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NETWORK Version 2.1 A Ladder Network Analysis Program REFERENCE MANUAL (Oct 30, 1988) Copyright 1988, 1989 by Kenneth D. Wyatt All rights reserved. 1 CONTENTS Section Page 1 Introduction .................................. 3 2 Equipment Required ............................ 3 3 Getting Started ............................... 3 4 Changing Colors and Other Parameters........... 4 5 Program Description ........................... 5 6 Network Analysis Basics ....................... 5 7 Before the Circuit is Entered ................. 6 8 Starting NETWORK .............................. 7 9 Changing Default Disk, Units, Title, & File.... 7 10 Creating the Circuit File ..................... 8 11 Editing the Circuit File ...................... 9 12 Saving the Circuit File ...................... 10 13 Loading a Circuit File from Disk ............. 10 14 Analyzing the Circuit ........................ 10 15 Plotting the Output Data ..................... 11 16 Examples ..................................... 11 Appendix A Converting from Wavelength to Degrees ........ 16 B Converting Polar to Rectangular Notation ..... 16 C Converting from Parallel to Series Circuits .. 17 References ................................................ 18 2 Section 1 - INTRODUCTION NETWORK is an electronic circuit analysis program which will analyze ladder networks. Ladder networks are combinations of components that are "chained" together in a "ladder" format. Many circuits, such as, filters and matching networks may be represented as a ladder topology. NETWORK has been optimized for use by working rf engineers. For example, many circuit analysis programs provide output data in the form of voltage and current. While this might be useful in a general sense, it may not be in a form which is desirable for rf designers. NETWORK, on the other hand, provides the following output data in either normal or scientific notation: 1) Insertion loss (dB) 2) Phase angle of insertion loss (degrees) 3) Return loss (dB) 4) Voltage Standing Wave Ratio, VSWR 5) Reflection coefficient, rho 6) Real component of the input impedance, Zin(R) 7) Imaginary component of input impedance, Zin(I) In addition, you may tabulate this output data either to the screen, or to both the screen and your printer. You may also plot the data graphically to the screen. If your Disk Operating System (DOS) includes the Microsoft program, GRAPHICS.COM, you may dump the resulting high resolution plots to an EPSON compatible graphics printer. This is detailed further in Section 15 - PLOTTING THE OUTPUT DATA. Section 2 - EQUIPMENT REQUIRED This program will run on the IBM-PC, or 100% compatibles, using DOS 2.1, or later versions. The minimum memory required is 256K bytes. Compatible video adapters include the Color Graphics Adapter (CGA), Enhanced Graphics Adapter (EGA), Hercules Graphics Adapter or Video Graphics Adapter (VGA) [in CGA or EGA modes]. A dot matrix EPSON-compatible graphics printer is suggested in order to print the various graphics output displays. Section 3 - GETTING STARTED Before beginning, there are certain conventions used in this manual. User-entered commands are indicated by upper case type. For example, the typed in program command, GRAPHICS. Labeled keys to be pressed are indicated by <KEY>; for example the <ENTER> or <RETURN> keys. Also to be noted; data may be entered in either upper or lower 3 case, and in either standard or scientific notation. To print out screen graphics, some computer keyboards have a single "<Print Screen>" key, others require you to hold down <SHIFT> and press <PrtScn>. Lastly, when the Microsoft program GRAPHICS.COM is mentioned, you may substitute GRAPHICS.EXE depending upon which version is included on your PC- or MS-DOS disk. For those who do not have access to these two screen graphics programs, the public domain program, EPSON.EXE, is included in the program package. It may be directly substituted in place of either GRAPHICS.COM or GRAPHICS.EXE. Start your computer in the usual way with your DOS disk installed in Drive A. After entering the Date and Time, and you have the DOS prompt A>, proceed as follows: Type: A> GRAPHICS <ENTER> This will load the program GRAPHICS.COM into your computer. This program will allow you to print the high resolution graphics displays to your printer by holding down <SHIFT> and pressing the <PrtScn> (print screen) key. When you again have the DOS prompt A>, remove your DOS disk from Drive A and insert your NETWORK Program disk in drive A. Type: A> SETUPNET <ENTER> The NETWORK Setup program will load and run, and you may now define various default color schemes, data disk drive letter, and video graphics adapters. The program is menu driven, so just follow the screen prompts or instructions. Further operational details may be found in the next section, CHANGING COLORS AND OTHER PARAMETERS. INSTALLING NETWORK ONTO YOUR HARD DISK Your NETWORK program may be copied to your hard disk in the usual manner. See your IBM DOS manual for instruction as to PATH, etc. In order to start NETWORK, change to the appropriate directory and type NETWORK. Section 4 - CHANGING COLORS AND OTHER PARAMETERS The program SETUPNET allows you to change the screen color scheme, reset the default data disk drive, reset the default units of frequency, resistance, capacitance, or inductance, and indicate the appropriate video graphics adapter. Type SETUPNET to start the program. The defaults are disk drive = A, units of MHz, ohms, pF, and nH, and CGA graphics. The screen colors are set to a readable scheme for EGA video adapters; but you might wish to adjust them to suit either CGA or monochrome monitors. 4 Be sure to choose (5) - Save Initialization File when you have completed your modifications. Normally, there should be an existing INITIAL.NET file on the disk. If there is, the message, "Initialization file already exists; OVERWRITE ? (Y/N)", will be displayed. Press Y to continue the save operation. If ever the initialization file becomes misplaced or lost, simply rerun SETUPNET, and another one will be created. Section 5 - PROGRAM DESCRIPTION There are 17 component models included in the program. These consist of resistors, inductors, and capacitors; either singly, or in various series or parallel network combinations. Transformers and various transmission line elements are also available. Circuits which may be modeled, include most filter networks, impedance matching circuits, and transmission line or microstrip designs. Transmission line data may be entered as either physical dimensions, or as electrical parameters. Once a circuit file is created, it may be edited, analyzed, and saved to disk. Units of frequency, resistance, capacitance, or inductance may be defined. These operations are described more fully within their appropriate sections later in the manual. This manual also includes a number of examples at the end (Section 16). For those who would like to try out the program before reading further, this might be a good time to skip ahead to Example 1. We will go through a simple step by step procedure, demonstrating the major features of NETWORK. The program is completely menu-driven and the operation has been designed to be intuitive to the user. Get ready for some powerful circuit analysis! Section 6 - NETWORK ANALYSIS BASICS NETWORK is based upon the ABCD parameters of the circuit element to be analyzed. The advantage in using the ABCD parameters lies in the ease with which cascaded networks may be represented and analyzed. The ABCD parameters make up a matrix that describe the voltages and currents into and out of four terminal (two port) networks. Each element model (resistor, inductor, transformer, etc.) has a unique ABCD matrix as shown in Reference 15. This program is based on the fact that the ABCD matrix of two cascaded circuits is equal to the product of their individual ABCD matrices. These matrices are stored as the various element models, and their associated component values are entered by the user. At each frequency to be analyzed, the individual matrices are formed and multiplied to gradually compute the overall matrix of the entire circuit. 5 Once the network is reduced to a single matrix, we may derive the insertion loss, phase (of insertion loss), return loss, voltage standing wave ratio (VSWR), reflection coefficient, and input impedance (both real and imaginary). For passive network analysis, the insertion loss is equal to the transducer power gain. Thus, when the source (Rs) and load (RL) resistances are matched, the gain is zero dB. Section 7 - BEFORE THE CIRCUIT IS ENTERED Before the program is run, it is useful to prepare the network for analysis in order to ease data entry. The circuit is drawn such that all elements are in cascade or "inline". The source resistance (Rs) should always be drawn in series and the load resistance (RL) should always be drawn in parallel. Neither the source nor load resistors count as one of the network elements. If the source or load is reactive (containing either capacitance or inductance), consider the reactive portion as part of the circuit model. Draw lines between each circuit element and then number each section in order from left to right. These will be the element numbers. Next, identify the element types (1 through 17) by referring to the Element Chart in Reference 15. (A copy of Reference 15 will be provided upon program registration) Record the element number and type below the network drawing. Last, decide on an appropriate value of units for each of the element types. Once the units are chosen, there is no way to change them without starting over. For the normal numeric notation, the output tabular data has room for six most significant digits plus two least significant digits. Thus you should choose component values such that they will all lie between 0.01 and 999999.99. For the scientific notation option, there is no such restriction and you may enter your component values using the "E" notation (for example, 1.234E-6). Available units are shown below. Available Units Resistance Inductance Capacitance Frequency ohms Henries Farads Hz mohms mH uF kHz kohms uH nF MHz nH pF GHz 6 Section 8 - STARTING NETWORK Turn your computer on, and, if appropriate, enter the date and time when prompted. This information will be inserted into your printed output data listing in order to aid in your document- ation. To start NETWORK, simply type NETWORK at the DOS prompt A>, and the program will start. The program requires the initialization program, INITIAL.NET, in order to run. This initialization file, which includes default program parameters, is included as a part of the package. You may load and run the NETWORK setup program, SETUPNET, in order to modify these default colors and other program parameters. Simply type SETUPNET to create your new initialization file prior to running NETWORK. After starting NETWORK, you should obtain the Main Menu as shown. 1 Create Circuit 2 Analyze Circuit 3 Edit Circuit File 4 Save Circuit File 5 Load Circuit File 6 Shareware Info 7 Quit Section 9 - CHANGING DEFAULT DISK, UNITS, TITLE, AND FILENAME Choose (1) CREATE CIRCUIT from the Main Menu. A window will open showing various parameters, such as, the circuit filename, title (up to 48 characters), desired data drive, and component units. First, the circuit file name must be entered. This will be the name used to store your circuit file to disk, and must correspond to the rules of DOS, (eight, or less, characters long). The program will automatically append the extension .CIR to the end of the file name in order to differentiate circuit files from others on your disk. The default data drive letter may be changed if desired. Depend- ing upon your equipment configuration, you may enter drive A through C. Drive letter C is assumed to be a hard disk. For a conventional two drive system, you might wish to place the Program disk in Drive A and a formatted data disk in Drive B. For a system with a hard and a floppy drive, you might wish to have the Program disk installed in the hard drive and use either the hard drive for data, or perhaps Drive A for data. The title is optional. If you wish, you may simply press <ENTER> to bypass this for now. The title will be displayed on any graphics plots or printed output for your documentation convenience. The default units of frequency, resistance, capacitance, and 7 inductance are also displayed. These default units are definable within the SETUPNET program. Frequency may be in Hz, kHz, MHz, or GHz. Resistance may be in milliohms (mohms), ohms, or kohms. Capacitance may be in F, uF, nF, or pF. Inductance may be in H, mH, uH, or nH. Section 10 - CREATING THE CIRCUIT FILE Creating the circuit file is straightforward. First enter in the source and load resistors. For filter circuits, these resistors might typically be 50 ohms. For matching networks, one will probably be 50 ohms, while the other will most likely be much smaller or larger. Next you will be asked the total number of circuit elements. Since this program analyzes ladder networks, simply separate each element by itself, from left to right. Do not count the source or load resistors. Count up the number of sections (30, maximum) and enter the number. Once you have completed these steps, you may next start entering the component values; again, from left to right (source to load). Refer to Section 6 - BEFORE THE CIRCUIT IS ENTERED, for details. Note that the appropriate units will be displayed next to each component to be entered. In order to prevent division by zero errors, any zero data is automatically converted to 0.00001. Data may be entered in either standard or scientific notation (1.27E-12). Possible circuit elements (or models) include resistors, capacitors, inductors, transformers, and transmission lines. These may be connected in series, parallel, or combinations of both. In order to differentiate the various circuit models, I have used the following conventions. Series or parallel elements are called just that. However, there are a number of multi- element models. For example, the series RLC combination, connected in series, is referred to as Series - Series RLC. The parallel RLC combination, connected in series, is referred to as Parallel - Series RLC, and so forth. The stub models are either series or parallel, and open or shorted. Upon registering, you will receive a copy of the various circuit models for your reference. Transmission Lines Transmission lines may be entered either in physical dimensions (inches) or in electrical parameters. Physical dimensions are useful for analyzing existing circuitry in order to verify performance. You will be asked for the dielectric constant of the circuit board, the length and width of the microstrip line, and the thickness of the circuit board material (all in inches). Although it is not mandatory, you should use the same dielectric constant and board thickness for each transmission line section, since the values for the last element entered, only, are stored and displayed in the EDIT mode file. 8 Alternatively, the electrical parameters may be entered. This method might be preferable if a new circuit is being designed. You will be asked for the characteristic impedance, the electrical length in degrees, and the center frequency of operation. The dielectric constant in this case is assumed to be one and in order to scale the line to the proper physical dimension, you must factor in the actual dielectric constant of the board material. Section 11 - EDITING THE CIRCUIT FILE Now that you have created a circuit file, the editor function will allow you to correct or redefine the circuit element type or component values. Choose (3) EDIT CIRCUIT FILE mode from the Main Menu. You will be asked whether you desire the component data in (1)Standard or (2)Scientific Notation. Choose either 1 or 2. If the component values are less than 0.01, or greater than 999999.99, you should choose (2)Scientific Notation. For example, if you had chosen standard notation and some of the circuit element values were displayed as zero, simply return to the Menu (choose M), re-enter the EDIT mode, and choose (2)Scientific Notation. Your circuit will then be displayed as a list of element types and component values. A menu bar at the bottom of the screen prompts you for items you may change or correct. As you change an item, the edit list updates, showing you the new values. Zeros in the column indicate that the particular value is not used in the indicated circuit element model. However, see paragraph above for an exception to this. Once you are in the Edit Mode, you may change the element type. For example, you may have entered a series inductor, and now wish to change it to a parallel capacitor. Simply enter the element number of the element you wish to change. A chart of the possible circuit elements will be displayed for reference. Choose the desired element type and its appropriate value(s) and the edit chart will reappear with the new element type and value listed. You may also wish to change just the element values. By changing the component value repeatedly, and then replotting the output data, it is possible to "tune" a circuit to the desired frequency response or return loss. Choose the element number to change. Press N, when asked if you want a different element type. Then enter the new component value when prompted. You may also redefine or correct the source or load resistors. Simply press S or L and enter the new value at the prompt. Pressing M will return you to the Main Menu. 9 Section 12 - SAVING THE CIRCUIT FILE Once you have Created your circuit file, you may wish to save it for future use. Choose (4) SAVE CIRCUIT FILE mode from the Main Menu. The file will then be saved to the desired disk drive with the .CIR extension appended automatically. That's it! The circuit files are stored as ASCII data and it is possible to examine the contents by using the DOS TYPE command. Refer to your DOS manual for this procedure. Please resist modifying these circuit files externally. The NETWORK program will get confused and give an error message if the file has the wrong number or type of elements. Section 13 - LOADING A CIRCUIT FILE FROM DISK In order to load in a previously saved circuit file, select (5) LOAD CIRCUIT FILE from the Main Menu. If there is already a circuit file in memory, you will be asked if you wish to save it first before loading in another. Next, a list of circuit files currently saved on the data disk will be displayed. Select the desired file name from this list and it will be loaded into memory, and the Main Menu will be displayed. If a mistake was made in the file name entry, an error message will be displayed. Press any key and reselect choice (5) from the Main Menu. When a circuit file loads, the units used, the title, and frequency steps for that circuit will be loaded simultaneously. Section 14 - ANALYZING THE CIRCUIT After the circuit is created, it may now be analyzed. Choose (2) ANALYZE CIRCUIT FILE from the Main Menu. At this point, you will once again have the option of (1)Standard or (2)Scientific Notation. If the output data is less than 0.01, or greater than 999999.99 when using standard notation, then simply reanalyze the data once again, this time using scientific notation. Note that all output data gets rounded off to the nearest 0.01 for either notation mode. Next, enter the start frequency, stop frequency, and frequency step. Then, choose either to display the output data to the screen (S), or to your printer (P). If printer output is chosen, the circuit topology (network listing), date, time, title, and file name will be added to the top of the page for your reference. The format of the circuit topology is identical to that of the Edit Mode. Output data of over 19 frequencies using the Screen option will scroll up automatically. Following the tabular output data, you may choose to reanalyze the data using new frequency limits, plot the data using high resolution graphs, or return to the Main Menu. Plotting the 10 output data is described next! Section 15 - PLOTTING THE OUTPUT DATA Often times it is difficult to interpret the analysis results by simply looking at the raw data in tabular form. In order to get a better picture of the data, choose (P)lot in the Analysis Menu. You may then choose five different data plots: 1) Insertion and Return Loss (IL/RL) 2) Phase Angle 3) Voltage Standing Wave Ratio, VSWR 4) Reflection Coefficient, rho 5) Real and Imaginary Input Impedances Once your choice of plot types is made, you must next enter the desired upper and lower Y-axis limits and step size. The calculated maximum and minimum Y-limits will be displayed for reference. You may choose any convenient limits, depending on the part of the data you wish to display. After you enter the Y-limits, the plot will be displayed. On plot types with two displayed curves, they will either be different colors (EGA monitor), or, the second will be dotted (CGA or Hercules monitor), in order to differentiate between the two. Assuming the Microsoft program GRAPHICS.COM has been previously loaded, you may print out a copy to your printer by holding the <SHIFT> key down and pressing the <PrtScn> key. If the plot requires rescaling in the x-axis (frequency), it will be necessary to reanalyze using the more optimal frequency limits. When you are finished with the plot, simply press any key to obtain the plot submenu. At this point, you may choose to (P)lot, (A)nalyze the data (using different frequency limits), or return to the Main (M)enu. Section 16 - EXAMPLES Due to difficulty in conveying drawings within this document- ation, the figures for the following examples will be sent following receipt of your registration. The example circuit files are included as a part of the program package. 11 EXAMPLE 1 - Low Pass L-C Impedance Match Let's try a simple low pass LC impedance matching network in order to become familiar with the program operation (LPMATCH). We wish to match a 50 Ohm source resistance to a 10 Ohm load. The circuit is given in figure 1. The component values may be found in the tabulated output data. We will verify that the match takes place at 10 MHz and then determine the 3 dB roll-off frequencies, the return loss, and VSWR within the passband. Choose (1) CREATE CIRCUIT mode. Enter a file name of up to eight characters. Enter the title or circuit description, if desired. You may simply press <ENTER> to bypass this. The title may be up to 48 characters. Use the program default units of MHz, ohms, nH, and pF. Select the desired data drive letter (A, B, or C) for circuit data storage. Press (5) - Quit Parameter Entry, to continue on. Enter a source resistor of 50 ohms and a load resistor of 10 ohms. This matching network contains only two sections (remember not to count the source or load resistors), so enter 2 and then press <ENTER>. At this point, the circuit element chart will appear. It contains each of the possible components within the component model library. Choose element type 6, Parallel Capacitor. Enter the capacitance value of 637 pF. Choose element type 3, Parallel Inductor. Enter the value of 318 nH. If the wrong element type is entered, it may be fixed within the Edit mode. Once all element values have been entered, you will be returned to the Main Menu. If you have made a data entry error, choose (3) - Edit mode, and go ahead and fix the problem now. See Section 11 - EDITING THE CIRCUIT FILE if you need assistance and then return back to this point in the example. Let's analyze the circuit. Choose (2) - Analyze and you will be asked to enter a title (if the title has not been entered yet). Next enter a start frequency of 1 MHz, a stop frequency of 20 MHz, and a step size of 1 MHz. You will then be prompted for (S)creen or (P)rinter output. Press S and the data will be displayed as the calculations progress. If P (for printer output) was pressed, the data would have appeared on both the screen and the printer. In addition, the printed output would have the date, time, file name, title, and circuit network listing at the top of the page. When the calculations are complete, you should have obtained the results shown in figure 2. Notice that at 10 MHz, the source of 50 ohms is indeed matched to the load of 10 ohms. At this point, the insertion loss is nearly 62 dB, the VSWR is 1.00:1, the reflection coefficient (rho) is zero, the real impedance is near 12 50 ohms, and the imaginary impedance is zero ohms. Note that the 3 dB cut-off frequency is about 14.5 MHz. The return loss varies from 3.57 to 61.93 dB, and the VSWR at the band edges is about 5.00:1. Following the output data chart, a menu bar will be displayed at the bottom of the screen. The choices are; (P)lot, (A)nalyze, or (M)enu. Pressing A will restart the analysis and allow you to modify the frequency sweep information. Pressing M will return you to the Main Menu. For our example, press P to restart the Plot mode. You may now choose to display plots of (1) insertion and return losses, (2) phase of the insertion loss in degrees, (3) VSWR, (4) reflection coefficient (rho), or (5) real and imaginary impedances. Choose (1) IL/RL in order to plot the insertion and return losses. You will be asked to enter the upper and lower Y-limits and the Y step size. Enter zero dB for the upper limit, -60 dB for the lower limit, and 10 dB for the step size. At this time, the plot will be displayed. See figure 3. You may dump this plot to your graphics printer by holding the <SHIFT> key and pressing the <PrtScn> key. After the printer is finished, press any key to obtain the menu bar. The choices will be; (P)lot, (A)nalyze, or (M)enu. At this time, you may want to save the circuit file to your data disk. Return to the Main Menu by pressing M. Choose (4) SAVE CIRCUIT FILE. See how easy the program is? It is possible to quickly enter a circuit, analyze it, plot the results and then save the circuit file to disk in the time it takes to merely enter the data into many other programs. EXAMPLE 2 - Three Section Transmission Line Impedance Match Suppose we wish to match a 50 Ohm source to a 100 Ohm load resistance by using quarter wavelength microstrip transmission line sections (TLINE3). Note that the more sections we use, the broader will be the effective bandwidth. Let us use three sections for this example. The center frequency will be 8 GHz, and the desired bandwidth should range from 6 to 10 GHz. We will verify the insertion and return losses and resulting 3 dB bandwidth. For a single quarter wave transmission line impedance match, the required line impedance may be calculated by multiplying the source and load resistances and then taking the square root. For example, the impedance of a single section line that is to match 50 with 100 ohms would be SQRT(50 x 100) = 70.7 ohms. For this example, the center section would be calculated as above. The first section will use 70.7 ohms as it's "load" and we calculate SQRT(50 x 70.7) = 59.5 ohms. Similarly, the third 13 section will use the 70.7 ohms as it's "source" and we calculate SQRT(70.7 x 100) = 84.1 ohms. The resulting three section quarter wave matching network is shown in figure 4. Choose (1) CREATE CIRCUIT. If there is a previous file in computer memory, you will be prompted to (S)ave the old circuit file, (C)reate a new file, or (M)enu. Choose C and then enter the new circuit filename, and title. Choose GHz, ohms, nH, and pF for the units. Next, enter the source and load resistances (50 and 100 ohms) and the number of sections, 3, in this case. Enter 12 for the transmission line element type. You now have the opportunity to enter the transmission line data as (1) Physical Dimensions (inches) or (2) Electrical Parameters (impedance in ohms, length in degrees, and center frequency). Choose 2, since the design is in electrical parameters. Starting with the first section, enter the characteristic impedance, length in degrees, and center frequency (59.5, 90, and 8, respectively). Enter the other two sections in a similar fashion. Return to the Main Menu. Choose (2) ANALYZE CIRCUIT mode from the Main Menu and enter the starting frequency of 5 GHz, a stop frequency of 11 GHz, and a step size of 0.25 GHz (250 MHz). You should obtain the results as shown in figure 5. Choose (P)lot and display the IL/RL. Use an upper limit of zero dB, a lower limit of -60 dB, and a step size of 10 dB. Note that since the insertion loss is so near zero, with the chosen scaling, it is superimposed on the upper edge of the plot. You will see that while the insertion loss is quite flat across the desired bandwidth, the return loss has only a single dip at 8 GHz and its bandwidth is not quite as wide as desired. See figure 6. We can widen out the return loss bandwidth by slightly offsetting the impedances of the first and third transmission lines. Select (M)enu and then choose (3) EDIT CIRCUIT. Let's try decreasing the characteristic impedance of the first section from 59.5 to 55 ohms and increase the impedance of the third section from 84.1 to 90 ohms. Press 1 in order to modify element number 1 on the Edit chart. Keeping all other parameters the same, change the impedance to 55 ohms. Next, choose element 3 and modify its impedance to 90 ohms. Press M to return back to the Main Menu. Now reanalyze and replot the insertion and return losses using the same frequency and step parameters. The final result is shown in figure 7. We can see that the return loss character- istic has widened out to include our desired bandwidth, while the insertion loss remains nearly unchanged. You may observe a potential disadvantage of the transmission line impedance match by re-analyzing the circuit with a start frequency of 1 GHz, a stop frequency of 60 GHz, and a frequency step of 2 GHz. Note the moding! This impedance matching circuit would not make a very good filter for the odd harmonics of 8 GHz 14 and generally it is not used for transistor amplifier outputs. EXAMPLE 3 - Broadband Interstage Impedance Match This circuit is used as a broadband impedance match between two transistor amplifiers (BBMATCH). The circuit to be used is shown in figure 8. The component values may be found in the tabulated output data. The desired operating frequency range is 225 to 450 MHz. Let us assume that the first transistor is the source and that the transistor resistive components are the source and load resistors. Include the transistor capacitances as separate circuit elements. You may have to convert from the parallel to series convention in order for the source or load resistors to be in the proper form for analysis. See Appendix C. Let's verify the insertion loss, the input return loss, and the input VSWR for this circuit. Note that in this case, the circuit to be analyzed may be broken up into four groups of either parallel-connected parallel RLC (element type 10), or series-connected series RLC (element type 7) sections. Since we have no resistances in this circuit, simply make the parallel-connected resistors 10,000 ohms and the series-connected resistors zero ohms. This will effectively eliminate any resistive component from the models. Since the calculations would fail with zero data, the software checks for zero and sets the value to 0.00001. As an alternative, you may choose to enter each circuit element as an individual series or parallel L or C model. Sweep the circuit starting from 200 to 450 MHz, with a step size of 10 MHz. The results are shown in figures 9 and 10. Note that the resulting output data shows a broadband response from 225 to 450 MHz. The insertion loss varies from 0.07 to 0.33 dB, the return loss varies from 11.45 to 18.81 dB, and the input VSWR is 1.73:1 or better at the band edges. EXAMPLE 4 - Cauer Low Pass Filter One of the more important types of low pass filters is the elliptic-function, or Cauer parameter, network, which provides equal attenuation minima in the passband region and equal attenuation maxima in the stopband (CAUER). A low pass filter with input and output impedances of 600 ohms is needed to pass frequencies up to 3.4 kHz with less than 0.05 dB attenuation and attenuate frequencies at 8.0 kHz and above by at least 45 dB. Using reference 14 (page 9-4), the following filter was designed. See figure 11. Analyze the circuit from 1 to 10.5 kHz with steps of 0.5 kHz. The results are shown in figures 12 and 13. Note the elliptic function passband and stopband. The 3 dB point occurs at about 4.75 kHz and we are 45 dB down at about 8 kHz. 15 Appendix A - CONVERTING WAVELENGTH TO DEGREES Some of you might be used to defining the electrical length of a stub or transmission line in fractions of a wavelength. For example, 0.2 lambda (wavelength) or 1/4 lambda. NETWORK uses the convention 360 degrees equals one wavelength (1 lambda). As an example, suppose the length of a stub is specified as .088 lambda. Converting, we have, degrees = wavelength x 360 or, 0.088 x 360 = 31.68 degrees. Appendix B - CONVERTING FROM POLAR TO RECTANGULAR FORM Some transistor input or output impedances may be specified in polar form, for example the input impedance of a transistor is found to be a magnitude of 26.9 at -21.8 degrees. NETWORK requires the source and load to be purely resistive, with any reactive component included as one of the circuit elements. In addition, the reactive component must be in series with the resistive component. Converting to rectangular notation will provide the correct form for our analysis. In order to convert the above example to rectangular form, use the following formulas. The real part of the impedance = magnitude x COS (degrees). So, 26.9 x COS (-21.8) = 26.9 x 0.9285 = 25 ohms. The imaginary part of the impedance = magnitude x SIN (degrees). So, 26.9 x SIN (-21.8) = 26.9 x (-0.3714) = -10 ohms. Thus, the combined impedance would be 25-j10 ohms. To calculate the reactive component value from the -j10 term, we may use the formulas below. Note that if j is positive, the component is an inductor, and if it is negative, it is a capacitor. Use the appropriate formula for inductive (XL) or capacitive (XC) reactance. L [Henries] = XL / (2 x PI x Freq [Hz]) C [Farads] = 1 / (2 x PI x Freq [Hz] x XC) In our example, the reactive component is a capacitive 10 ohms. Let us assume that the operating frequency is 12 MHz (12E6 Hz). Thus, C = 2 x 3.14 x 12E6 x 10. Or C = 1.326 nF (or 1326 pF). 16 Appendix C - CONVERTING FROM PARALLEL TO SERIES CIRCUITS In some cases, the transistor impedances might be specified in a parallel form. This does not matter if it is the load end of the network to be analyzed, but the source resistance must be in series form. In order to convert from parallel to series impedances, use the formulas below. Rs = Rp / (1 + (Rp / Xp)^2) Xs = (Rs^2 x Rp^2) / Xp The rectangular form would then be Rs+jXs. See Appendix B to convert this reactance (Xs) to the actual component value. For example, if the output impedance of a transistor at 120 MHz (to be used as the network source) was a 2100 pF capacitor in parallel with a 5.3 ohm resistor, we have: Rp = 5.3 ohms, and Xp = 1 / (2 x PI x Freq [Hz] x C [F]) = 0.632 ohms. Thus, Rs = 5.3 / (1 + (5.3 / 0.632)^2) = 0.074 ohms and, Xs = (0.074^2 x 5.3^2) / 0.632 = 0.243 ohms, or C = 5.45 nF. 17 REFERENCES If you would like to read more about ladder network theory or applications, filter design, or matching network synthesis, the following may be used as references. 1. W.H. Hayward, "General Purpose Ladder Analysis with the Handheld Calculator", RF Design, Sept./Oct. 1983. 2. T.R. Cuthbert, Jr., Circuit Design Using Personal Computers, Chapter 4, Wiley-Interscience, 1983. 3. W.H. Hayward, Introduction to Radio Frequency Design, Chapter 2, Prentice-Hall, 1982. 4. G.W. Williams, "Ladder Network Analysis: Poor Man's CAD", Microwaves, Jan. 1981. 5. Hewlett Packard, HP-41 EE Circuit Analysis Module Instructions, Ladder Network Analysis Program (LNAP). 6. C. Bowick, RF Circuit Design, Chapters 3 and 4, Howard W. Sams & Co., 1982. 7. R. Kellejian, Applied Electronic Communication, Chapter 11, Science Research Assoc., 1980. 8. W.I. Orr, Radio Handbook, Chapter 3, Howard W. Sams & Co., 1981. 9. T.T. Ha, Solid State Microwave Amplifier Design, Chapters 1 and 2, Wiley-Interscience, 1981. 10. C.A. Vergers, Network Synthesis, Chapter 8, TAB Books, 1982. 11. Motorola, RF Device Data, 1983. 12. A.I. Zverev, Handbook of Filter Synthesis, Chapter 2, Wiley, 1967. 13. G.L. Matthaei, L. Young, E.M.T. Jones, Impedance-Matching Networks, and Coupling Structures, Chapter 2, Artech House, 1980. 14. E.C. Jordan, Reference Data for Engineers, Chapter 9, Howard W. Sams & Co., 1985. 15. K.W. Wyatt, "A Ladder Analysis Program", RF Design Magazine, November 1986, pages 68 to 79. 18