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TRLINE User's Guide - Department of ECE

1. At the generator terminals Uoltoge 566 7 millivolts RMS phase Current 6 667 milliomps RMS phase 0 0 degrees A A degrees Power 4 444 milliwatts Admittance 10 000 j0 09O milliSiemens Back A Fig 2 20 The power flow report for the generator Click Generator to get the power delivered by the generator as in Fig 2 20 This screen reports the voltage and current at the generator terminals the input admittance into the transmission line circuit and the power delivered by the generator to the circuit Change the settings to impedance to have the program report input impedance 25 300 200 MHz 1 LINE 1 Pi i j ion Line angle Rt the inputs 166 7 ongle millivolte RMS Unttage millivalts RMS phose A A degrees Current 6 667 milliomps RMS phose 8 degrees Power 4 444 milliwatt Admittance 18 800 j2 0 0 milliSiemens At the output Voltage 3 3 millivolts RMS phose 10 G degrees Current 13 33 milliomps RMS phase 90 0 degrees Power 4 444 milliwe Fidmittance 42 Q00 j0 milliSiemens Back arg sia pana a pao Fig 2 21 The power flow for line 1 Click Line 1 in the power menu of Fig 20 to obtain the report of Fig 2 21 The voltage on the transmission line is given by V z Vte V e where V is the complex amplitude of positive going voltage travelling wave and V is the complex amplitud
2. button changes back to red Also when you are editing a field you can use the tab key to change to the next field or use the up or down arrow key to change fields Again type Enter to finish editing the numerical value fields ee EE LS ci TRLINE VERSION 1H b Des 1 2014 ttt Ble at lew Sate Wiowey He Transmission Line Proper ites Menu Transmission Line Properties Menu Transmission line 1 Transmission line length 95000 meters Characteristic impedance 50 000 Ons Propagat ion velocity 300 00 meters per microsecond Cont inue ion Feme anaE a Aa Fig 2 7 The transmission line properties menu To set the properties of transmission line 1 in Fig 2 4 click the mouse on Line 1 at the top of the screen to get the transmission line properties menu of Fig 2 7 This menu has fields for typing the characteristic impedance of the line the length of the line and the phase velocity of waves on the line Click the mouse on a blue field to change the value Transmission lines in TRLINE are lossless so there is no loss parameter To return to the main menu click Continue 12 TRLINE VERSION 1H b Dec 1 2014 Load Impedance Nenu Load Impedance Menu Load Impedance Menu Load 1 Load impedance resistance reactance Resistance 50 00 Ohms React ance 0 000 Ohms Specify the load with an SnP file Cont inue
3. fuming eussinpatpendingin Guan Application Fig 2 8 The load properties menu Fig 2 8 shows the properties menu for a load Type the resistance and the reactance into the fields Loads have a constant value as the frequency varies If the load varies with frequency the prepare an SnP file giving the value of the load at each frequency and use the Specify the load with an SnP file button to give TRLINE the file name for the SnP file TRLINE reads either the input impedance or the S11 scattering parameter from the SnP file Some commercial electromagnetic solver programs prepare SnP files as output Also some network analyzers can write an SnP file of measured scattering parameters This allows TRLINE to be used to work with load impedance as a function of frequency that has been measured as part of a lab experiment 13 Je Edt View So Window heb Click the mouse on a red nome to change the properties 3 Gener ator Line 1 Load 1 Frequency Line 2 Load 4 e m Line 3 4 2 Frequency 309 000 MHz ra p vv 3 r E s 5 rd Eg 1 2 A 2 J Tranmission line menu Click on red text Plot Ulz on Line 3 Line 1 Line 2 Plot the voltage amplitude on all lines Plot the current amplitude on all lines Plot both the voltage and the current Plot the voltage including phase Plot the current including phase Draw a Smith Chart as d function of line length Back _ an sep maT RN p
4. 5 2 shows the transmission loss as a function of frequency from 0 1 GHz to 8 GHz The figure shows a low pass filter with a ripple of 3 dB and a cutoff frequency of 4 GHz as expected At the cutoff frequency the transmission loss is 3 dB In Fig 5 2 the markers have been set to demonstrate the 3 dB ripple aw Se Wraae fp Click the mouse on o red label to change the properties Generator Line 1 Load 1 Frequency Line 2 Load 2 Line 3 Lood 3 Pi Line 4 Load 4 Lood nh Line 5 n 3 Line 6 Frequency 2 000 He ipp 4ps e Z Lot 13 F sa 4 a a3 es 2 Choose on action by clicking the mouse on o red text string Plot Ulz or Ilzi ond find the USWR Find voltages currents ond power Drow a Smith Chart Smith Chart Calculations Plot a parameter os o function of the frequency the circuit to o dato file e o new circuit ange the settings Exit Fig 5 3 Circuit template for the bandstop filter 72 5 3 Bandstop Filter Pozar 2 explains the design of a Chebyshev bandstop filter In Example 8 8 2 he presents the design of a Chebyshev bandstop filter with N 3 a center frequency of 2 GHz a bandwidth of 15 a ripple of 0 5 dB and an impedance of 50 ohms Fig 5 3 shows the circuit template Line 1 is the input and line 7 is the output and these lines have characteristic impedance 50 ohms The load is Z 50 ohms Lines 2 3 4 5 and 6 comprise the filter Al
5. Smith Chart Imag 5 Admittance Chort i For line 3 ba Frequency 688 088 MHz rs Length j 2 810 m Y at port lo 20 048 j142 738 IN G meraotor Characteristic Admittance 20 0 m3 Load Admittance 0 1802R00E 06 j0 BGE Load Reflect 1 0202A angle Input Admittonce 0 200 j158 Input Refl 1 0020 angle 185 6 degrees irri Penanganan aa Ay Fig 3 7 Monitor the impedance at the output of line 1 to adjust the stub length Another way to adjust the length of the tuning stub is to monitor the impedance at the output of line 1 In the Smith Chart Calculations menu of Fig 3 1 click on port lo as the port to monitor With the length of line 2 set to 0 048 m as in Fig 3 3 draw the Smith Chart for Line 3 the tuning stub as in Fig 3 7 The admittance at port 1o appears as a small cross enclosed in a circle on the g 1 circle near the arrowhead of the INPUT arrow in the figure Use the Change length function to make the stub longer 42 Ble Eat Uw som Widow He Smith Chart Admittance Chart For line 3 Frequency 600 020 MHz Length 9 041 m Y at port lo 20 040 j19 984 Click the mouse in the Smith Chort ta choose a new Length Lo Characteristic Admittance 20 0 mS Load Admittance 0 18G2000E 06 j0 002 mS Load Reflection Coefficient 1 02080 ongle 188 08 degrees Input Admittonce 200 j35 562 mS Input Reflection Coefficient 1 B008
6. The graph then reports the frequency difference or bandwidth between the markers Snap to value 20 00 Snap the markers and cont inue The snap menu lets the user enter the desired value for the return loss at the marker locations in this case 20 dB Click Snap the markers to continue Marker 1 489 833 15L a 4 19 94 J Morker 2 718 1147 a 8 J 20 00 3 Morker 1 Morker 2 m Bandwidth 8 esl 220 280 4 4 E B 30b 4 v J a Ft 7 35L d RPLOT Snep Ani L Back Si 1 L 1 1 f f oa Se son Soa Ban maa eog Sao 100a Freauencu MHz Fig 2 27 programs snaps the markers to 20 dB and reports the bandwidth between the markers as 220 26 31 Fig 2 27 shows that the TRLINE program positions the markers at 20 dB and reports the bandwidth between the markers as 220 26 MHz ROT i top occ el Cie sat ew sme Widow Hep Uoltoge Stonding Wave Pattern on Line l a aie Ee ee a E frase haere pe elie 200 300 408 520 500 700 Baa Fae 1801 equency TMz SUEEP RPL 1 areariets Fc RR Fig 2 28 Click the RPLOT button to run RPLOT to graph the return loss as a function of frequency In Fig 2 27 click the RPLOT button to create a file called sweep rpl and then run RPLOT to graph the frequency sweep data as shown in Fig 2 28 Execution of TRLINE is suspended until the user exits from the RPLOT program RPLOT lets the user
7. 1 cm line is 158 316 mS much larger than the desired value of j15 578 mS Click on the Change length button 40 Smith Chart Admittance Chart For line 3 Frequency 600 020 MHz Length 8 072 m cowards Generator D Characteristic Admittance 20 0 mS Load Admittance 0 18O2000E 06 j0 002 mS Load Reflection Coefficient 1 02020 ongle 162 8 degrees Input Admittonce a 0 080 j15 573 mS ense grid Input Reflection Coefficient Change length 1 88020 angle 75 8 degrees Back Fig 3 5 Adjust the length of line 3 for an input admittance close to j15 578 mS Fig 3 5 shows the Smith Chart for line 3 after the Change length function has been used to adjust the length to 0 072 m for an input admittance of j15 573 mS close to the desired value of j15 578 mS 1 USUR 1 0820 y Line 2 USUR 2 1377 Line 3 USUR Tafinity 1 U 2 1 Frequency 500 080 MHz Uoltage amplitude os a function of distance To verify that we have a match go back to the main menu and select Plot V z and then Plot the voltage amplitude on all lines to obtain Fig 3 6 Line 1 shows that it is well matched with an almost constant voltage amplitude along the line The VSWR is reported as 1 0020 Making fine adjustments to the line length and the stub length can obtain a perfect match of 1 0000 hopian TT ple Eat dien Som aow Heto
8. 2 877 m Y at port lo f 19 940 j8 006 5 8 Click the mouse By in the Smith Chort s to choose a new length LOI Characteristic Admittance 20 0 mS Load Admittance 0 18O2000E 06 j9 002 mS Load Reflection Coefficient 1 02080 ongle 162 0 degrees Input Admittonce 200 j13 685 nS Input Reflection Coefficient Finish 1 B0020 angle 68 8 degrees Fig 3 18 A stub length of 0 077 m makes the admittance at port 1o equal to 19 939 j0 006 mS Fig 3 18 shows that with a stub length of 0 077 m the input admittance is very close to the center of the Smith Chart The design of the double stub matching circuit is complete E pe EAM View som woow He Line 1 USWR 1 8031 y Line 2 USUR 1 9586 Line 3 USIUR Tat inity Line 4 USWR Infinity 1 U eL Frequency 500 080 MHz Ualtage amplitude os a function of distance Fig 3 19 The VSWR on the input line is 1 0031 which is a good match Back Fig 3 19 shows the voltage waveforms on the transmission lines The voltage is almost constant with distance on line 1 so we have a good match The VSWR on line 1 is 1 0031 J Morker 1 575 634 SP J aor 18E J Morker 2 i 627 166 a 19 99E I 15b 4 o Bonduiath o y J 51 531 Ee 4 Marker pear 2 c 5 esf 4 2 x 30 4 aiii 4 RPLOT Snap i liriilis rial ae Back 308 sotiae l fir
9. 733 ohms Z 91 278 ohms and Z 113 610 ohms Enter these values for lines 2 3 4 and 5 in Fig 4 4 Set the frequency to 600 MHz The input line length is 0 25 m and the four transformer sections have length 0 125 m Line Line Line 5 USUR y y y 1 s2 3 a s5 Voltage amplitude os o function of distonce Fa RR RT Fig 4 5 The four section quarter wave transformer obtains a perfect match at 600 MHz Fig 4 5 shows the voltage on each transmission line at 600 MHz and demonstrates that the transformer matches the 50 ohm line to the 120 ohm load perfectly 68 ible gor yev sae wntow sep T T T T T T T 7 3 A j J Morker 1 5p J 311 354 19 99 Morker 2 ar 888 652 a orker X1 orker E 19 991 as Bandwidth oo J 577 297 i pi 3 3 30 4 g fl asl J RPLOT Snap 4 1 L NEEN 1 1 Lusa Bock oa 380 408 500 500 700 aoa s00 1908 Freauencu MHz K Fig 4 6 The bandwidth of the four step quarter wave transformer Fig 4 6 shows the return loss of the four step quarter wave transformer The bandwidth for a return loss of 20 dB or better is 577 297 MHz Choose o parameter to graph Input impedance USWR al Reflection coefficient Return loss Transmission loss Input admittance From line 1 2 3 8 5 6 47 To line 1 He 3 Mh 5 76 7 taa n cannes A hawi E We 6 Sy Rs Zi U ag Fa Parometer Transmission loss Fr
10. Admittance 20 0 mS Load Admittance 40 000 8 030 mS Load Reflection Coefficient 0 33333 ongle 180 0 degrees Input Admittonce 10 2024j0 080 vS Input Reflection Coefficient 8 33333 angle 0 0 degrees Fig 2 18 The Smith Chart drawn with a dense grid of constant g and constant b contours where y g jb Change length The Dense Grid button at the lower right is used to increase the number of circles used for the Smith Chart axes Fig 2 18 illustrates the dense grid The sparse grid of Fig 2 16 is usually more effective on the computer screen The Back button returns to the Smith Chart menu 23 Frequency 300 000 MHz TR a 7 O j 4 1 1 p 2 Click the mouse on a name lin rad to report the voltage and power Generator Line 1 Load 1 Line 2 Lood 2 Line 3 Change the settings Fig 2 19 The power menu provides buttons to report the power flow in every part of the transmission line circuit 2 5 The Power Menu In the main menu of Fig 2 2 click the button labeled Find voltages currents and power This gets the power menu of Fig 2 19 This menu provide a button for each part of the circuit to report on the power flow 24 Epe Eat Yew Saw Wow ie Frequency 308 208 MHz p 3 d TR ur f The generator Us 1 000 volts RMS phase degrees Internal resistance 5 2 ohms
11. Ilzl and find the Find currents ond power Drow a Chart Smith Chart Calculations Plot a porameter os a function of the frequency S the circuit to a data file a new t the settings isi Soap aa yn Fig 4 4 The circuit template called three step quarter wave transformer 4 2 Three Step Quarter Wave Transformer To improve the bandwidth of the match we can use a multi step quarter wave transformer The circuit template called three step quarter wave transformer Fig 4 4 consists of five transmission lines in series The component values demonstrate matching a 50 ohm line to a 100 ohm load with a three step transformer consisting of lines 2 3 and 4 Let s use the circuit template to demonstrate a four step transformer to match a 50 ohm line to a 120 ohm load at 600 MHz The transformer can be designed using the method in 2 Evaluate coefficient A with N 4 and Z 120 ohms Anas 21220 _ 9 4 120 50 _ 4 4 0 _ 9 995735 Z Z 120 50 170 The binomial coefficients are given by wi M N and are Ge sai 4 00 4 Cae n 4 DI 6 to A __ 284 59 6 2 4 2 2x2 c 4 2x3x4 TUBI Lx2x3 67 4 a 4 44 The characteristic impedance values of the lines are found with n ma Cyin Z n Z 0 hence n s C7 In Ze 9 xxn 0 054716 Zo Zo 50 So Z Zye Ys 500 52 812 ohms The characteristic impedances of the remaining sections are calculated with the same formula Thus Z 65
12. described below The fifth function of the program is obtained by clicking Plot a parameter as a function of the frequency This menu lets you graph one of five parameters as a function of frequency You can set the frequency range with a sub menu You can graph the input impedance as a function of frequency at any port that is looking into any transmission line in the circuit You can graph the reflection coefficient or VSWR looking into any transmission line You can plot the return loss And you can graph the transmission loss between any two junctions in the circuit These are usually chosen as the input terminals and the load terminals The frequency sweep graphs include two markers that can read back points from the graph Also there is a snap function which lets you snap the position of the markers to a desired level say 20 dB return loss Then the program reports the bandwidth between the markers There are three buttons at the bottom of the screen Save the circuit lets you save all the parameter values to a trl file so that you can recall the circuit later with all the parameter values set correctly Choose a new circuit takes you back to the circuit template menu Change the settings lets you choose to work in MHz or GHz with RMS values or amplitudes with impedance or admittance and whether to report complex numbers as magnitudes and angles or as real part and imaginary part The following describe
13. filter the mouse on a red Click label to change the properties Generator Line 1 Load 1 requency Line 2 Load 2 Line 3 Load 3 Line 4 Load 4 Line 5 i a Line AB Lip WH He Loba Wa y Loba et 2 4 ae 41 Fal as P a7 Fig 2 3 0 N 3 Bandpass filter Click mouse on a red label to change the properties ine L u1 Line 2 Load 2 Line 3 Lood 3 ine 4 Load 4 Line 5 goad 5 P P ine Ab Load g6 Frequency si TETA EPAL TET AN a s R amp 48 B 1 s7 ay P inp t o L lt s Fig 2 3 p N 5 Bandpass filter Click the mouse on a red label to chonge the properties Generator Line 1 Load 1 Frequency Line 2 Load 2 ne Load Line 4 ne 5 ine 6 Frequency 300 000 MHz AN gt 4 s R za bz lz lz UC ei J w5 We Fig 2 3 1 Six transmission lines in series with shunt loads Fig 2 3 The circuit templates available in TRLINE 2 1 Choosing a Circuit The circuit template menu of Fig 2 1 offers a variety of circuits that are useful in learning about transmission lines at the elementary and intermediate level The simple circuit of Fig 2 3 a consists of a generator one transmission line and a load It is used as discussed below to demonstrate travelling waves and standing waves and explore mismatch It is also used to demonstrate the operation of the Smith Char
14. set all the parameters associated with the display such as the range of the horizontal axis and of the vertical axis the titles and legends and so forth Expert users can collect several different frequency sweep curves into one rpl file to visually compare the bandwidths of various matching schemes 32 20 L fi fi bia fi L fi val 200 300 400 500 500 72a B00 08 100t Frequency MHz GASE Mouse irpat pending in GuckWin Application Fig 2 29 The input impedance as a function of frequency In the sweep menu of Fig 2 23 choose Input Impedance as the parameter and then click on Calculate the frequency response The TRLINE program creates a file called sweep rpl that contains the real and imaginary parts of the input impedance at the specified port and then runs RPLOT to graph the input impedance as shown in Fig 2 29 At 600 MHz the graph shows that the input impedance is 50 j0 ohms a perfect match The execution of TRLINE is suspended while RPLOT is running Terminate RPLOT to continue with TRLINE Note that TRLINE can also graph input admittance as a function of frequency 33 Standing Wave Rotio J Morker 1 580 433 1 199 Morker 2 699 914 1 20g Bondwidth ae 199 4812 4 4 f F 4 y L Marker 1 Marker 2 4 1E AS J 4 RPLOT V y i Fi Snap Eeri teaiin Ma Back zaa aa sana saa Gaa zaa aaa a aaa Freauencu MHz S _ Running Wouseirpatpen
15. single stub tuning circuit is to set the length of line 2 so that the input admittance to line 2 lies on the g 1 circle on the admittance chart Change the settings so that TRLINE displays admittance Then click on Line 2 in Fig 3 1 to see the Smith Chart for line 2 which is shown in Fig 3 2 Tipe Eth Lew Som Meare hart nee Chort Se 2 as p sag Chorocteristic Admittance a mS d Admittance 4 j 10 414 j5 849 mS if Load Reflection Coo 36259 Input Ad Fg eases a RES Fig 3 2 The starting point for line 2 Fig 3 2 shows the Smith Chart for line 2 This shows the LOAD admittance and the INPUT admittance close together on the Smith Chart because of the short length selected for line 2 Click on Change length and click the mouse inside the Smith Chart circle to adjust the length of line 2 until the INPUT admittance lies on the g 1 circle 38 Smith Chart Admittance Chart For line 2 600 028 MHz Generator Click the mouse in the Smith Chart to choose a new Length Toward Characteristic Admittance 20 0 mS Load Admittance 10 414 j5 849 mS Load Reflection Coefticien 0 36259 ongle 42 3 Input Admittonce 20 040 j15 578 mS i Input Reflection Coefficient Finist 0 36259 ongle 111 4 degrees unt aussi pang ce Aaa i Fig 3 3 Use the Change length function to adjust the length of line 2 so that the input admit
16. to choose a circuit for study from the list shown In all the menus in TRLINE menu choices are shown as red character strings and are called buttons Click the mouse on any red text string in any menu in the program to get an action In the circuit template menu the names of the circuits are buttons and the user clicks the mouse on a circuit name to select that circuit Also a saved circuit can be recalled from the disc using the Read a saved circuit button In the lower right hand corner of the screen we see an Exit button The exit button terminates execution of the TRLINE program There are more circuits in TRLINE than conveniently fit on one screen so there is a more circuit templates button in the list Click more circuit templates to get the sub menu of Fig 2 1 b This offers five additional circuits Section 5 of this manual describes the demonstration associated with each of the circuits NUN qo a a lexwds1 ital Ble Eat Yaw sot Widow ee ale a red label to change the properties Line 1 Load 1 2 000 GHz Sg l at L Choose on action by clicking the mouse on a rad text string Plot Tizl and find the USUR Find currents and power Draw Chart Smith iiculations os a function of the frequency ive the circuit to c ta file Chang Runs Fouseipaipendng in Guck Vn Apelor Fig 2 2 The TRLINE main menu When a circuit has been chosen the program go
17. 0 angle 121 3 degrees Real Towards Generator Fig 3 8 The Smith Chart for Line 3 with a longer stub length As the length of the stub is increased the admittance at port lo moves around the g 1 circle For example in Fig 3 8 we see the Smith Chart for a stub length of 0 041 m The input admittance is on the g 1 circle at approximately 1 j1 mS Making the stub longer move input admittance around the g 1 circle towards the origin 43 7 Ble Eat Uw sw Wisaa HD Smith Chart Admittance Chart For line 3 Pima TNeur je PS S Frequency 600 0 MHz Length 8 072 m 5 Y at port lo 5 20 040 j0 009 S 8 A 3 3 zee Lof Characteristic Admittance 20 0 mS Load Admittance 1802000E 065 j0 002 mS Load Reflection Coefficient 1 02080 ongle 168 0 degrees Input Admittonce 0 020 j15 569 mS Input Reflection Coefficient 1 B8080 angle 75 8 degrees Fig 3 9 Adjust the length of line 3 to move the admittance at port 10 around the g 1 circle to the origin Real Z we gt Dense grid a p Change length Back Fig 3 9 shows that the length of line 3 can be adjusted to put the admittance at port 10 very close to the origin With a line length of 0 072 m the admittance is 20 040 j0 009 mS close to a perfect match The admittance at port 1o appears in Fig 40 as a small cross at the origin surrounded by a small circle Morker 1
18. 1 a Dew Se oe Ee Smith Chart Admittance Chart For line 1 300 080 MHz or Click the mouse 8 n the Smith Chart i to choose a new ae i Characteristic Admittonce 20 0 mS iN Load Admittance 40 000 8 030 mS Load Reflection Coefficient N 0 33333 ongle 180 0 de Input Admittonce 10 2024j0 080 vS Input Reflection Coefficient 8 33333 angle O O degrees arning userpage GuckWn Appiicaiion Fig 2 17 Changing the length of transmission line 1 to change the input admittance The Change length button in Fig 2 16 is handy for modifying the length of the transmission line to bring the input admittance to a desired value Click Change Length to get the Smith Chart of Fig 2 17 Click the mouse within the Smith Chart circle The program calculates the position of the mouse click and sets the length of the transmission line so that the input reflection coefficient has the angle associated with the mouse click In Fig 2 17 the user has click the mouse on the positive side of the real I axis making the angle of the reflection coefficient zero The program has adjusted the length of line 1 so that the input impedance of line 1 gives rise to a reflection coefficient with angle zero that is a reflection coefficient that is real and positive 22 Smith Chart Admittance Chart For line 1 Frequency 300 020 MHz Length 2 758 m Towards Generator Characteristic
19. 27 2 6 Frequency Response Extensive calculations are needed to determine the behavior of a transmission line circuit as a function of frequency and such calculations are beyond pencil and paper homework in a fields and waves course or a microwave engineering course Yet most real applications are concerned with the bandwidth over which a required performance is met Thus in an impedance matching problem the bandwidth of the match for a return loss of better than 10 dB is often required Pee T Be kat Gen Sot Ww ao Choose o parometer to graphs Input impedance USWR E efficient eturn loss ransm se 3 Port 2 Port 3 Perf a4 onge of t requency res graph on rectangulor oxe quency respo on SMTHCHT Back a Fig 2 23 The frequency response menu for the quarter wave transformer Click Plot a parameter as a function of frequency in the main menu of Fig 2 2 to get the frequency response menu of Fig 2 23 shown for the quarter wave matching circuit template To demonstrate frequency sweeping the circuit is set up with line 3 with characteristic impedance 100 ohms terminated by a 100 ohm load Line 1 is a 50 ohm line and the transformer impedance is line 2 The characteristic impedance of line 2 is chosen as 450x100 70 71 ohms A perfect match is wanted at 600 MHz With a wave speed of 299 79 meters per microsecond the wavelength at 600 MHz is 0 49965 meters and so the transformer length is
20. Across the center in Fig 2 15 below the circuit schematic there is a button for each transmission line If we click the mouse on the button for Line 1 we obtain the Smith Chart calculation of the input impedance shown in Fig 2 16 20 Smith Chart Admittance Chart For line 1 200 020 MHz Generator Towards G Se Choracteristic Admittonce 20 0 mS Load Admittance 40 000 j 020 mS Load Reflection Coefficient 0 33333 ongle 180 0 deg Input Admittonce 31 8943 j13 707 mS S De Input Reflection Coeffic Change length 8 33333 angle 144 0 degrees Back Fasani peningin Guck Apelor Fig 2 16 The Smith Chart for Line 1 The Smith Chart of Fig 2 16 shows the load impedance that terminates line 1 which is the parallel combination of the input impedance of line 2 and line 3 Since both of these lines have a 50 ohm characteristic impedance and are terminated with a 50 ohm matched load the input impedance of each of these lines is 50 ohms and the parallel combination is 25 ohms or 40 mS Normalized to the 20 mS characteristic admittance of the transmission line the 40 mS load admittance is equal to 2 so the LOAD admittance graphed in Fig 2 16 is 2 j0 As we move along the transmission line from the load to the input the admittance moves on a constant q circle in a clockwise direction as shown in Fig 2 16 The INPUT impedance of the line is reported as 31 093 j13 707 in Fig 2 16 2
21. It is centered on 2 GHz as expected The markers are set to show the bandwidth of 0 259 GHz for a transmission loss of 0 5 dB which corresponds approximately to the expected 15 bandwidth 75 T T T i Morker 1 Se J 2 0001 1a J Morker 2 Pi 2 062 fal brker 2 10 93 2 5 3 o 5 ea E E a g 5 esf 4 2 v E 30 bii JRPLOT Snap 7 i EE VE con L Las r ty e e u Bock Pa Da 2 0 3 0 Freauedcul BHz Fig 5 7 Return loss of the bandpass filter Fig 5 7 shows the return loss of the Chebyshev filter The peaks in the pass band are at 10 9 dB return loss Choose o parameter to graph Input impedance USWR Reflection coefficient Return loss Transmission loss Input admittance Choose a port 1 HE 3 4 5 G 7 O 49 10 11 12 Pi P 7 Pleated ar eae i y HI a 4 ine ep or a ERI a4 e 10 oof 11 Por U 1 4 ay tt s 5 J 3 Port 1 Port W Port 3 Port Wt Port WS Port WG Por 7 3 a Parometer Return loss Use port T N Specify the range of the frequency sweep Calculate the frequency response graph on rectangulor oxes Calculate the frequency response on a Smith Chart SMTHCHT Back Fig 5 8 Bandpass filter with N 5 76 5 5 Bandpass Filter with N 5 We can make a bandpass filter using N 5 with the circuit template of Fig 5 8 This template has six transmission lines in series and five stubs To design a bandpass filter
22. J 545 784 20 00 T H Morker 2 654 415 ao 20 08 amp y J Bondwidth 2 eab 118 630 4 Marker Marker 2 a S e 3 v ir 30 4 35 RPLOT Snap pgs se cde dd hd Td Back oa D 4A saa eda 7a saa qa aoa Freauencu MHz Fig 3 10 The bandwidth of the match 44 To assess the bandwidth select Plot a parameter as a function of frequency from the main menu and set the frequency range to 200 to 1000 MHz Display the return loss at port 1 and snap the markers to 20 dB as shown in Fig 3 10 The bandwidth is 118 63 MHz for a return loss of 20 dB or better i ute EE EE ca OF Ble Eat Den Sate Window ee Choose a port to monitor cify the rotatio Frequency 680 208 MHz DR uC li Line 1 Line 2 Monitor port Co Chart Type Admittance Switch Eo an impedance chart iii Sst nang OTE A Fig 3 11 The double stub matching circuit 3 2 Double Stub Matching We can design a double stub matching circuit interactively with TRLINE The circuit is shown in Fig 3 11 The lines have speed of travel 300 meters per microsecond and characteristic impedance 50 ohms The load is Zi 73 j41 ohms and the frequency is 600 MHz The input line length is 20 cm The stubs are to be separated by 0 0625 m or about 1 8 of the wavelength at 600 MHz which is the length of line 2 in Fig 3 11 Start by setting the stub lengths to be short say 2 cm as shown in Fig 42 Choose the Smith Chart Calculat
23. TRLINE User s Guide 1 Introduction Dr C W Trueman Professor Department of Electrical and Computer Engineering Concordia University Trueman ece concordia ca TRLINE Version 1H e User s Guide Version 1B g Revised February 12 2015 Program TRLINE or Transmission Line solves transmission line circuits in the frequency domain The program contains 15 circuit templates for circuits commonly solved in a Fields and Waves course and a course in passive microwave circuits simple transmission line transmission lines in series quarter wave transformers branching transmission lines single double and triple stub tuners low pass filter and band stop filter TRLINE provides a software laboratory for testing pencil and paper solutions to homework problems in transmission line theory The program emphasizes frequency response which is difficult to evaluate with pencil and paper solutions The program provides interactive design for single and double stub tuning circuits TRLINE is useful for testing designs in a passive microwave engineering course This User s Guide explains the features of the TRLINE program It illustrates transmission line problems commonly encountered in the introductory Fields and Waves course and in the Microwave Engineering course TRLINE was described in a paper published in the IEEE Transactions on Education 1 TRLINE VERSION 1Hle by Or C W Trueman ECE Dept Cl
24. aa Fig 2 9 The transmission line menu offers various options for graphing the voltage 2 3 Graphing the Voltage on the Transmission Lines To solve the circuit and graph the voltages on the transmission lines click Plot V z in Fig 2 4 to get the transmission line menu of Fig 2 9 This menu lets the user graph voltage and current as a function of position on any of the transmission lines Across the top of the menu we find the properties buttons used to change the parameters of the generator lines and loads as discussed above At the bottom we find the menu s action buttons You can plot the voltage the current both the voltage and the current and the voltage or current including the phase You can also draw a Smith Chart 14 E T TEL pe Em pe Bai Yordon ie Line 1 USWR 2 0008 y Line 2 USUR 1 2000 Line 3 USWR 1 2000 N w 1 Ux 1 i 300 020 MHz amplitude os a function of distance Back Fig 2 10 The voltage on all the transmission lines Click Plot the voltage amplitude on all lines to get the schematic diagram of Fig 2 10 We see the voltage standing wave on line 1 On line 2 we have a matched load and a constant voltage with position Branching lines are shown across the top of the screen and we see a constant voltage on line 3 which also has a matched load The Back button at the lower right retu
25. across the load In the Smith Chart Calculations menu click Line 4 to display the Smith Chart for the tuning stub connected across the load This is shown in Fig 3 13 The admittance at port 20 is reported as 10 414 j72 046 and appears as a target symbol a small cross enclosed in a circle near the INPUT arrowhead in Fig 3 13 We want to move the admittance at port 2 onto the rotated g 1 circle Click Change length and make the tuning stub longer 47 ore ran ai TE pe Em ye see sore ae Smith Chart Admittance Chart For line 4 Frequency 600 020 MHz Lengths 9 889 m Y at port 20 18 414 j3 962 S 8 Click the mouse BY in the Smith Chort 3 to choose a new teigta LORI Characteristic Admittance 20 0 mS Load Admittance L 1002000E 06 j0 000 m5 A Load Reflection Coefficient N 1 02020 ongle 188 0 degrees Input Admittonce 0 088 j9 811 mS Input Reflection Coefficient 1 BBABA angle 52 3 degrees _ uring Wautepa pening in Guin Applica Fig 3 14 Change the length of the tuning stub with the Change length function As we increase the length of the tuning stub the admittance at port 20 moves around the Smith Chart towards the rotated g 1 circle In Fig 3 14 we see that for a stub length of 0 089 m the normalized admittance at port 20 appears as the target symbol at approximately 0 5 j0 2 mS The stub is not long enough to put the admittance on t
26. admittance at port 20 which is the output port of the line joining stub 1 to stub 2 We want to adjust the length of stub 2 to put this admittance onto the rotated g 1 circle Fig 3 27 shows the admittance at port 20 as the target symbol at left in the Smith Chart It is very close to the g 1 circle 59 Smith Chart Admittance Chart For line 5 Frequency 600 020 MHz Se Lengths i K 3 178 m 3 Y at port 2o 4 24 237 j0 956 S 8 LOA a Characteristic Admittance 20 0 mS N AA Load Admittance lt a pe G 1G0200GE 06 j0 002 mS so Load Reflection Coefficient N Pea y Fi 1 0820 ongle 188 8 degrees N 7 F Input Admittonce x 7 P 0 208 j15 874 nS e grid Input Reflection Coefficient Change length 1 80020 angle 75 9 degrees INPUT Back Fig 3 28 Change the length of stub 2 to put the admittance onto the rotated g 1 circle Adjust the length of stub 2 line 5 to move the admittance at port 20 onto the rotated g 1 circle Fig 3 28 shows that with the stub length adjusted to 0 178 m the admittance at port 20 is on the rotated g 1 circle Note that although we start with the admittance close to the g 1 circle itself in Fig 3 27 no length for stub 2 moved the admittance to the origin for the desired match The best we can do is move close to the origin Fig 3 28 and then use stub 1 to achieve the match 60 Ble Eat Uw Som Widow Bea Smith Chart Admittan
27. can be used in classroom demonstration to show the voltages on the lines and the transmission loss Similarly the bandstop filter is set with values useful for demonstrating the concept The following describes the features of the program that can be used to demonstrate the operation of these various circuits Click the mouse on a red label to change the properties Generator Line 1 Load 1 Frequency Line 2 Load 2 4 Line 3 Pa 7 Frequency 300 000 MHz 7 7 Ww 7 R 3 7 vO a ze L L 2 J Choose on action by clicking the mouse on o red text string Plot U zl or Ilzl nd the Find volta curren and power Draw a Smith Chart Smith Chart Calculations Plot a porameter as a function of the frequency Save the circuit to o data file Ch a new circul Ct ange the settings Exit un aussi pang eR Aaa Fig 2 4 The main menu showing the properties buttons across the top of the screen 2 2 Setting the Component Values Properties Menus Start the TRLINE program and choose a circuit say the transmission line branching to two loads This gets the main menu shown in Fig 2 4 To set the component values to correspond to those of the circuit we wish to solve we use the properties buttons across the top of the screen Recall that buttons in the program are red text strings so you can click the mouse on any red text string to select a function in the program 10 W
28. ce Chart For line 3 Frequency 600 020 MHz Length 3 010 m E Y ot port lo E 20 062 j162 257 INE SFouards G a Characteristic Admittance 20 0 mS Load Admittance 0 1802000E 06 j0 000 mS Load Reflection Coefficient 1 02020 ongle 188 0 degrees Input Admittonce 0 088 j158 316 mS Z Fig 3 29 Monitor port 10 to adjust stub 1 which is line 3 s a ot Dense grid Input Reflection Coefficient lt Change length 1 88020 angle 165 6 degrees Back Fig 3 29 shows the starting point for adjusting stub 1 line 3 Monitor the admittance at port 1o the input port to the matching circuit shown by the target symbol at left in Fig 3 29 Then change the length of stub 1 to move the admittance around the g 1 circle to the origin 61 Smith Chart Admittance Chart For line 3 Frequency 600 020 MHz Length B 141 m 3 Y ot port lo 5 20 062 j0 023 S 8 3 LOI Characteristic Admittance 20 0 mS Load Admittance 0 18O2000E 06 j0 002 mS Load Reflection Coefficient 1 02080 ongle 162 0 degrees X Input Admittonce 0 208 j3 973 mS 1 Dense grid Input Reflection Coefficient gren length 1 02020 angle 22 5 degrees Back Fig 3 30 Adjust the length of line 3 to put the admittance at the center of the Smith Chart In Fig 3 30 the length of stub 1 has been set to 0 141 m and the admittance at port 10 is a match to the 20 mS transmission line L
29. chosen as 0 12491 m The program can plot five different parameters as a function of frequency input impedance VSWR reflection coefficient return loss and transmission loss Choose a parameter by clicking the mouse on a parameter button at the top of the screen For this demonstration choose Return Loss In Fig 2 23 each junction represents a port Parameter values are reported for the part of the circuit to the right of the port Thus the input impedance at port 1 is that for the entire circuit whereas the input impedance at port 2 is that of line 2 connected to line 3 terminated with the load Chose a port by clicking the mouse on one of the port buttons for this demonstration choose Port 1 se TRLINE VERSION 1H c Jan 7 2015 Frequency Sweep Nenu Frequency Sweep Menu tt Start ing frequency 200 0 W Stopping frequency 1000 We Nunber of frequenc ies 2001 Cont inue fuming easeinpat pencingin Guan Apelor Fig 2 24 The frequency range menu In the sweep menu of Fig 2 23 click on Specify the range of the frequency sweep to obtain the menu of Fig 2 24 which has numerical fields for the starting frequency the stopping frequency and the number of frequencies in between The quarter wave transformer circuit of Fig 2 23 is designed to provide a perfect match at 600 MHz so set the frequency range to start at 200 MHz and finish at 1000 MHz Then click Ca
30. dngin auekin Apn Fig 2 30 The VSWR as a function of frequency Choose the VSWR in the menu of Fig 2 23 then clicking Calculate the frequency response TRLINE graphs the VSWR at the specified port as shown in Fig 2 30 The markers can be used to determine the bandwidth for a given VSWR value such as 1 2 The VSWR is unity at the design frequency of 600 MHz but rises rapidly as we move away from the design frequency 34 T T T T T T 8 30 4 ash 5 E 5 8 28 E a ask 4 a is F Ei a f Bi z Marker 2 3 7 j as 4 glrrsilitislii oo Witty saa 40 sen 7a ABA qaa Aan Frequencu MHz J Morker 1 499 933 2 099 J Morker 2 710 814 g 0999 Bonduidtn 220 081 RPLOT Snap Back gous pat penngin Gun ee Fig 2 31 The reflection coefficient as a function of frequency Choose reflection coefficient in the frequency response menu of Fig 2 23 and then clicking Calculate to get the reflection coefficient magnitude as a function of frequency as in Fig 2 31 Here the markers have been snapped to show the bandwidth for a reflection coefficient of less than 0 1 round off error in the program finds the reflection coefficient as 0 0999 close to 0 1 The TRLINE program can also calculate transmission loss and this feature will be demonstrated in conjunction with the Chebyshev filter below 35 a TRLINE VERSION 1H e Ja
31. e of the negative going wave Distance z is zero at the left hand end of the transmission line and is equal to the length of the line at the right hand end TRLINE reports the values of V and V below the circuit schematic The voltage current and power at the input of the line is reported as well as the input admittance The voltage current and power at the output of the line is also reported The output power is always equal to the input power because the transmission lines in TRLINE are lossless The admittance at the output of the transmission line is also report and is equal to the input admittance of the remainder of the circuit lying to the right of the output port of the transmission line 26 Ast Ble Ein Yew Sow Yisiow He Frequency 300 200 MHz Ape Ra A UC 1 Lood l Lood admittance 20 0 j2 20 millisiemens Uoitage 333 3 millivolts RMS phase 169 2 degrees Current 6 667 milliomps RMS phase 169 2 degrees Power 2 222 milliwatts Back Finn Wauzsirpat ponding in Gdn Appleton Fig 2 22 The power report for load 1 Click Load 1 in Fig 20 for the report on the power flow at load 1 in Fig 2 22 The load admittance is given The voltage and current at the load are given The power flow into the load is given Using the power flow menu we can determine how much power the source delivers and how much of that power finds its way to each of the loads
32. e the admittance to a point on the Smith Chart that can be matched with a double stub tuner made up of stub 1 line 3 in Fig 53 and stub 2 line 5 and the line joining the two stubs line 2 Choose the Smith Chart Calculations menu to start the design Choose the rotation of the g 1 circle to be the length of line 2 the line between stub 1 and stub 2 54 Smith Chart Admittance Chort line 600 080 MHz amp 3 Ox 5 fe S Generator Toward o Characteristic Admittance 28 8 mS Load Admittance Load Reflection Ci 1 02080 ongle Input Admitt 2 280 j158 e grid Input Reflection Coefficient Change length 1 88020 angle 165 6 degrees Back 7 Fonsi pendng a aaa pen Fig 3 23 The load admittance is 40 j40 mS or normalized admittance 2 j2 on the lines of characteristic admittance 20 mS The load admittance is Y 40 j40 mS To show where the load admittance lies on the Smith Chart choose to monitor port 60 where the load is connected and then draw the Smith Chart for Line 7 shown in Fig 3 23 The target symbol at normalized admittance 2 j2 is the load that we are trying to match Note that the constant g circle for g 2 intersects the rotated g 1 circle so it is possible to match this load with a double stub tuner with a 5 cm stub spacing Stub 3 can move the admittance anywhere on the g 2 circle Line 4 in Fig 3 23 rotates the g 2 circle towa
33. es to the main menu in Fig 2 2 which gives access to a menu for each of the program s functions The main menu is organized with a schematic diagram for the circuit across the center of the menu properties buttons at the top and action items at the bottom The properties buttons are used to tell the program about the properties of each part of the circuit Click frequency to specify the operating frequency Click generator to specify the voltage of the generator and its internal resistance Click line 1 to specify the length characteristic impedance and wave speed for line 1 Ifthe circuit has say five transmission lines there will be five properties buttons one for each transmission line Click Load 1 to specify the resistance and reactance of the load The properties buttons appear on other menus such as the transmission line menu and the Smith Chart menu The bottom of the main menu has buttons which give you access to the computations that the program can do for you When you have set the lengths and characteristic impedances of the transmission lines and the values of the loads and so forth you can save the values to a disk file by clicking Save the circuit The program asks you for a file name The program uses the extension trl for its data files The TRLINE program has five principal functions Clicking Plot V z gets the transmission line menu This is used to
34. graph the amplitude and phase of the voltage or the current on the transmission lines There are two kinds of graphs that the program creates The first is a schematic of the transmission line circuit with V z or I z graphed above it The second is a graph of the voltage amplitude on any one of the lines as a function of distance including two markers which let you read back values from the graph These are described further below The second function is Find voltages currents and power This gets the voltage and power menu This menu lets you ask for the voltage current and power delivered by the generator or for the voltage current and power delivered to any load or for the voltage current and power flowing into and out of any transmission line The third function is obtained by clicking Draw a Smith Chart and is used to graph the load impedance and input impedance of any transmission line in the circuit This button starts the Smith Chart menu which can draw a Smith Chart for any transmission line in the circuit The chart can be an impedance chart or an admittance chart The Smith Chart display shows the Smith Chart with the load impedance for that line being transformed back to an input impedance The Smith Chart display reports the load and input impedance or admittance The fourth function is Smith Chart Calculations The TRLINE program lets you design single and double stub matching interactively as
35. he circuit Choose a port to monitor li lo 2i 203i 30 Specify the rotation of the g 1 circle P A bond 2 Frequency 300 200 MHz ff ae j ars Rg r x Y Zi vl i o aiy 2o s Z Line 3 Line 1 Line 2 Chart Type Admittance Back Switch Eo an impedance chort Fig 3 1 The Smith Chart Calculations menu 3 Interactive Calculations with TRLINE The main menu in Fig 2 2 provides a Smith Chart Calculations button This invokes the menu of Fig 3 1 You can use this menu to design single and double stub matching circuits interactively Each transmission line has an input port and an output port Thus for transmission line 1 the input port is li and the output port is lo TRLINE monitors the impedance at a specified port by drawing a for the impedance on the Smith Chart as shown in the following 3 1 Single Stub Matching Fig 3 1 shows the single stub matching circuit Line 1 is the input line and is 20 cm long In this example the load is Zi 73 j41 ohms All three lines have characteristic impedance 50 ohms and speed of travel 300 meters per microsecond The branch which is line 3 is the tuning stub and the problem is to choose the length of line 2 and the length of the stub to obtain a perfect impedance match to a 50 ohm line at 600 MHz Start with a short line length and a short stub length Set the length of lines 2 and 3 in Fig 3 1 to 1 cm The first step in designing the
36. he rotated g 1 circle so make the stub longer 48 Smith Chart Admittance Chart For line 4 Frequency 600 020 MHz Length B I m 8 Y at port 2o g INPUT 10 414 j2 412 S 8 By Ri Loft a Characteristic Admittance 20 0 mS Load Admittance 1002000E 06 j0 002 mS Load Reflection Coefficient 1 02080 ongle 188 08 degrees Input Admittonce a KX 0 208 j3 437 mS Sk ee Dense grid Input Reflection Coefficient SL Change length 1 88820 angle 19 5 degrees Back Fig 3 15 With the tuning stub length set of 0 111 m the admittance at port 20 lies on the rotated g 1 circle Continue to increase the length of the tuning stub until the admittance at port 20 moves onto the rotated g 1 circle Fig 3 15 shows that with a stub length of 0 111 m we are on the rotated g 1 circle Note that there is a second solution for a longer stub length not shown in Fig 3 14 TE pe Eon vee Sot My eee Smith Chart Admittance Chart For line 3 Frequency 600 020 MHz Length 2 028 m Y at port lo 19 940 j54 215 owards General Real T Characteristic Admittance 20 0 mS Load Admittance 0 1802000E 05 j0 002 mS Load Reflection Coefficient 1 02820 ongle 162 0 degrees Input Admittonce 8 200 j77 895 mS Input Reflection Coefficient rad Dense grid Change length 1 88020 angle 151 2 degrees Back Change the port to the admittance seen at the output of l
37. heir lengths to 0 25 m Line 3 is the transformer so set its length to 0 125 m and its characteristic impedance to 77 459 ohms Set the load to 120 ohms Set the frequency to 600 MHz Then click Plot V z and then Plot the voltage amplitude on all the lines to demonstrate the match as in Fig 4 2 We see that the voltage is constant with position on lines 1 and 2 with a VSWR of 1 0000 65 DE a S i rs ipie got pew sme Wnion ep 1a F J Morker 1 15b J Morker 2 _ 685 739 19 99 ee 19 Marker 1 Morker 2 Bandwidth g 171 354 tap E Return M s 4gL 1 im rere ore lu 1 toa 3m0 lt a Soa Sea 7Ba aoa SD Freauencu MHz Ronni cS np penig SN ATO Fig 4 3 Use the frequency sweep function to find the bandwidth as 171 35 MHz To find the bandwidth of the match for a return loss of 20 dB or better click on Plot a parameter as a function of frequency then Specify the range and set the start and stop frequency to 200 and 1000 MHz respectively Then click on Calculate the frequency response to get the return loss Use the snap function to snap the markers to 20 dB to get Fig 4 3 The bandwidth is 171 35 MHz 66 e on a red label to change the proper Line 1 Load 1 Line 2 Line Line 4 Line 5 Frequency 308 808 MHz we s R UC Choose tion by clicking the t string Plot U or
38. ick the mouse on ony RED text tO Feb 10 2015 a cordia University Montreal ng to on select action in this program Click the mouse on any BLUE text string to change the value Choose a trans ssion line circuit Transmi line with Two tran n lines Two transmission lines ert ne branching Powe plitt S stub motching ib matching b matching Triple stub matching M ircuit templ o sove irou arter wave eries with shunt load b across the load Furing Poussa panangin Guan Appenin Fig 2 1 a TRLINE s circuit template menu Je Edt Dew Sou Window eb TRLINE VERSION 1Hle KR Feb 10 2015 a sandpass filter bandpass filter transmission lines ir Back Fang asap oa RES Fig 2 1 b The more circuit templates sub menu 2 TRLINE Menus TRLINE starts by showing the circuit template menu of Fig 2 1 a The menu reports the version number and date of the TRLINE exe file at the top of the screen New versions that correct errors or add features are available from time to time It is often convenient to make a directory for your TRLINE project and to copy the TRLINE exe file into the directory To run TRLINE open the directory as a window and double click TRLINE exe or open a DOS window change to the project directory and type TRLINE The circuit template menu of Fig 2 1 a asks the user
39. ig 5 10 Return loss for the N 5 filter Fig 5 10 shows the return loss of the N 5 filter We have five sharp minima in the return loss separated by four peaks of equal magnitude as expected from a Chebyshev bandpass filter 6 Conclusion Program TRLINE s circuit templates make it easy for the student to study typical circuits encountered in a fields and waves course or in a microwave circuits course TRLINE illustrates the basic behavior of transmission lines well TRLINE provides a computational laboratory for students to test their solutions to pencil and paper homework problems involving series transmission lines transformer matching stub matching and branching circuits TRLINE s frequency sweeping capabilities make it possible to study the bandwidth of these circuits TRLINE provides circuit templates for more advanced topics such as power splitters band pass and bands top filters Reference 1 C W Trueman Interactive Transmission Line Computer Program for Undergraduate Teaching IEEE Trans on Education Vol 43 No 1 pp 1 14 February 2000 2 P Pozar Microwave Engineering 3 edition Wiley 2004 78
40. iitiin n 40A 500 BAA 720 Aaa saa 1800 Frequencu MHz 2 Meuse input pendingin Guck Win Application Fig 3 20 The bandwidth of the match for a return loss of 20 dB or better is 51 53 MHz Use the frequency sweep function to assess the bandwidth of the match as 51 53 MHz for a return loss of 20 dB or better as shown in Fig 3 20 52 e on a red label to change the proper Lin ad 1 Line 2 Line j Line 4 ii 2 Ein ig j Lis Frequency 300 000 MHz I Ve a ek 3 i 3 a Z 7 Rs Z Z O 1 s 1 e te 2 d J Choose tion by clicking the mous o red text string Plot V or Ilzi and find the Find currents ond power Draw a Chart Smith Chart Calculations Plot a porameter os a function of the frequency S the circuit to o data file a new t Cha the settings fig apa aR Fig 3 21 TRLINE s triple stub matching circuit template 3 3 Triple Stub Matching Triple stub matching can be used to match loads which are impossible to match using double stub matching Fig 3 21 shows TRLINE s circuit template for triple stub matching There are three stubs which are lines 3 5 and 7 in Fig 3 21 The circuit includes a length of transmission line between stub 3 line 7 and the load but we don t need this line so set it to a short length say 0 01 cm Line 1 is the input line and we want to design the triple stub tuner to obtain a
41. impedance of each of the five transmission lines making up the filter in Fig 5 1 Table 1 Design of a low pass filter 2 Component Value Replace by Equivalent Shunt Stub Scaled Impedance equivalent stub of Stub R 1 a for Fig 5 1 characteristic oe resistance R Line R R 1 Series L 3 3487 Series short 1 Stub i circuited stub with Rei 1 33gg7 71286 R 64 9 ohms Rog L 3 3487 Ra R 1 4 3487 Line R 217 5 ohms Shunt C 0 7117 Shunt open R 70 3 ohms circuited stub with Ryo U C 1 405 Series L 3 3487 Series short 1 Stub circuited stub with Ras 51 3 3487 1 2986 R 64 9 ohms 70 R 1 3 3487 R R 1 4 3487 Line R 217 5 ohms load R 1 0000 R 1 for 50 ohms normalized impedances The line lengths for the filter are one eighth wavelength at the cutoff frequency of 4 GHz At a speed of travel of 30 cm ns the wavelength is 7 5 cm and one eighth wavelength is 0 9375 cm so lines 2 3 4 5 and 6 in the circuit of Fig 5 1 are set to this length The series lines in the filter lines 2 and 4 are set to characteristic impedance 217 5 ohms Stub 1 is line 3 and is set to 64 9 ohms stub 2 is line 5 and is set to 70 3 ohms and stub 3 is line 6 and is set to 64 9 ohms The input line 1 and the output line 7 have arbitrary lengths set to 1 875 cm for this example and characteristic resistance 50 ohms The load Z i
42. indow He TRLINE VERSION 1H b Dee 1 2014 et tettetett Generator Properties Menu Generator Properties Menu Voltage source value 1 000 Volts RMS Internal resistance 50 00 hns Frequency 300 0 NH Cont inue Fig 2 5 The generator menu Click on Generator to get the generator menu of Fig 2 5 This menu has fields to specify the R M S value of the open circuit voltage of the generator and the generator s internal resistance Also the frequency can be set At the bottom of the list we have a red Continue button Click Continue to return to the main menu ow peo TRLINE VERSION 1H b Dee 1 2014 ett seeeesee Generator Properties Menu Generator Properties Menu Voltage source value 1 000 Volts RMS Internal resistance SI Ons Frequency 300 0 WH Cont inue Fig 2 6 Changing the value of a parameter in a field 11 In TRLINE any text string shown in blue is a field containing a value that the user can set Click the mouse on the blue text string 50 00 in Fig 2 5 to change the value of the source internal resistance to obtain the screen shown in Fig 2 6 The field changes to inverse video and you can type the new value Note that the Continue button is black because it is not active when you are editing a field Type the Enter key to finish and return to the menu of Fig 2 5 The Continue
43. ine 1 USWR 1 8833 y ul y Line 2 USWR 1 2177 N Line 3 USWR Infinity a Line 4 USUR 2 1579 Line 5 USUR Inrinity N Line 6 USUR 4 2655 43 A 7 Line 7 USUR Intinity u u A Loha a4 Frequency 500 080 MHz Uoltage amplitude os a function of distance Back Fig 3 31 The triple stub matching circuit achieves a good match on line 1 62 Fig 3 31 shows the voltage waveforms on all the transmission lines Line 1 is the input line and has a VSWR of 1 0033 a good match Ten dB b 5L Return Loss L Marker 1 Marker 2 Morker 1 559 683 19 99 J Morker 2 615 540 319 98 Bondwidth 45 956 4 RPLOT Bake Back Fig 3 32 A bandwidth of 45 96 MHz is obtained for a return loss of 20 dB or better vol soa 550 Frequencu oth L sja 650 700 MHz aa Fig 3 32 shows that for a return loss of 20 dB or better the bandwidth of the match is 45 96 MHz 63 Click the mouse on o red label to change the properties Generator Line Load 1 Frequency Line Line 3 Frequency 300 000 MHz N gt LR l Zi uO a ae 3 L Choose on action by clicking the mouse on o red text string Plot Ulzl or Ilzl and find the USUR Find voltages ents ond power Drow a art Smith Chart Calculations Plot a porameter os a function of the frequency Save the circuit to o data file Choose o new circuit Change the sett
44. ine 6 y the range of the frequency alculate the frequency response graph on rectangular oxes SMTHCHT Back engin BUA Apo ning pT Fig 5 5 The N 3 bandpass filter uses short circuited stubs 5 4 Bandpass Filter with N 3 We can make a bandpass filter by terminating the quarter wave stubs with short circuits At the center frequency the input impedance of a quarter wave stub terminated by a short circuit is an open circuit so the stubs do nothing and the signal passes through the filter with no attenuation To demonstrate the bandpass filter design a filter with N 3 a center frequency of 2 GHz a bandwidth of 15 a ripple of 0 5 dB and an impedance of 50 ohms The low pass prototype has elements from Pozar s Table 8 3 2 g 1 5963 8 1 0967 and g 1 5963 For the bandpass filter Pozar gives the characteristic impedances of the stubs as EA O 4g where Z 50 ohms and the fractional bandwidth is A 0 15 For stub 1 Z 3 690 ohms for stub 2 Zo 5 731 ohms and for stub 3 Z 3 690 ohms 74 T T T Marker 1 orker 2 sie AL 1 878 5f J 0 5124 a wp J Morker 2 2 2 12 8 5105 e 5b 4 f j Bondwidth 2 8 259 _ 2af al 5 s 2 esk 4 E o 8 304 4 E p JRPLOT 7 Snap z EE SEEE Ce Sa a Lo PY yo Me rf Pa 1S 2 5 3 0 Fig 5 6 Transmission Toss of the bandpass filter Fig 5 6 shows the transmission loss of the Chebyshev filter
45. ine 1 port 10 Then draw the Smith Chart for the second tuning stub which is line 3 The admittance at port 10 lies on the g 1 circle at a normalized value of approximately 1 j3 5 shown as a cross enclosed in a circle in Fig 3 16 Increase the length of line 3 to move the admittance at port 10 around the g 1 circle to the center of the Smith Chart erat Ble Eat Yew Sele aow He Smith Chart Imag PUT Admittance Chort aa ae For line 3 aa Ee 1 Frequency 600 020 MHz j Length 2 068 m Y at port lo 19 948 j3 922 Generator Click the mouse in the Smith Chort ta choose o new length io Choracteristic Admittance 20 0 m3 Load Admittance 0 1G02R00E 06 j0 002 mS Load Reflection Co 1 02080 ongle 1i Input Admittonce a 200 j17 601 mS Input Reflection Coefficient 1 Q8008 angle 82 7 degrees B degrees Farming essinpat pending awa iain Fig 3 17 A tuning stub length of 0 068 m is not long enough to put the admittance at port 1o at the center of the Smith Chart Fig 3 17 shows that as the length of the stub increases the admittance at port 10 moves around the g 1 circle towards the origin With a stub length of 0 068 m the normalized admittance is about 1 j0 2 The stub is not long enough so continue to increase the length to move the port admittance to the origin 50 Smith Chart Admittance Chart For line 3 Frequency 600 020 MHz Length
46. ings Exit TTT Fig 4 1 The quarter wave transformer circuit template 4 Transformer Matching for Real Loads TRLINE offers circuit templates for two three four and five transmission lines in series These can be used to demonstrate quarter wave transformers 4 1 Simple Quarter Wave Transformer Fig 4 1 shows that the circuit template called quarter wave transformer consists of three transmission lines in series The parameters are set up to match line 1 a 50 ohm line to a 100 ohm load comprising line 3 with characteristic resistance 100 ohms and the load Z of 100 ohms at 300 MHz Click Plot V z and then Plot the voltage amplitude on all the lines to demonstrate the match Suppose we want to match a 50 ohm line to a load of Zi 120 j0 ohms at 600 MHz The wavelength is 0 5 m and the quarter wave transformer length is 0 125 m The required characteristic impedance for the transformer is 450x120 77 459 ohms All the lines have speed of travel 300 meters per microsecond so set all three transmission lines to this speed of travel 64 ipie got Yew fee Wynton ep Line 1 USWR 1 090 Line 2 USUI w o Frequency 600 200 MHz Uoltoge amplitude os a function of distance Back FRc VT GT RATS Fig 4 2 A quarter wave transformer to match a 50 ohm line to a 120 ohm load For this example use lines 1 and 2 as input lines and set their characteristic impedances to 50 ohms Set t
47. ions function in the main menu to get Fig 3 11 45 NEEL M cet Diese bere ie OOTRLINE VERSION AH Jan 7 2015 e tiiit i Rotation Menu Rotation Menu Rotation Menu Oraw a rotated g 1 circle on the Smith Chart Rotate through distance 0 2506 01 m Rotate the length of line 1 2 3 4 Cont inue Fossin pui pandin Gen pao Fig 3 12 The rotation menu To design double stub matching we need to rotate the g 1 circle by the length of line 2 Click on Specify the rotation of the g 1 circle in Fig 3 11 to obtain the rotation menu of Fig 3 12 Click on 2 to set the rotation of the g 1 circle to the length of line 2 which is 0 0625 m then click Continue Then in the menu of Fig 3 11 choose the port to monitor as the output port of line 2 which is port 20 46 OF Fle Edn View Stu Window Helo Smith Chart Admittance Chart For line 4 Frequency 600 028 MHz Length put i X 2 028 m y a A Y at port 2o g 10 414 j72 045 s it ait fee Characteristic Admittance iN 20 0 mS 7 Load Admittance J 1G0200GE 06 j0 002 m5 AS Load Reflection Coefficient N A if 1 02020 ongle 188 8 degrees gt J Input Admittence YS ye 208 77 895 mS S Dense grid Input Reflection Coefficient gt A Change length 1 B0080 angle 151 2 degrees Back Fig 3 13 The Smith Chart for line 4 which is the stub connected
48. j Back o Ww 20 3 40 50 6 7 8 Distance cm jr ssp aa ye Fig 2 13 The voltage as a function of position on line 1 To obtain a labeled graph of voltage as a function of position on any one of the transmission lines click the line name in red in the menu of Fig 2 9 Click Line 1 to obtain the graph of Fig 2 13 We seea labeled voltage axis and a labeled distance axis The graph shows a standing wave pattern The display includes two markers for reading back values Click the mouse on the red string Marker 1 then click the mouse again on the desired position of the marker The marker jumps to the new location and the distance and voltage are reported in the upper right hand corner of the screen The distance between the markers is also reported hence the markers are easily used to determine the distance from the load of the first standing wave maximum and of the first minimum This information is used to compute the load impedance from a knowledge of the standing wave pattern shown in Fig 2 13 18 tanding Wave Uoltage on line Voltage 66a 63a 62a Uoltage n A 8 stirtirtiit a jar ia pa OR oo Fig 2 14 RPLOT graph of the voltage standing wave on transmission line 1 Click the RPLOT button in Fig 2 13 to write a data file vt rp for graphing with the rectangular graphing program called RPLOT This program draws the standing wave in the fo
49. l of these lines are a quarter wavelength in length at 2 GHz The series lines 3 and 5 have characteristic impedance 50 ohms The stubs are terminated in open circuits The low pass prototype circuit elements are taken from Pozar s Table 8 3 2 and are g 1 5963 g 1 0967 and g 1 5963 The characteristic impedance of the stubs are then calculated using _ 4 aA where Z 50 ohms the fractional bandwidth is A 0 15 Thus for stub 1 Z 265 9 ohms and this is line 2 in Fig 5 3 For stub 2 Z 387 0 ohms and this is line 4 and for stub 3 Z 265 9 ohms and this is line 3 These values are used in the bandstop filter circuit template in the entry menu of Fig 2 1 on OR T Le Morker 1 1 904 lt 5 4 988 8 Marker Morker 2 apts 9 990 o 15 E 2 Bonduldth i 8 190 g P E i RPLOT Snap r A S S 1 lil iof ee oe ack t a 1 5 2 0 evil 3 0 Freauencu GHz Co Fig 5 4 Transmission loss of the bandstop filter Fig 5 4 shows the transmission loss of the bandstop filter from the input line 1 to the output line 7 We see that the filter is centered at 2 GHz as expected For a transmission loss of 0 5 dB the bandwidth is 0 260 which is approximately the expected 15 bandwidth The figure shows that the bandwidth for a transmission loss of 10 dB is 0 190 GHz 73 i Inpu Return loss Transmission loss l to l
50. lculate the frequency response in the menu of Fig 2 23 29 J Morker 1 475 534 im J asr N Morker 2 eh 4 J 17a a Morker i Marker 2 19 465 2 g esl 4 S z 5 ce J i 35H 4 RPLOT Snap plete desea dhs he te els a Back maa aa aa saa eaa aa aaa a aaa Freauencu MHz cI ara aust pena Ge Apel Fig 2 25 The return loss as a function of frequency Fig 2 25 shows the return loss from 200 to 1000 MHz The return loss is very large at the design frequency of 600 MHz To determine the bandwidth for a 20 dB or better return loss use the markers Click on Marker 1 then click the mouse on the curve at approximately 20 dB below 600 MHz Similarly position Marker 2 at about 20 dB above the center frequency Then click Snap at the lower right 30 Fig 2 26 The snap menu lets the user enter a snap value in this case 20 dB e TRLINE VERSION 1H c Jan 7 2018 0t tettet Snap Nenu Snap Menu Snap Wenu Snap Menu ttt How to use snap Snap is used to find the bandwidth between two poinis of say equal return loss of 20 dB First set marker 1 to the lower frequency where the return loss is roughly 20 dB Then set marker 2 to the higher frequency of return loss approximately 20 dB Then use this menu to set the snap value to 20 dB and snap the markers to frequencies where the return loss is exact ly 20 dB
51. length Jack _ Burning use np png GucRWn Application Fig 3 26 A stub length of 0 220 m puts the input admittance to line 4 close to the rotated g 1 circle Fig 3 26 shows the Smith Chart for stub 3 with the input admittance to line 4 port 4i shown with the target symbol The length of the stub has been adjusted to put the admittance at port 4i as close as possible to the rotated g 1 circle This is the admittance that will be matched with the double stub matching circuit Adjusting stub 2 and stub 1 for this load proceeds as described above for the double stub matching circuit The first step is to move the admittance onto the g 1 circle by adjusting stub 2 58 a Ble Ein View sow Yisiow He Smith Chart Admittance Chart For line 5 Frequency 600 020 MHz Length _ 2 810 m Y at port 2o l4 24 235 j175 148 IN SJE LOAD Characteristic Admittance 20 0 mS Load Admittance Ga 1002000E 06 j0 002 mS Load Reflection Coefficient y J 1 02080 ongle 188 8 degrees y d P Input Admittonce Ao ort 8 088 j158 316 mS Dense grid Input Raflection Coefficient ee Char a lanes 1 B8020 angle 165 6 degrees Back _ Running Mouse input pendingin GuckWin Appiicaiion a Fig 3 27 Monitor the admittance at port 20 and draw the Smith Chart for stub 2 which is line 5 To adjust the length of stub 2 line 5 monitor the
52. n 7 2015 tettetett Save File Menu Save File Menu Save File Menu e File Neme fig24 tri Look for files on the diss Exit from the program Save and cont inue Faring ssp pag GUE pon Fig 2 32 In the main menu of Fig 2 click Save the circuit to get the save file name menu 2 7 Saving the Circuit to a File When all the parameters of a circuit have been set using the menu system it is convenient to save the circuit to a data file so that it can be recalled later including all the parameter values The main menu of Fig 2 2 has a button labelled Save the circuit to a file which is used to create a data file with extension trl containing all the information about a circuit When TRLINE is re started at a later time the entry menu of Fig 2 1 is shown and you can click read a saved circuit to recall your circuit 36 rg OP TRLINE VERSION 1H Jan 7 2015 tettetett File Name Menu File Name Menu File Name Menu File Neme fig24 tri Look for files on the diss Exit from the program Open a new file Cont inue Fig 2 33 You can specify the name of the trl file for a saved circuit when you start the program The menu of Fig 2 33 lets you enter the file name for your saved circuit then reads the circuit and shows the main menu You can re start your work from where you left it when you saved t
53. n Fig 5 1 is set to 50 ohms for the transmission loss calculation 5 2 Transmission Loss The TRLINE program can calculates the transmission loss as a function of frequency Fig 5 1 shows the frequency sweep menu where the user has selected the transmission loss as the parameter TRLINE calculates the transmission loss from input line m to output line n The travelling wave complex amplitudes on the input line m are V and V The output line n should be terminated with a matched load The travelling wave amplitudes are V and V 0 The transmission loss from line m to line n is defined as TL 201 v 20log Ia For the low pass filter use the From line button in Fig 5 1 to select line 1 coming from the generator as the input line Use To line to select line 7 as the output line leading to the matched load Then click on Calculate the frequency response TRLINE then solves the circuit at each frequency in the sweep and uses the travelling wave amplitudes on lines 1 and 7 to evaluate the transmission loss as TL 201 w z oei TRLINE graphs the TL as in Fig 5 1 71 1 T Marker 1 2 364 5F Marker 1 3 3 203 apie Morker 2 oe J 3 67 8 0261 o 15E 8 8 al i q a s 4 S a 4 a J 5 ie d 5 sab 4 t JRPLOT Snap ag I L I f I Back 1 eil 1 2 3 4 5 6 7 Freauencu GHz Fig 5 2 The transmission loss of the low pass filter Fig
54. ne 2 as a quarter wave transformer to match the real part of the load Fig 2 3 h is a problem commonly given as a homework exercise consisting of a transmission line that branches to two loads of different complex valued characteristic impedance The student must find the input impedance then the power delivered to each load impedance The problem of choosing the line lengths and characteristic impedances to better match the source can be considered Fig 2 3 i is the same circuit as h but is set up to be a power splitter A transmission line branches to two lines of equal characteristic impedance terminated with matched loads A quarter wave transformer is included to match the source to the branch We can note in passing that the TRLINE program could solve this circuit with two or three step transformers but the program does not provide a circuit template The user could construct a trl data file to create such a circuit Fig 2 3 j k and l provide circuit templates for single double and triple stub matching These circuits have default values that achieve a good match again for classroom demonstration purposes Fig 2 3 m and n use open circuited stubs to demonstrate a low pass and a bandstop filter respectively These circuit templates are actually the same as the triple stub matching circuit with the loads on the stubs set to high impedances rather than short circuits The low pass filter comes with default values that
55. om line l to line T Specify the ronge of the frequency sweep Colculate the frequency response graph on rectangulor oxes SMTHCHT Back Fig 5 1 The low pass filter circuit 69 5 Filters The TRLINE program can be used to demonstrate filters constructed with shunt stubs The built in circuits show a low pass filter and a bandstop filter as described in the following 5 1 Chebyshev Low Pass Filter Fig 5 1 shows TRLINE s low pass filter circuit comprised of four transmission lines in series with three shunt stubs The circuit comes set up to demonstrate Pozer s low pass filter in Example 8 5 of Reference 2 The problem is to design a Chebyshev or equal ripple low pass filter with a ripple of 3 dB a cutoff frequency of 4 GHz and N 3 elements The impedance of the transmission lines and load is 50 ohms In Fig 5 1 line 1 is the input line connecting the generator to the filter and line 7 is the output line both of characteristic resistance R 50 ohms The load is Z 50 ohms The filter consists of series lines 2 and 4 of characteristic resistance R and R respectively and three open circuited stubs lines 3 5 and 6 of characteristic resistance R R and R respectively Lines 2 3 4 5 and 6 all have length one eighth wavelength at the cutoff frequency To design the filter we must specify the characteristic resistance of the five lines making up the filter R R R R sand R Pozar 2 explains
56. perfect match at the output of line 1 Consider a load of Zi 12 5 j12 5 ohms The frequency is 600 MHz and the transmission lines have speed of travel 30 cm ns and characteristic impedance 50 ohms The stubs are to be separated by one tenth of wavelength Since the wavelength is 0 5 m the length of lines 2 and 4 is set to 5 cm Set the loads on the stubs to zero impedance corresponding to stubs terminated with short circuits Set the length of the stubs to 1 cm as the starting point for the design 53 Click the mouse on a red label to change the properties Generator Line 1 Load 1 Frequency Line 2 Load 2 7 Line 3 Load 3 Line 4 Load 4 Line 5 Line 6 Frequency 600 208 MHz ine 47 in A n A i i Ge AP ea 1 ze s4 i ki Gi a Choose on action by clicking the mouse on a red text string Plot Ulzl or Ilzl and find the USUR Find voltages currents ond power Drow a Smith Chart Smith Chart Calculations Plot a porometer os a function of the frequency Save the circuit 9 dato file Cho a new circuit Change the settings _ Runa eubeipat panangin Guck Appleen Fig 3 22 The triple stub circuit is set up to design the triple stub tuner Fig 3 22 shows the circuit with 5 cm spacing between the stubs and the stubs set to short circuit terminations and to 1 cm length In the design stub 3 and the line joining stub 2 to stub 3 line 4 in the TRLINE circuit template are to be used to mov
57. rds the generator by the length of line 4 which is one tenth of the wavelength TRLINE does not have the feature of drawing the rotated g 2 circuit this would be a stepping stone in triple stub design SS Smith Chart Admittance Chart For line 7 Frequency 600 020 MHz 4 F 3 Length 9 010 m 01g Y at port 4i 880 j 2 557 Ih Characteristic Admittance 28 8 mS Load Admittance x 1002000E 06 j0 000 m5 Load Reflection Coefficient N 1 02880 ongle Input Admittonce 8 020 j158 Input Reflection Coefficient 1 BBABA angle Reo NS 7 182 08 degrees Fd B mS e grid Change length 165 6 degrees Back To set the length of stub 3 monitor the input to line 4 in Fig 3 24 which is port 4i This is the load that must be matched by the double stub tuner made up of lines 2 3 and 5 in Fig 53 Fig 3 24 shows the Fig 3 24 The Smith Chart for stub 3 line 7 with a 1 cm stub length showing the admittance at port 4i Smith Chart for stub 3 which is line 7 The admittance at port 4i is the target symbol at the top of the Smith Chart We want to change the length of the stub with the change length function to move this admittance to a desirable location 56 lee et ye se sore tae Smith Chart Admittance Chart For line 7 Frequency 60 020 MHz Lengths 8 114 m Y at port 4i 7 081 j15 081 Generator SSS Click the mo
58. rmat shown in Fig 2 14 The RPLOT program provides the user with full control over the axis format the axis titles the graph titles and so forth The graph can be formatted by the user to be suitable for inclusion into a report or other document RPLOT can be used to make an encapsulated postscript file of the graph which looks much better than the bitmap shown in Fig 2 14 Note that when you click the RPLOT button in TRLINE the execution of the TRLINE program is suspended until you exit from RPLOT Then TRLINE resumes execution 19 e the pr Frequency 300 000 MHz 3 L s2 1 2 a b Line 3 Line 1 Line 2 Click the mouse on a tronsmission line nome to drow the Smith Chart Chort Type Admittance Switch to an imp chort Back arg OaE Fig 2 15 The Smith Chart menu 2 4 Smith Chart and Input Impedance The last button on the transmission line menu in Fig 2 9 is Draw a Smith Chart as a function of line length Click this button to get the Smith Chart menu of Fig 2 15 In the main menu of Fig 2 2 if you click Draw a Smith Chart you will also get the Smith Chart menu of Fig 2 15 This menu has the properties buttons across the top of the screen so that you can easily change the line lengths and so forth The bottom of the menu has a button labeled Switch to an impedance chart which is used to change the Smith Chart from the admittance format to the impedance format
59. rns to the transmission line menu 15 Ble Eat Uw Sit Woaw HD Line 1 USWR 2 0008 Line 2 USUR 1 2000 Line 3 USUR 1 2000 YU m Frequency 380 820 MHz Uoltage amplitude cs a function of distance Current amplitude as a function of distance Back Fig 2 11 The voltage and current on all the transmission lines In Fig 2 9 click Plot both the voltage and the current to obtain the schematic of Fig 2 11 We see the voltage in black and the current in blue In the standing wave pattern where the voltage has a maximum the current has a minimum Note that both Kirchoff s Voltage Law and Kirchoff s Current Law are satisfied at the junction 16 Line 1 USUR 2 0002 UY gg Line 2 USUR 1 2000 p Line 3 USUR 1 2000 uly UC m Frequency 300 080 MHz Uoltage amplitude cs a function of distance Voltage phase as a function of distance Back Fig 2 12 The voltage including phase In Fig 2 9 click Plot the voltage including phase to obtain the display of Fig 2 12 The phase varies between 180 and 180 degrees The lines that are matched have linear phase variation with distance as expected of a simple travelling wave The phase behavior of the voltage is more complicated on the unmatched line 17 Marker 1 2 sale 2aab 1 1aa 7RPLO fi L fi L 1 ali
60. s Fig 2 3 h Line branching to two loads Click the mouse on o red lobel to change the properties Generator Line 1 Load 1 Frequency Line 2 Logi 2 Line 3 SLI Line 4 F lt e Frequency 300 000 MHz y N E R er UC s1 2 s3 l i Fig 2 3 i Power splitter Generator Line 1 Lead 1 Frequency Line 2 Load 2 Line 3 4 Za Frequency 308 028 MHz 3 gt U R j a Nid 1 a JL Fig 2 3 j Single stub matching circuit Generator Line 17 Frequency Line 2 Line 3 Line 4 Frequency 300 200 MHz 5 a a R Pa 41 va UE 1 ge f 7 Z Fig 2 3 k Double stub matching circuit Generator Line 1 Load 1 Frequency Line 2 A Load 2 Line 3 oa 2 Loog 3 Line 4 Lose 4 Ling S fo Pi Frequency 300 208 ne Die ead A Ls j 5 7 Z UC P vA is a a Fig 2 3 1 Triple stub matching circuit Generator Line 1 Load 1 Frequency Line 2 Load 2 Line 3 Load 3 Line 4 Load 4 Line 5 Pi p 7 Frequency 4 000 GHz pee ie of isi is SL es ae im 3 5 5 a s a uE a ap Pa Pa 1 A A Fig 2 3 m Low pass filter Click the mouse on a red label to change the properties Generator Line 1 Load 1 Frequency Line 2 Load 2 Line 3 Load 3 Line 4 Load 4 Line ae a a Frequency 2 008 GHz ip W wz Lud 93 Load w CR a 5 a7 R z uO a pay 1 Pa L r Fig 2 3 n Bandstop
61. s each of the program s functions in more detail with some examples Generator ine Load 1 Frequency Frequency 2 080 GHz Fig 2 3 a Simple transmission line Generator e 1 oad 1 ke Li Frequency Li 308 000 MHz VO Fig 2 3 b Two transmission lines in series Generator Line 1 Lood 1 Frequency Line 2 Lood 2 Frequency 302 000 MHz WA Re Z a 1 41 ze Fig 2 3 c Two transmission lines in series with shunt load Generator Line 1 Laad 1 Frequency Line 2 Line 3 Frequency 308 020 MHz We s UC i s 3 Fig 2 3 d Quarter wave transformer Generator Line 1 Load 1 Frequency Line 2 Line 3 Line 4 Frequency 388 288 MHz N A Ra a1 2 3 th Fig 2 3 e Two step quarter wave transformer erator Line 1 Lood 1 Frequency Line 2 Line 3 Line 4 Line 5 Frequency 308 288 MHz a a1 se 3 4 5 Fig 2 3 f Three step quarter wave transformer N a Generator Line 1 Load 1 Frequency Line 2 Lood 2 Line 3 Frequency 850 020 MHz y fe 3 R s Ay UC 1 2 L Fa Fig 2 3 g Two lines in series with a stub at the load Generator Line 1 Lood 1 o Frequency Line 2 Lood 2 Line 3 pe Frequency 300 000 MHz Pi KR w aL 2 o
62. t Two transmission lines in series Fig 2 3 b is used to show transition from a line of say 50 ohms characteristic impedance to a line of a different characteristic impedance say 25 ohms or 100 ohms Fig 2 3 c puts a shunt load at the junction and provides an exercise in the use of the Smith Chart to find the input impedance Also the length and characteristic impedance of the interconnecting line can be chosen to try to obtain a specified relationship of the voltage amplitude and phase across the two loads Fig 2 3 d provides a circuit template with three transmission lines in series with the parameters chosen to demonstrate a quarter wave transformer at 300 MHz Figs 2 3 e and f provide templates for two step and three step quarter wave transformers for a microwave engineering course The default values for the line lengths characteristic impedances and the frequency achieve a good match in these circuits This is convenient for classroom demonstration of the program for the circuits can be invoked rapidly from the circuit template menu The match can be demonstrated by graphing the amplitude of V z on each transmission line and the frequency sweep feature used to demonstrate the bandwidth of each transformer Fig 2 3 g has two transmission lines in series with a tuning stub across the load The circuit can be used to introduce impedance matching for a complex valued load Use the stub to tune out the imaginary part of the load and li
63. tance lies on the g circle Fig 3 3 shows the Smith Chart for line 2 after the length of line 2 has been adjusted The input admittance is 20 040 j15 578 mS not quite on the g 1 circle which would require g 20 mS Choosing the length with the mouse does not provide fine enough control to obtain a real part of exactly 20 mS The length could be adjusted manually using the transmission line properties buttons in the main menu to obtain a real part of exactly 20 mS Also note that there is a second solution A longer transmission line could put the input admittance on the g 1 circle in the top half of the Smith Chart 39 ee a enw mmo Smith Chart Admittance Chart For line 3 Frequency 600 020 MHz Characteristic Admittonce 20 0 mS X y Load Admittance tic A 1002000E 06 j0 000 mS NS N Load Reflection Coefficient N _ 1 82020 ongle 188 8 degrees gt s Input Admittence Length 8 018 m 8 080 j158 316 m5 e grid Input Reflection Coefficient Change length 1 82028 angle 165 6 degrees Back Fig 3 4 The Smith Chart for line 3 with a stub length of 1 cm The next step is to adjust the stub length to cancel the susceptance of 15 578 mS so we want the stub input admittance to be 0 j15 578 mS Draw the Smith Chart for the stub Line 3 Fig 3 4 shows the Smith Chart with a 1 cm line length The Load admittance is infinity corresponding to a short circuit The input admittance of the
64. the design in detail with instructive circuit diagrams Table summarizes the steps in Pozar s design A lumped element low pass prototype consists of a series inductance L a shunt capacitance C and another series inductance L terminated with a matched load R The prototype is designed using element values taken from Pozar s Table 8 4 2 for a Chebyshev filter with a 3 dB ripple The prototype has a normalized impedance of 1 ohm and a normalized cutoff frequency of 1 rad sec The second step is to replace the L and C elements by short circuited and open circuited stubs of length one eighth wavelength at the cutoff frequency The characteristic impedance values of the equivalent stubs R R and R are derived from the L and C values as in Table 1 The third step is to add a unit element transmission line line to each end of the filter of length one eighth wavelength and then use one of Kuroda s Identities to replace the line and series short circuited stub with a shunt open circuited stub and series line of appropriate characteristic impedance as given in column 4 of Table 1 Thus each inductor in the prototype circuit is replaced by a shunt open circuited stub of characteristic resistance R and a series line of characteristic impedance R The final el step is to scale the impedance to 50 ohms by multiplying all the characteristic impedances by 50 ohms The last column of the table gives the characteristic
65. use in the Smith Chort to choose a new Length LO i Characteristic Admittance 20 0 mS N Load Admittance lt I pe 0 100BOOOE 06 j0 0AB mS EA Load Reflection Coefficient 1 02020 ongle 188 0 degrees Input Admittonce 0 208 j2 750 mS Input Reflection Coefficient 1 BBABA angle 15 7 degrees Toward _ Faring ssp png GUE on Fig 3 25 Change the length of stub 3 to get close to the rotated g 1 circle As we change the length of stub 3 the monitored admittance at port 4i moves on a circle Fig 3 25 shows the admittance with stub 3 set to 0 114 m But the admittance can be moved closer to the rotated g 1 circle by making the stub longer There is no unique solution for choosing the length of stub 3 we want the admittance at port 4i to be one that can be matched by stub 1 and stub 2 as a double stub matching circuit The criterion to be used here is that the admittance at port 4i be as close as possible to the rotated g 1 circle S7 cr is Ye te Smith Chart Admittance Chart For line 7 Gok a Generator Toward Characteristic Admittance 28 8 mS Load Admittance G 1G02000E 06 j0 000 mS Load Reflection Coefficient 1 82880 ongle Input Admittonce 0 080 j49 B78 mS Input Reflection Coefficient 1 BBABA angle 600 080 MHz 188 0 degrees 135 3 degrees E final yee ley A p f y eX y INPUT XQ 4 oa ai Change
66. with N 5 a 3 dB ripple a center frequency of 4 GHz and a 15 bandwidth use Table 8 3 in 2 to get the component values for the low pass prototype listed in Table 5 5 Then calculate the characteristic impedance for each stub using 2 with A 0 15 and Z 50 ohms Enter these values for the stub characteristic impedances into TRLINE and then use the frequency sweep menu to compute the transmission loss and the return loss Tale 5 5 Component values for the N 5 bandpass filter Element Value Characteristic Impedance gi 3 4817 1 692 ga 0 7618 7 732 8 4 5381 1 298 ga 0 7618 7 732 gs 3 4817 1 692 oe gute a lt xii a i Ble Bat View Sut Yisdow He T T M VV q Morker 1 3 743 Marker 4 Morker 2 3 008 Morker 2 4 256 2 9921 Bonduldth 8 513 RPLOT Snap ppt to tht bd Back 7 5 x 3 5 4 8 4 5 1 8 5 5 Freauencu GHz S fuming ssinpat pencingin Guan Apelor Fig 5 9 Transmission loss of the N 5 filter for a 3 dB ripple Fig 5 9 shows the transmission loss of the N 5 filter The filter is centered at 4 GHz The ripple is approximately 3 dB and the bandwidth for a return loss of 3 dB is 0 513 GHz 77 Marker 1 hy 3 743 orker 2 2 996 J Morker 2 4 6 ENF Bandwidth 0 5131 Los Return r YS R CTE N Paine fi BT sp A ae Bs 3 0 3 5 sj 4 5 5 0 5 engin BUA Apo nnn Maset F

TRLINE User's Guide - Department of ECE

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