDS neg Ni 4 2 1 Incident and reflected waves in a two port network ccc ccc cece cece eee e ee ee ee 5 4
14. to learn a new programming language since MATLAB is included in almost all the electrical and computer engineering programs at the undergraduate and graduate level in most universities CAMDS can be used in upper division courses or at the graduate level Moreover CAMDS itself is quite user friendly 3 3 CAMDS Structure CAMDS is a selection of scripts or m files Most of the files are capable of running independently Files for filters have subroutines The file called takename m cannot run independently Other files to fetch input from the user call this file CAMDS as a package includes just one graphical user interface GUI named StartHere m This file helps the user to navigate through the software easily 4 3 4 Capabilities of CAMDS CAMDS is useful in solving problems involving microstrip stripline waveguides transmission parameters impedance matching and filter design For the waveguide problem the user can calculate up to ten propagating modes for a given signal frequency in the waveguide This feature is included in the design program for the waveguide For the stub tuner CAMDS is capable of plotting a graph for reflection coefficient vs frequency for a defined band The filters section in CAMDS is unique even though the current version of CAMDS is limited to filters with no more than six elements 11 11 3 5 A Brief User Guide for CAMDS This is a brief user guide for the CAMDS software The user follows the steps list
15. tool has been part of course work in many universities 8 10 This chapter discusses Bais s Computer Aided Microwave Design System CAMDS which was developed with undergraduate and graduate students in mind 11 The CAMDS software was written in MATLAB to deal with many of the problems presented in microwave engineering textbooks such as Pozar 1 3 1 Advantages and Disadvantages of CAMDS Azemi and Stook clearly identify the advantages and disadvantages of CAD tools such as CAMDS in 9 10 A major advantage is the capability to solve complicated problems that would be rather unrealistic for paper and pen solutions Another advantage is the possibility of increasing student interest in the subject 4 This tool can benefit advanced undergraduate and graduate students as they develop microwave devices by providing soft design and simulation capabilities 8 As for disadvantages many CAD tools require a special computer configuration Some CAD tools require a license or fee which might be beyond the means of the student or the school Moreover the time and energy required to learn new software can be a major problem 11 CAMDS can be used by any student who has access to a computer that has MATLAB installed It includes 93 pages of code but is less than 1 MB in size 10 3 2 Uses of CAMDS CAMDS overcomes some of the disadvantages given above while providing some advantages CAMDS was written using MATLAB so the user doesn t have
16. with Pozar The results shown in Bais 4 for lengths are slightly different This example problem from Pozar is practically realizable as was shown earlier in this section 5 2 Filter Design Using Stubs A stub is a very useful tool when designing microwave circuits It can consist of a section of open or short circuited transmission line It can be used in many applications such as impedance matching or filter design by strategic placement along the main transmission line circuit in order to achieve some desired effect The stub of length 1 located at a distance d from a load or source provides a required impedance for the circuit These parameters can be altered to create reactive or susceptive elements in a transmission line circuit This property is used to create capacitors and inductors in the circuit when use of the lumped element is inconvenient or impractical One very important use of stubs is in the design and implementation of filters The lumped element filter generally works well at low frequencies but there are many disadvantages when they are applied at microwave frequencies First when using analytically designed 37 lumped element filters actual components are only available in certain values Therefore desired component values may need to be approximated by using multiple components Another disadvantage of using lumped elements is that at microwave frequencies the trace distances between elements are non negligible This
17. with those reported by Pozar simulated using the Agilent Advanced Design System ADS and then fabricated using an ADS layout In appropriate cases device performance is checked using independent computer analysis or measurement of the device response using a microwave network analyzer The main results are an improved version of CAMDS and rigorous verification of its capabilities to produce useful designs for practical passive microwave devices 111 ACKNOWLEDGMENTS First I would like to thank my advisor Dr David Rogers for his immense encouragement patience and guidance along the path of this research I would like to offer a special word of appreciation to him for spending innumerable hours on my paper in an effort to enhance my technical writing abilities which aided in my professional development Without his support I would never have successfully completed as much as I did Sincere thanks to Dr Benjamin Braaten for helping me with the ADS and fabrication of the devices I would like to thank him and my other committee members Drs Sudarshan Srinivasan and Orven Swenson for serving on my graduate committee I am very grateful for their support and participation I would like to thank Muhammad Mubeen Masud Bilal Ijaz and FNU Irfanullah for their feedback and support with all aspects of this research I have a deep sense of gratitude to all my friends for all their support during my graduate tenure Last but not least I would like
18. 1 Start page with Microstrip selected from the drop down men 16 4 DS OUCSIION EE 17 4 3 Box to enter relative Pod las ENEE 17 4 4 Box to input the characteristic mmpedance ccc ecee ence eee eee eeeeeeeaeenaeees 17 4 5 Box to enter the operating MeQuency EE 17 ER Cine eee Se ak Ne tl a a eek aa cA oe ee a Sa 18 4 7 Box to select the type of loss for the microstrip cece eect eee ee teens eeenees 18 4 8 Box to enter the loss tangent value ccc cee ce ence eee e eee ee eee ene sees eneenaeeaeees 18 5 1 Transmission line equivalent circuits for a small fl b small Bl and large Zo c small Bland EE 221 5 2 Progression from a sixth order lumped element prototype through b transmission line equivalent circuit to c microstrip implementation of a Stepped imipedanoe Her oleo cnt EE me EES 24 5 3 ADS schematic of stepped impedance filter oooooooocorcorcconnccorcronacso 26 5 4 ADS layout of stepped impedance filter 00 c cece cece eee neces enee eae ens 27 5 5 ADS calculations for the scattering parameters S11 S12 S21 and S22 expressed in EE 28 5 6 S21 in dB versus frequency in GHz for the low pass filter implemented using a lumped elements and b microstrip Ines 29 5 7 Fabricated stepped impedance filter 0 cece ccc cece eee eee e ee eee ene eee eee 30 5 8 Experimental setup with the network analyzer of the stepped impedance filter 31 5 9 Clear view of the response obt
19. 6 493117e 001 The output obtained using CAMDS produced the same results as Pozar Thus this verified that the CAMDS could produce correct and accurate results for Kuroda s low pass filter These values obtained from CAMDS can be used to implement the device practically The example problem from Pozar has been verified using ADS CAMDS and MATLAB demonstrating that this example problem is practically realizable 46 CHAPTER 6 IMPEDANCE MATCHING Impedance matching refers to matching a load impedance to a source such that maximum power transfer occurs This avoids unnecessary loss of power Often the source and load impedance is the same as the system impedance Zo in a microwave network If the load impedance Z is different from Zo an impedance matching network such as that shown in Fig 6 1 might be necessary Ideally a matching network is constructed using reactive components so that the network is lossless The importance of impedance matching is as follows 1 1 It delivers maximum power to the load when it is matched to the line 2 Itimproves the signal to noise ratio of the sensitive receiver components such as the antenna low noise amplifier etc 3 It reduces amplitude and phase errors in the power distribution networks such as antenna array feed networks Two types of matching networks are discussed in this chapter the L match and the single stub tuner Most microwave devices work over a band of frequencies and not for jus
20. Box to choose the filter configurations iia ENEE ENEE 65 7 6 Start page showing microstrip selected dd NERNEAEEEN NES NNN NENNEN ire 66 A Ee EE 66 7 8 Box to input relative PELI din 67 7 9 Input box for characteristic mmpedance 6 cece cece eee e een cence nena eee nee 67 7 10 Input box for Ee 67 ge E CUES TOT ER 67 xi CHAPTER 1 INTRODUCTION Much of modern radio frequency communications occurs in the microwave region of the frequency spectrum This band extends from about 300 MHz to as high as 300 GHz The microwave engineering student is usually introduced to the design and analysis of devices in the lower portion of this frequency range or the range of about 500 MHz to 10 GHz Design and analysis of these devices is customarily done with the aid of digital computers and programs specifically formulated to serve the needs of the designer working in this frequency range This paper presents the software and hardware verification of example problems from a standard advanced microwave engineering textbook 1 using the Agilent Advanced Design System ADS 2 the Computer Aided Microwave Design System CAMDS 3 and independent computer analysis using MATLAB This work also checks to see if the results generated by CAMDS as developed by Bais 4 are similar to those of Pozar Furthermore it focuses on fabrication of these example problems and checking their response using a network analyzer to see if these problems are practically re
21. IN mm 12 a A TL6 um Subst MSub1 z Subst MSub1 ieee Subst MSubt Z 50 Ohm W 3 05 mm Weg W 3 05 mm L 749 mm L 749mm Fig 5 22 Filter schematic for the low pass filter using stubs Fig 5 23 Physical layout of the low pass filter using stubs 40 The ADS simulation of the schematic generated the scattering parameter results as shown in Fig 5 24 As in Fig 5 5 of particular interest is S21 which is indicated as dB S 2 1 This is the magnitude of S2 expressed in dB H 0 10 NI ER 20 J 1007 30 40 BEN EE 0 2 4 6 CEET a T 8 10 12 14 16 18 20 AA 0 77 0 dB S 1 1 dB S 2 1 freq GHz LN ATTN dB S 1 2 dB S 2 2 2004 a 0 2 rr T T T TT 4 6 8 10 12 14 16 18 20 5 AAA AHHH freg GHz 0 2 4 6 8 10 12 14 16 18 20 freq GHz Fig 5 24 Scattering parameters obtained using ADS for the low pass filter using stubs The response obtained from ADS dB S 2 1 is very similar to the graph given in Pozar It had a cutoff of 4 GHz The same example was implemented using MATLAB for the lumped element and distributed element cases The result that was obtained using MATLAB is shown in Fig 5 25 The response that was obtained is very similar to the one obtained using either ADS or Pozar 41 Low pass filter constructed with a lumped elements and b stubs OE EAN e PO gea F l d Se A bb Y 5 AAA AA
22. PTER 8 CONCLUSION In this paper the Computer Aided Microwave Design System CAMDS as originally developed by Divya Bais was the central focus This work presents improvements to CAMDS and verifies its performance A context for this paper was developed by reviewing the scattering parameters since they are of such great importance throughout the paper This was followed by a review of the basic processes involved in using CAMDS The section of code in CAMDS that has such great importance is the script that performs the microstrip calculations This material was reviewed and significant improvements in this script are reported This improvement had a profound impact on the rest of the paper since this led to significant changes in the microstrip lines designed using CAMDS Line dimensions calculated by CAMDS as a function of frequency substrate thickness and dielectric constant are now much more reliable than before For the devices considered in this paper the improved CAMDS was the starting point CAMDS was first used to obtain a recommended design Then for example the improved CAMDS design results for microwave stepped impedance filters or filters constructed with stubs were rigorously verified by comparison with results 1 reported by Pozar 11 simulated by ADS 111 fabricated and tested using ADS layouts and 1v obtained by independent computer analysis CAMDS designs for the L match and for single stub tuners were carefully verified by c
23. THE COMPUTER AIDED MICROWAVE DESIGN SYSTEM CAMDS IMPROVEMENT VERIFICATION AND DEVICE FABRICATION A Paper Submitted to the Graduate Faculty of the North Dakota State University of Agriculture and Applied Science By Swetha Somshekar Sharma In Partial Fulfillment for the Degree of MASTER OF SCIENCE Major Department Electrical and Computer Engineering June 2012 Fargo North Dakota North Dakota State University Graduate School Title THE COMPUTER AIDED MICROWAVE DESIGN SYSTEM CAMDS IMPROVEMENT VERIFICATION AND DEVICE FABRICATION By Swetha Somshekar Sharma The Supervisory Committee certifies that this disquisition complies with North Dakota State University s regulations and meets the accepted standards for the degree of MASTER OF SCIENCE SUPERVISORY COMMITTEE David A Rogers Chair Benjamin D Braaten Sudarshan Srinivasan Orven F Swenson Approved June 14 2012 Rajendra Katti Date Department Chair ABSTRACT This paper presents a review of the Computer Aided Microwave Design System CAMDS as originally developed by Divya Bais Its goal was to deal with microwave design and analysis problems presented in standard textbooks such as David Pozar s Microwave Engineering This work presents improvements to CAMDS and verifies its performance The paper focusses on passive devices using microstrip transmission lines such as filters or stub tuners Designs developed with CAMDS are compared
24. age gain and S22 output port voltage reflection coefficient Also V and VI are the incident and reflected voltages at the input port while V and Vz are the incident and reflected voltages at the output port The S parameters are better suited for microwave circuit design than impedance and admittance parameters because impedance measurement requires measurement of voltage and current which is difficult at microwave frequencies Commercial software also uses S parameters for circuit analysis and design 6 The scattering parameters are often used in this paper Pozar 1 presents an extensive discussion of what is commonly known about the S parameters The only S parameter components used commonly in this paper are S11 and S31 S11 is the voltage reflection coefficient at the input Often it is desired that the device match the impedance of the system If this is the case the magnitude of S41 will be small or ideally zero S31 is very useful since it requires that the source impedance and the load impedance of the device be the system characteristic impedance Zo This is the situation almost universally seen in this work S34 is the ratio of the backward traveling voltage from the perspective of the output port to the forward traveling voltage at the input port This is commonly referred to as the voltage gain It is conveniently expressed in dB 20 logio ISI If the output voltage is greater than the input voltage S21 in dB will be greate
25. ained from the network analvzer 31 Vili 5 10 S21 in dB vs frequency in GHz for stepped impedance filter using network analyzer as E rta 32 5 11 Box to input the order of the EE 33 5 12 Box to input the filter impedance EN ee dE ENEE ege 33 5 13 Box to input the highest practical line mmpedance eee ee ees 33 5 14 Box to input the lowest practical line mmpedance cece ee eeeeeeee eee eeeenes 34 5 15 Box to input the prototype Value dees edel ad eeng dagegen geg 34 DAG RE EE 34 S17 EC 35 5 18 Box to input the relative Dermtttvity cece cece cece eee e eee e eee e teas eeeeeeenea 35 5 19 Box to input the CES EE An 35 5 20 Box to input the operating frequency see dE ENNEN EEN NES NEEN 36 5 21 Two0f nl A EEGEN 39 5 22 Filter schematic for the low pass filter using stp b 0 eee eec ence eee eens 40 5 23 Physical layout of the low pass filter using stube cee ceeee eee e eee eee e eee 40 5 24 Scattering parameters obtained using ADS for the low pass filter using stubs 41 5 25 MATLAB response of the lumped element and distributed element low pass EU e o o dd healer 42 5 26 Fabrication of low pass filter using stubs se 43 5 27 ADS display of S24 in dB vs frequency in GHz using the network analyzer 43 5 28 Box to enter the order of the filter vic ii KEEN EE EA 44 5 29 Box to input the HEED is i n it 44 30 QUESTION DOX a tt A 44 5 31 Box to input the prototype VAIUES derrita sitios eR EE EE ege 45 1X
26. alizable This paper deals only with microstrip lines The scattering parameters are mostly used in this paper This paper suggests improvements in Bais 4 Numerical examples have been solved using CAMDS to show the usefulness of the software These numerical results are compared with the experimental results This paper also gives a user manual for CAMDS Some example problems have been verified with MATLAB also The ADS software that has been used is an industry standard microwave engineering computer aided design CAD program Agilent ADS allows microwave engineers to analyze design and simulate active and passive microwave components and systems 1 1 Project Overview This paper is organized in eight chapters The first chapter lays out the introduction about the project It discusses the basic concepts involved with CAMDS and ADS The second chapter gives a detailed explanation about the scattering parameters Scattering parameters are used in this paper in analysis and in the measurement phase The third chapter reviews the CAMDS software The fourth chapter deals with microstrip It provides formulas for the effective dielectric constant and characteristic impedance of microstrip lines It gives detailed steps for microstrip problems using the CAMDS software and explains basic microstrip concepts The fifth chapter discusses microwave filters It deals with stepped impedance low pass filters and the design of low pass filters using stubs It a
27. could lead to undesired behaviors in the circuit 1 To implement low pass filters with certain cutoff frequencies in the microwave range it is useful to employ Richard s transformation and Kuroda s identities 4 which focus on uses of 1 8 transmission lines for which jX jZo Richard s idea is to use the variable Z determined by the width of the microstrip for example to create equivalent lumped elements from transmission lines A lumped low pass prototype filter can be implemented using 1 8 lines of appropriate Zo to replace lumped L and C elements So if we need an inductance of L for a prototype filter normalized to a cutoff frequency 1 and admittance go 1 we can substitute a 1 8 transmission line stub that has Z L The last step of the filter design will be to scale the design to the desired and Zo typically 50 Q Kuroda s idea is to use the 1 8 line of appropriate Zo to transform awkward or unrealizable elements to those with practical values and geometry As an example the series inductive stub represented by the inductor in Fig 5 21 can be replaced by a shunt capacitive stub and a series 1 8 transmission line with different values of characteristic impedance determined by a constant Z4 and Z as shown in Fig 5 21 are transmission line characteristic impedances The constant n 1 Z Z gt The Kuroda identities convert a series element and transmission line into a shunt element and transmission line and vice ver
28. dielectric constant W d ratio the angular velocity phase velocity guide wavelength H filling factor and capacitance The output obtained using the improved CAMDS code follows The Relative Permitivity 1s 4 The characteristic impedance is 10 The effective dielectric constant is 3 64109 W d ratio is 16 4834 Operating Frequency in Hz is 1 5e 009 kO per meter is 31 4159 The angular velocity in rad sec is 9 42478e 009 Phase velocity vp in m s is 1 57219e 008 Guide wavelength Lambda_g in meters is 0 104813 beta in per meter is 59 9467 Filling Factor in Hz is 0 967142 Capacitance per unit length of the line in farads is 6 36054e 010 The same steps are repeated for characteristic impedances of 20 Q and 40 Q The output displayed in the command window of the CAMDS software for 20 Q is given below The Relative Permitivity is 4 The characteristic impedance is 20 The effective dielectric constant is 3 42395 W d ratio is 7 3367 Operating Frequency in Hz is 1 5e 009 kO per meter is 31 4159 68 The angular velocity in rad sec is 9 42478e 009 Phase velocity vp in m s is 1 62128e 008 Guide wavelength Lambda_g in meters is 0 108085 beta in per meter is 58 1318 Filling Factor in Hz is 0 94392 Capacitance per unit length of the line in farads is 3 08399e 010 Similarly for the characterisctic impedance of 40 Q the output obtained using the improved CAMDS software is as follows The Relative Permitivity is 4 The characteris
29. e problem using CAMDS is given below 1 Select Kuroda s Low pass Filter from StartHere fig and then click on GO 2 Enter the order of the filter as shown in Fig 5 28 For the above problem the order is 3 order oxi Please give the order of filter cs Fig 5 28 Box to enter the order of the filter 3 Enter the line impedance as 50 Q as shown in the Fig 5 29 BEE AS Please enter the line impedance Fol omen Fig 5 29 Box to input the line impedance 4 Select other from the question box as shown in Fig 5 30 Please select your filter Fig 5 30 Question box 44 5 Enter the prototype values of the elements as shown in Fig 5 31 GER 1 E 2 E 17 3 E coc Fig 5 31 Box to input the prototype values 6 Choose the LC configuration as shown in the Fig 5 32 GER Please choose the configuration EN Fig 5 32 Question box for the filter configuration 7 The output will be displayed in the command window The output that was generated is shown below The order of filter is 3 The line impedance is 50 The filter configuration is LC Starting from right end load end of the filter the line and open circuited stub values are Open Circuited Stub impedance 6 493117e 001 Followed by line of impedance 2 174350e 002 Followed by open stub of impedance 7 025432e 001 45 Followed by line of impedance 2 174350e 002 Followed by open stub of impedance
30. e short circuited stub _ d OO O gt 0O Zo Zo lt gt Lo e Sr ss _ tt Open or shorted stub Fig 6 11 Single stub tuning a shunt stub and b series stub 56 To check the CAMDS software we verify 1t by solving a problem from 1 The problem requires the user to design a single stub short circuited matching network for a load impedance of 60 j80 Q to match this load to 50 Q at 2 GHz and to plot the reflection coefficient vs frequency for the range of 1 GHz to 3 GHz The procedure to solve this problem is as follows 1 Select single stub shunt tuner from StartHere fig and then click GO 2 Once the Go button is pressed a box will pop up asking for the load impedance Zi Enter the desired value of ZL In the above problem the load impedance is 60 380 Q Fig 6 12 shows the box for the load impedance Enter the value and then press OK BCE ZL bon Cancel Fig 6 12 Box to enter the value of load impedance 3 Enter the value of the characteristic impedance and then press OK In the above problem the value for characteristic impedance is 50 Q Fig 6 13 shows the box for the characteristic impedance Beer TE ZO Cancel Fig 6 13 Box to enter the characteristic impedance 57 4 A question box asking the user if they want the plot for reflection coefficient vs frequency appears as in Fig 6 14 Press Yes to plot the response Plot ell x
31. ective dielectric constant G Ge Hz Helle and fp Note that Z is the impedance of the line d is the substrate thickness ois the permeability in free space and pris the relative permeability of the material 4 Wheeler and Schneider give the following expression for the effective dielectric constant 15 4 4 Equation 4 4 is used by Pozar 1 and in CAMDS Bahl and Trivedi have given expressions for Zo and e Their formulas for the characteristic impedance Zo and the effective dielectric constant are given in equations 4 5 and 4 6 Expressions for z follow as 4 7 4 8 W For lt 1 60 d WwW Zo woe Ww 0 25 D 4 5 where 14 1 Ee Deh D K 125 2 EEN w bor gt 1 d T 120 y Zo Toate ocean 1 444 CD we 667 In 7 1 444 where t 2 14 gara 2 2 w Ee Pozar and CAMDS use only the second expression for as shown above For the given characteristic impedance and dielectric constant the value for 7 IS given as follows For lt 2 d W _ 8exp A a exp 24 2 Sa w For 7 gt 2 w 2 SE 0 61 2 l B 1 InG8 0 fine 1 039 SH 4 8 where Zo lep 1 1 0 11 E ee 0 23 60 2 Er 1 Er and BUN 2 nd r To verify the functionality of the CAMDS software developed by Bais an example from Pozar Example 3 7 is solved using this software The width and length of a microstrip line for a characteristic impedance o
32. ed below to install and run CAMDS 12 1 Store all files in CAMDS at one location for example CAMDS_folder 2 Open MATLAB 3 Change MATLAB s current directory from work to CAMDS_ folder 4 Type guide at the command prompt 5 Open StartHere m from the CAMDS folder 6 Press the play button little triangular symbol in the menu bar from StartHere fig 7 Choose the program you want to run from the list box and press the Go button 8 Refer to the appropriate chapters later in this paper and in Bais 4 for specific examples 12 CHAPTER 4 MICROSTRIP Transmission lines in which the conducting metal surfaces that are etched on a dielectric surface lie completely on a parallel plane are known as planar transmission lines 1 There are several common forms of planar transmission lines microstrip stripline twinstrip slotline coplanar suspended stripline and finline Only microstrip planar transmission line will be discussed in this paper since it is so widely used Microstrip lines can be fabricated with a photolithographic process or on a milling machine Various passive and active microwave devices are suitable for implementation with microstrip 13 Bahl and Trivedi define a microstrip line as a transmission line that consists of a strip conductor and a ground plane separated by a dielectric medium 14 A conductor of width W is applied on a thin substrate of thickness d which has a relati
33. f 50 Q and a phase shift of 90 are required The thickness of the substrate d is given as 0 127 cm and 2 2 CAMDS is used for calculating the design parameters of the microstrip CAMDS has two procedures available design and analysis The 15 microstrip m file contains the code The design part of the software assumes that the user ee e w knows the characteristic impedance whereas the analysis part assumes the user knows the SS ratio the ratio of the conductor width to the substrate thickness To solve the above problem using CAMDS a detailed description of the steps to be followed is given below 1 Open StartHere fig by typing guide in the command prompt and then select the run button from the menu A start window will open From the drop down menu the user selects Microstrip as shown in the Fig 4 1 Rectangular Waveguide TM Circular Waveguide TE Circular Waveguide TM Fig 4 1 Start page with Microstrip selected from the drop down menu 2 Next the user chooses either to analyze a microstrip line or to design a microstrip line For the Pozar example the user chooses Design from the menu Fig 4 2 16 Microstrip 2 5 x Please select for your microstrip Design Fig 4 2 Question box 3 As per the given example problem the user enters the relative permittivity as 2 2 as shown in the Fig 4 3 Relative Permit P m x Please enter Relative Permitivit bi omen Fig 4
34. he desired response The difference from the response obtained with the original schematic was because the values of width and length given in Pozar 1 cannot generate the same response with more than 20 db insertion loss at 4 GHz when it is applied practically So the var function tunes the values of length and width to obtain a cutoff frequency of 2 5 GHz and a 20 dB insertion loss at 4 GHz The new values for length and width that were obtained using the tuning function to obtain the response as given in Pozar are shown in Table 5 3 25 GK MSUB WSUB H 1 58 mm EA CX i Weit CS pa e qi de Ge Coed fer S EE Hien S PARAMETERS E e lt Usmi eene ch d WS Sai inf at Plaid 2 mec Rougt 0 mil SP nt Seit SEN am gt nog ds ESCH m wee MN ee MN MN vere LN fee ee T om MN DIE Snug SHEE WS gp SSI pp yg SSI gy UE MOLT pg SSE SUD yn USE WELT gg up SUSE E ah O t uel Sy A De le E ent URS OE E Eet ca tte derer O RE aen o EI o EE ge a n pas O Nuet 3 ee ae aeons 7 60 Obi Le e E o e gt A b gt 5 5 Term Ce g e 8 e ee e r Term A Num 2 VAR Ip eis EN 7280 Ohin Bh Ei D Ge dE SE ar L1 2 5 mm 26 45 mm X1 9 89 mm E UR ES Ey fin VAR VAR VAR y di Ch SC Di Ele a Liam L4 8 36 mm ft 15 5 36 mm ft Fig 5 3 ADS schematic of stepped impedance filter Table 5 3 Filter dimensions as determined by ADS Section Microstrip Micr
35. he sum of the two individual overall admittance matrices Since we are usually interested in the scattering parameters the combined overall admittance matrix is then converted to a scattering matrix Each additional parallel cascade can be accounted for by adding its admittance matrix to the previously obtained combined admittance matrix From the combined matrix the individual elements of the scattering matrix of greatest interest are Aan and S11 S21 gives the device voltage gain under matched conditions S41 is the voltage reflection coefficient at the input given that the output is matched The focus of this paper is that situation in which whatever simple or complicated device might be under study it will be studied under matched conditions which is the most common situation in microwave engineering practice The phrase matched conditions here indicates that the source impedance at the input and the load impedance at the output are both equal to a standard impedance Z which is usually 50 Q S21 is of greatest interest for devices like microwave filters or couplers S41 is important for devices whose primary function is impedance matching All the devices in this paper are customarily used under matched conditions If this is not the case a more generalized version of scattering parameters could be used as suggested by Brown er al 7 Considering the matched conditions mentioned previously the device input impedance as a complex number ca
36. is 4 gives values for the line lengths for this example that differ significantly from those given by Pozar and from those obtained here The updated output which was obtained is shown below The order of filter is 6 The Filter impedance is 50 The highest line impedance is 120 The lowest line impedance is 20 The filter configuration is CL Filter is implemented on a microstrip The Relative Permitivity is 4 2 The dielectic slab thickness in meters is 0 00158 The operating frequency in Hz is 2 5e 009 For element of prototype value 0 517 Impedance 20 Ohms electrical length 11 8488 degrees width 0 011268 meters length 0 0020883 meters For element of prototype value 1 414 Impedance 120 Ohms electrical length 33 7568 degrees width 0 00043025 meters length 0 0066789 meters 36 For element of prototype value 1 932 Impedance 20 Ohms electrical length 44 2782 degrees width 0 011268 meters length 0 007804 meters For element of prototype value 1 932 Impedance 120 Ohms electrical length 46 1231 degrees width 0 00043025 meters length 0 0091257 meters For element of prototype value 1 414 Impedance 20 Ohms electrical length 32 4065 degrees width 0 011268 meters length 0 0057116 meters For element of prototype value 0 517 Impedance 120 Ohms electrical length 12 3425 degrees width 0 00043025 meters length 0 002442 meters The output that was generated using CAMDS showed results that are consistent
37. lso explains the design of a stepped impedance filter and the design of a low pass filter using stubs with ADS This chapter also includes detailed instructions for solving these filter problems using the CAMDS software This is done to verify that the results generated using this software are the same as those obtained in Pozar The fifth chapter also shows the experimental results obtained after fabricating the device with a comparison with an analytical solution The sixth chapter presents impedance matching which is also known as tuning Two types of matching networks are discussed in this section the L match and single stub tuning Results obtained from CAMDS are compared with Pozar The seventh chapter discusses a microwave design project presented in Bais 4 and suggests improvements to that work Conclusions and recommendations for future work are given in the eighth chapter 1 2 Advanced Design System ADS The Advanced Design System ADS is a leading design automation system used for RF microwave and high speed digital applications It provides an integrated environment for designing RF electronic products It is easy to use and self explanatory The designer uses ADS to design a circuit schematic and produce a layout to meet certain design goals A major advantage of ADS is that the user can change one or more design parameter values and quickly see the effect on the output without re simulation of the entire design ADS has a large librar
38. lter as shown in Fig 7 1 StartHere Single Stub Series Tuner Double Stub Shunt Tuner Kurodas Low Pass Filter Stepped Impedance Low Pass Filter I Fig 7 1 CAMDS start window with Kuroda s Low Pass Filter selected 2 According to the project given in 4 enter the order of the filter as 3 Then click OK as shown in Fig 7 2 gt order a Please give the order of titer Cancel Fig 7 2 Box to input the order of the filter 64 3 Input the line impedance as 20 Q and then select OK as shown in Fig 7 3 gt Line mere Please enter the line impedance ko conca Fig 7 3 Box to enter the line impedance 4 As per the given project select the filter type to be Butterworth as shown in Fig 7 4 Kaes ES O Please select your filter Other Fig 7 4 Box to select the filter type 5 Choose filter configuration as LC as shown below in Fig 7 5 Filter Configuration iol x Q Please choose the configuration EEN Fig 7 5 Box to choose the filter configuration 6 The command window of CAMDS provides the following results Open Circuited Stub impedance 40 Followed by line of impedance 4 000000e 001 Followed by open stub of impedance 10 Followed by line of impedance 4 000000e 001 Followed by open stub of impedance 4 000000e 001 65 The result shows that we have three transmission line sections of 10 Q 20 Q and 40 Q each These three microstrip sections now ha
39. n be calculated directly using S41 1 The device designer than analyzes the input impedance as a function of frequency to evaluate the merit or utility for a certain type of matching device such as a single stub tuner At the same time the designer can view S gt in dB to investigate the transmission characteristics of the device In the case of a filter or a coupler usually San in dB is of primary importance while S411 is of secondary importance For a filter S24 in dB should be zero in the passband and negative outside of the passband Often the value of S in dB at the transition point between passband and stopband or band edge is specified at a cutoff frequency Two typical examples of this are the stepped impedance filter and the filter constructed using stubs For a coupler such as the ninety degree quadrature hybrid 1 S21 in dB will be 3 dB below the input signal at the usual output ports and nonexistent in the isolated port S24 0 or S21 in dB approaches negative infinity CHAPTER 3 CAMDS The use of a CAD tool has become an important part of radio frequency RF and microwave engineering courses The study of microwave engineering requires understanding the concepts involved and developing strong analytical skills for implementing these concepts through complicated and lengthy mathematical solutions 4 Although it is important to be well acquainted with hand calculations for the designer to understand the method use of a CAD
40. nd filters constructed using stubs CAMDS transforms the lumped element filter generated from insertion loss method using Kuroda s identities 4 into a transmission line filter Filters are classified depending on their response type The commonly used ones are Butterworth and Chebyshev filters The Butterworth has a flat passband with no ripples whereas the Chebyshev response has ripples in the passband In a Chebyshev filter it is observed that an increase in the ripple in the passband is also accompanied by a sharper slope in the stopband 5 1 Stepped Impedance Filter The stepped impedance filter is a low pass filter that can be implemented in microstrip It uses alternating very high and very low characteristic impedance lines It is also referred to a hi Z and low Z filter It is superior to a low pass filter designed using stubs since it uses less space and is easy to implement There are three equivalent circuits for the transmission line circuits that are useful in the design of the filters as shown in Fig 5 1 where X and X are inductive reactances and Bis a susceptance Yo is the reciprocal of Zo 21 jX 2 jX 2 X ZoBl AT OO a T equivalent circuit for transmission b Equivalent circuit for small 61 and line section Bloe large Zo T Bc Yo l c Equivalent circuit for small 61 and small Zo Fig 5 1 Transmission line equivalent circuits for a small pl b small Bl and large Zo and c small 61 and
41. of CAMDS in a class project for a university course in microwave engineering Bais 4 suggested a class project using a third order low pass filter with a Butterworth characteristic designed with open circuited stubs using microstrip lines The cutoff frequency was 1 5 GHz The source resistance load resistance and characteristic impedance were each equal to 20 Q Certain improvements were made in the microstrip code The original CAMDS code used this formula for the effective dielectric constant Ep 1 Er 1 1 which was corrected to Ep 1 1 Es St OD p where ais the microstrip line width divided by the substrate thickness Furthermore the calculation of the propagation constant was improved These corrections led to changes in the values of effective dielectric constant phase velocity guide wavelength propagation constant filling factor in Hz and the capacitance per unit length of the line In 4 the project description involves calculation of the dimensions of the physical filter using the design parameters realization of the physical form of the filter on circuit board and checking the experimental result using the network analyzer The steps to design this device with the improved result are given below 63 1 The first step would be to design it using Kuroda s identities For this start CAMDS by typing guide in the command prompt This will open StartHere fig Then select Kuroda s Low Pass Fi
42. omparison with results reported by Pozar and by independent computer analysis of the device designed using CAMDS Taken together as a whole this work shows that the improved CAMDS is a reliable package The work reported here builds on the comprehensive original work of Divya Bais CAMDS That work consisted of approximately 5 400 lines of computer code and dealt with a wide spectrum of devices including those designed not only in microstrip but also in stripline and waveguide The improved version of CAMDS and the experiences reported in this paper 71 will provide future users with increased benefits due to the improvements made and the demonstrations of reliability CAMDS is an excellent design tool for microwave engineering since 1t generates complete lists of parameters for a given specification and has established a pattern or structure for future inclusion of transmission lines implemented in other technologies and for future inclusion of more advanced microwave devices It also could be enhanced by future improvement of the graphical user interface The main results of this paper are an improved version of CAMDS and rigorous verification of its capabilities to produce useful designs for practical passive microwave devices 72 1 2 3 4 5 6 7 8 9 REFERENCES D M Pozar Microwave Engineering John Wiley and Sons Inc Hoboken NJ 2005 Advanced Design System ADS 2004A Agilent Technologies Computer
43. ons for the use of CAMDS occur later in this paper starting in Chapter 3 Sage ENNER Fig 1 1 The CAMDS Start page CHAPTER 2 THE SCATTERING PARAMETERS The scattering or S parameters describe the electrical behavior of various electrical networks S parameters do not use short and open circuited networks to characterize an electrical network Instead matched loads are used These terminations are used at high signal frequencies thus making measurements possible Scattering parameters are defined by using incident and reflected waves instead of port voltages and currents 5 A two port network with its incident and reflected waves is shown in the Fig 2 1 Here a and a are the incident waves and b and b are the reflected waves Fig 2 1 Incident and reflected waves in a two port network The relation between the incident and reflected waves and the scattering matrix is as follows a VII sia Ce a Expanding the matrix into equations gives by S111 124 2 2 and b2 S71 07 S2242 2 3 Each equation gives the relationships between the incident and reflected waves at network ports 1 and 2 with parameters S11 S12 S21 and S22 The S parameters are defined as follows b e SE 2 4 So Ba bag 2 5 Se 2s ee 2 6 and Si z bes 2 7 The description of each S parameter is as follows S1 1 input port voltage reflection coefficient S12 reverse voltage gain S271 forward volt
44. onsider a source impedance of 50 Q a load impedance of 100 Q and an operating frequency of 1 5 GHz This is of educational interest since the 100 Q load impedance can be provided in the laboratory by a 50 Q load as seen through an appropriately designed quarter wavelength impedance transformer The L match routine in CAMDS returns The load impedance is 100 The characteristic impedance is 50 53 The load is inside 1 jx circle in Smith Chart SOLUTION 1 b on Smith chart is at 0 5 x on Smith Chart reactance is at 1 B is a capacitor of value in farad 1 06103e 012 X is a inductor of value in henry 5 305 16e 009 SOLUTION 2 b on Smith chart is at 0 5 x on Smith Chart is at 1 X is a capacitor of value in farad 2 12207e 012 B is a inductor of value in henry 1 06103e 008 The first solution is a series inductance of value 5 30516 nH and a shunt capacitor of value 1 06103 pF which will be called the LC solution The second solution is a series capacitance of value 2 12207 pF and a shunt inductor of value 10 6103 nH which will be called the CL solution Since in the laboratory the system impedance is 50 Q and the voltage gain is often of great interest the CAMDS result is here demonstrated by plotting S21 in dB versus frequency Fig 6 10 Note that the expected ideal value of 0 dB is definitely achieved at the design frequency 54 L Match with Load Provided by Impedance Transformer SRR SEE 0 i F loss
45. ostrip Length Lj in mm Width Wj in mm Li 9 89 2 50 La 0 45 5 67 L 9 89 6 53 L4 0 45 8 36 Ls 9 89 5 36 Le 0 45 2 44 26 The lengths and widths vary slightly from the values given in Pozar 1 Pozar s results are theoretical numerical results The above values of lengths and widths are experimental values The ADS layout of the stepped impedance is shown in the Fig 5 4 ADS is able to compensate for edge effects at the junctions between elements and for the modal effects of the low impedance elements Fig 5 4 ADS layout of stepped impedance filter The ADS program also provided an analysis of the device performance as shown in Fig 5 5 The response obtained has a cutoff frequency of 2 5 GHz and 20 dB insertion loss at 4 GHz Fig 5 5 is taken directly from ADS Of particular interest is S2 expressed in dB or 20 logio 18211 This is shown in Fig 5 5 and indicated as dB S 2 1 27 Re SU 5 107 107 a a E 157 E 157 a ao Ki Ki 204 207 257 257 30 Oe 11177 304 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 1 0 1 5 2 0 25 3 0 3 5 4 0 4 5 5 0 freq GHz freq GHz o e Di LOL dB S 2 2 D E O O US LS LUS TERE 1177717 TIT T T 1 0 1 5 2 0 2 5 3 0 3 6 4 0 4 5 5 0 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 freq GHz freq GHz Fig 5 5 ADS calculations for the scattering parameters S11 S12 S21 and S22 expressed in dB The device layout shown in Fig 5 4 i
46. r than zero This is often the case in active devices If the output voltage is less than the input voltage S21 in dB will be less than zero This is most common with passive devices For passive devices we often refer to the attenuation of the device For the devices considered in this paper the attenuation is simply the absolute value of S21 in dB If an individual element in a device under study is not operated at matched conditions often these elements and its neighbor elements can first be analyzed using the ABCD or chain matrix 1 Then the characteristics of the scattering parameters may be applied to the overall device provided that the device is operated under matched conditions All of the devices in this paper that have been designed using CAMDS can be verified or analyzed with computer programs written using standard computer code Each device can be viewed as a cascade of two port devices or as the parallel combination of two or more cascades of two port devices Each device can be characterized by its ABCD or chain matrix A cascade of devices can be viewed as the overall ABCD matrix formed by the product of each individual ABCD matrix taken one by one from source to load In the case of a parallel combination of two cascades the two overall ABCD matrices can be combined by first converting each to an overall admittance matrix or Y matrix and then by using the well known result that the combined overall admittance matrix will be t
47. ring McGraw Hill Inc New York 1966 14 I J Bahl and D K Trivedi A Designer s Guide to Microstrip Line Microwaves vol 17 pp 174 182 Jan 1978 15 W J Getsinger An Introduction to Microwave Transmission Lines Proc 35 Midwest Symp Circuits and Systems vol 2 pp 1016 1019 1992 74
48. rms of wavelength is 4 020434e 001 60 The short circuited stub length in terms of wavelength is 1 520434e 001 SOLUTION 2 The distance of stub from load in terms of wavelength is 3 479566e 001 The open circuited stub length in terms of wavelength is 9 795664e 002 The short circuited stub length in terms of wavelength is 3 479566e 001 The first solution is an open circuited stub of length 0 4020434 wavelengths located 0 1520434 wavelengths from the load The second solution is an open circuited stub of length 0 09795664 wavelengths located 0 3479566 wavelengths from the load As with the L match since in the laboratory the system impedance is 50 Q and the voltage gain is often of great interest the CAMDS result is here demonstrated by plotting S gt in dB versus frequency Fig 6 19 Note that the expected ideal value of 0 dB is definitely Stub Tuner with Load Provided by Impedance Transformer S21 in dB 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 Frequency in GHz Fig 6 19 Plot obtained using MATLAB for S31 in dB versus frequency 61 achieved at the design frequency Comparison of Figs 6 10 and 6 19 shows that the L match provides a significantly wider bandwidth The stub solution has the advantage of the possibility of fabrication without requiring discrete components 62 CHAPTER 7 IMPROVEMENTS AND SUGGESTIONS FOR CAMDS This chapter describes improvements made in CAMDS 3 It also describes the use
49. s one that can be constructed using commercially available copperclad circuit board The analysis shown in Fig 5 5 is reasonably consistent with the theoretical predictions reported by Pozar As Pozar states the microstrip implementation is within about 0 5 dB of the lumped element simulation for the frequency range 0 to 3 GHz As the frequency increased from 3 GHz to 4 GHz the microstrip implementation continues to serve as a low pass filter but the attenuation is reduced by a few dB The lumped element prediction of Pozar was verified using MATLAB and the result is presented in Fig 5 6 Above 4 GHz the microstrip implementation performance deteriorated substantially as can be seen by comparison of Fig 5 6 a and Fig 5 6 b Fig 5 6 was obtained by using the ABCD matrix of the each element computing the product of the cascade of ABCD matrices and extracting S2 throughout the entire frequency range 28 Low pass filter using a lumped elements and b stepped hi Z lo Z OPO POPPPP POOP CC BES Ft F r g T S21 in dB a l A A a OO E 0 0 5 1 1 5 2 2 5 3 Frequency in GHz Fig 5 6 S21 in dB versus frequency in GHz for the low pass filter implemented using a lumped elements and b microstrip lines Fig 5 6 shows how closely the microstrip device approximates the lumped element performance with each device giving performances close to the design specifications at 2 5 GHz and at 4 0 GHz Beyond 3 5 to 4 0 GHz
50. sa The first two Kuroda identities are illustrated in the Fig 5 21 below where each box represents a unit element or a transmission line The inductors and capacitors represent short circuited and open circuited stubs respectively 38 Fig 5 21 Two of Kuroda s identities The values obtained for a low pass filter design using stubs following Pozar are listed below The example problem from Pozar has a 3 dB equal ripple third order characteristic a cutoff frequency of 4 GHz and an impedance of 50 2 So the normalized prototype elements values for this filter are as follows g 3 3487 Li g 0 7117 CH g 3 3487 L g4 1 0000 Ri The above problem was verified using ADS to check if it can be implemented practically The same problem was solved using CAMDS 3 to check the validity of the software The schematic of the above problem using ADS is shown in Fig 5 22 following by the layout in Fig 5 23 The layout was generated from the schematic which is shown in Fig 5 23 The layout generated a very thin 217 5 Q line of width 0 064 mm 39 S PARAMETERS S Param SP1 Start 10 0 MHz MSub Stop 20 0 GHz Step 10 MHz MSUB MSub1 MLIN MLIN MLIN MUN a an T1 13 15 17 SC i S bsi MS b1 Subst MSub1 Subst MSub1 Subst MSub1 SE 1E 7 VW 4 65 mm W 0 064 mm W 0 064 mm W 4 65 mm AE a E L 7 38 mm L 8 03 mm L 8 03 mm L 7 38 mm e T 0 035 mm TanD 0 0005 4 Term Rough 0 mm Tomm 3 Num 1 4 Jem 2 50 Ohm MLIN ML
51. sed to solve the above example problem are given below The procedure to use to design this network is given below 1 Go to the StartHere fig page click on L Match and then select GO 2 Once the user presses GO CAMDS will ask for the load impedance Z1 The user enters 200 100 as shown in Fig 6 4 BER fal Go ol cos Fig 6 4 Input box for Zi 50 3 Enter the characteristic impedance as per the given example problem For the above problem the characteristic impedance is 100 Q Fig 6 5 Beer TE zo oo Cancel Fig 6 5 Box to input characteristic impedance 4 Enter the design frequency for the match as shown in Fig 6 6 Matching Frequency ali al Please enter the frequency at which the load is to be matched Fones EH Fig 6 6 Input box for the design frequency 5 Then a question box will appear asking if the user wants to plot the reflection coefficient vs frequency Click on Yes Fig 6 7 If the user clicks No it will generate an output in the command window without any graph Plot ell xj Do you want to see a plot for reflection coefficient vs frequency SS Fig 6 7 Question box 51 6 Enter the frequency range for the plot and then press OK as shown in Fig 6 8 For the above problem the range is 100 MHz to 1 GHz Frequency Range jes lei E Frequency from Die Frequency to ES cancel Fig 6 8 Input box asking frequency range 7 The ou
52. small Zo In the stepped impedance filter the series inductors of a low pass prototype are replaced with a high characteristic impedance line with Zo Zn and shunt capacitors are replaced by a low impedance section with Zp Z1 The ratio Z Z should be high Pozar 1 shows that the electrical length of the transmission line section can be calculated as determined by the following equations For the inductor pl 2 7 inductor 5 1 where R is the system characteristic impedance Lg is the inductance and l is the physical length In this paper R Zo For the capacitor 22 Bl e capacitor 5 2 g where Cy is the capacitance The lengths of the microstrip lines can be calculated as follows nZ CH SS 5 3 e LE on where Len and L give the lengths of the equivalent transmission lines Lg and Cy are the normalized element values and g is the low pass prototype value 1 The development of the stepped impedance filter from a lumped element circuit sixth order prototype to the microstrip implementation is shown in Fig 5 2 As an example of the filter consider a study of Example 8 6 from Pozar 1 with CAMDS and ADS The detailed values obtained for the stepped impedance low pass filter using Pozar are listed in Table 5 1 in which the material described in Table 5 2 was used 23 b Stepped impedance implementation c Microstrip line filter layout Fig 5 2 Progression from a sixth
53. t one design frequency Waveguides and transmission lines generally have long electrical lengths Electrical lengths are functions of frequency Small changes in frequency can cause considerably large changes in the electrical length The impedance of transmission line devices is dependent on the electrical length of the devices A matching network is inserted between the line and the load 4 An impedance matching network that can match the load to the line at one frequency may act differently at another frequency 4 Two different methods for designing the matching network between a load and a line are the Smith chart method and the analytical method CAMDS uses the analytical method to find a matching network for a given load and line A figure showing a 47 lossless network matching a load impedance Z R jX to a transmission line as reported in 1 is given in Fig 6 1 Matching Network 7 L Fig 6 1 A matching network 6 1 The L Match The L match is the simplest type of matching network It uses two reactive elements to Eoi Z match the line to the load The normalized load impedance is given as Z A r jx where Z 1s 0 the load impedance and Zo is the characteristic impedance There are two configurations for this network If Z is inside the 1 x circle on the Smith chart then the circuit in Fig 6 2 should be used El Fig 6 2 Circuit for Z inside the 1 jx circle
54. ta and then apply that information manually to the data provided by CAMDS Returning now to the microstrip example suggested by Pozar his Example 3 7 the width and the length of a microstrip line are required Using the results from the improved version of the CAMDS microstrip code the user has obtained Z 3 08117 and a guide wavelength Ay of 0 0877245 meters Using d 0 127 cm the user can calculate W 0 391 cm Pozar requires a quarter wavelength line Thus the user can calculate the required line length as 2 19 cm The improved version of CAMDS yields exactly the same results as those shown in Pozar This example shows that the improved CAMDS does solve the problem correctly but still leaves some simple decisions to the student 4 20 CHAPTER 5 MICROWAVE FILTERS A microwave filter is a two port network used to control the frequency response at a certain point in a microwave system by providing transmission at the frequencies within the passband of the filter and attenuation in its stopband 1 There are two methods of filter design the image parameter method and the insertion loss method 4 Both of these circuits have lumped elements For the practical circuits at microwave frequencies the lumped element circuit is transformed into transmission line sections using Richards transformation and Kuroda s identities 1 This section of the paper deals with the transmission line filters using stepped impedance filters a
55. the lowest Impedance of line ZI ol cos Fig 5 14 Box to input the lowest practical line impedance 6 Enter the prototype values for the given problem as shown in Fig 5 15 A table of prototypes values is given in Pozar 1 Protype Yalues ial x 1 517 2 414 3 932 4 932 5 414 6 517 cw Fig 5 15 Box to input the prototype value 7 Choose the CL configuration for the above problem as in Fig 5 16 Filter Configuration Q Please choose the configuration ES Fig 5 16 Question box 8 As shown in Fig 5 17 choose Microstrip 34 Implementation AE What do you want to implement this filter in Stripline Fig 5 17 Question box 9 Enter the relative permittivity For the above it is 4 2 Fig 5 18 below shows the input box for the relative permittivity Please enter Relative Permitivit h2 omen Fig 5 18 Box to input the relative permittivity 10 Enter the thickness as 0 158e 2 as given in the problem Fig 5 19 shows the input box for the thickness ES Please enter thickness of dielectric slab d in meters 158e 2 con Fig 5 19 Box to input the thickness 35 11 Enter the value of the operating frequency as 2 5 GHz is shown in Fig 5 20 Operating Frequency Jof x Please enter the operating frequency in Hz D Cancel Fig 5 20 Box to input the operating frequency The output that was obtained in the command window is as follows Ba
56. tic impedance is 40 The effective dielectric constant is 3 16219 W d ratio is 2 90469 Operating Frequency in Hz is 1 5e 009 kO per meter is 31 4159 The angular velocity in rad sec is 9 42478e 009 Phase velocity vp in m s is 1 68705e 008 Guide wavelength Lambda_g in meters is 0 11247 beta in per meter is 55 8655 Filling Factor in Hz is 0 911684 Capacitance per unit length of the line in farads is 1 48188e 010 The results obtained from the improved CAMDS software are shown in Table 7 1 for a substrate of thickness 0 0015748 meters 69 Table 7 1 Improved project results obtained using CAMDS Characteristic Ww W Guide Section Impedance Q meters Wavelength Length meters meters 10 16 48 0 025953 0 10481 0 01310 20 7 337 0 01154 0 10809 0 01351 40 2 905 0 004575 0 11247 0 01406 Table 7 1 above provides improvements to Table 7 1 in Bais 4 due mainly to the improvement made in the microstrip code The main practical result was the reduction by about ten percent in the section lengths The resulting project is interesting but it is not physically realizable due to the excessive width of the 10 Q line A better option for a student project would be something like Pozar s example 8 6 Even his example 8 5 though difficult to fabricate can serve as a suitable project for the more advanced students Details about these examples were provided earlier in Chapter 5 of this paper 70 CHA
57. tput shown in the command window for the above problem is as follows It produces two solutions for the given problem It produces results for b and x on the Smith chart and gives values for the capacitance and inductance The solution to the above problem using CAMDS is as follows The load impedance is 200 1001 The characteristic impedance is 100 The load is inside 1 jx circle in Smith Chart SOLUTION 1 b on Smith chart is at 0 289898 x on Smith Chart reactance is at 1 22474 B is a capacitor of value in farad 9 22774e 013 X is a inductor of value in henry 3 89848e 008 SOLUTION 2 b on Smith chart is at 0 689898 x on Smith Chart is at 1 22474 52 X is a capacitor of value in farad 2 59899e 012 B is a inductor of value in henry 4 61387e 008 8 The following plot Fig 6 9 was obtained using the CAMDS software note new toolbar buttons data brushing amp linked plots sZ fa Play video x 1 S Solution 1 0 9 H Solution 2 0 8 Absolute Reflection Coefficient r Frequency Hz x 10 Fig 6 9 Plot of the reflection coefficient vs frequency for the L match using CAMDS The results produced by CAMDS are similar to those shown in Pozar 1 CAMDS produces an accurate and fast result as compared to an analytical pen and paper solution As has been shown CAMDS produces the design for the L match network given the source impedance the load impedance and the design frequency As another example c
58. ve permittivity r In the absence of a dielectric 1 the line can be considered as a two wire line consisting of two strip conductors each of width W and separated by a distance of 2d with a simple TEM transmission line phase velocity equal to the velocity of light 1 In practice the dielectric does not fill the region above the strip This complicates the behavior and analysis of an actual microstrip line since it cannot support a TEM wave At lower frequencies the wave is almost TEM quasi TEM but at higher frequencies the travelling mode no longer remains quasi TEM due to dispersion caused by the changing effective dielectric constant and characteristic impedance Hybrid modes coupled TE and TM modes travel in a microstrip at high microwave frequencies 4 Good approximations for the phase velocity and propagation constant can be obtained from the quasi static solution 1 These can be expressed as as follows Y 4 1 and B ko Jee 4 2 where is the effective dielectric constant of the microstrip line and kois the propagation constant in a vacuum The effective dielectric constant satisfies the relation 1 lt e lt and depends on the substrate thickness d and the strip width W The analytical expression for the effective dielectric constant in a dispersive microstrip line is given by 4 Ef Er A 4 3 fp where f is the effective dielectric at that frequency in GHz is the static eff
59. ve to be designed Due to the improvements made in the computer code for microstrip new results are obtained The design steps for the microstrip section are as follows 1 Select microstrip from the startHere fig and select Go as in Fig 7 6 AA Computer Aided tool for Microwave Design Systems CAMDS Rectangular Waveguide TM meto rh artment of Electri Circular Waveguide TE Circular Waveguide TM hanks for using this program Fig 7 6 Start page showing microstrip selected 2 Choose Design from the next window as shown below in Fig 7 7 SE Please select for pour microstrip Design Fig 7 7 Option box 66 3 Enter a relative permitivity of 4 in the next box Fig 7 8 Relative Permitus je EZ Please enter Relative Permitivity cra Fig 7 8 Box to input relative permitivity 4 Input characteristic impedance equal to 10 Q DEEE Loix Please enter Z0 Ohms 0 cuen Fig 7 9 Input box for characteristic impedance 5 Enter the operating frequency as 1 5 GHz as per the question Operating Frequency TE Please enter the operating frequency in Hz h Ze cs Fig 7 10 Input box for operating frequency 6 Then a question box will appear Fig 7 11 asking if the user wants to calculate the loss Here the user clicks NO and proceeds os A Q Do you want to calculate loss No Fig 7 11 Question box 67 The command window will output the effective
60. y of transmission line and passive component models 2 1 3 Computer Aided Microwave Design System CAMDS The Computer Aided Microwave Design System is structured to help student engineers solve problems in microwave engineering It is a graphical user interface GUI program written in MATLAB 7 This software is used to solve problems such as filters designed using Kuroda s identities stepped impedance filters and impedance matching devices Microwave engineering requires the understanding and use of complex mathematical calculations Various graphical user interface CAD tools are available in CAMDS to solve these microwave problems CAMDS is a collection of scripts or m files It is an interactive program Most of the files are capable of running independently CAMDS was developed using MATLAB to overcome some problems related to the use of CAD tools They include maintenance and operation of such tools and the extra time required by the students and instructors to learn to use such tools CAMDS overcomes these disadvantages because MATLAB is widely used and can be easily installed on computers Moreover CAMDS itself is self explanatory and easy to use 4 CAMDS uses only one GUI in the suite as shown in Fig 1 1 The StartHere m file helps the user to navigate A user can choose a program to be executed and then press the GO button to run it The screen shot of the start page of the CAMDS software is shown in Fig 1 1 Additional suggesti

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