





          
          
          
          
          
          
          
          
                                 NETWORK Version 2.1
          
          
                          A Ladder Network Analysis Program
          
          
                                   REFERENCE MANUAL
          
          
          
          
          
                                    (Oct 30, 1988)
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
                       Copyright 1988, 1989 by Kenneth D. Wyatt
          
                                 All rights reserved.
          







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                                       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
          










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                               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



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          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.



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          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.



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          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
          







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                             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



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          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.
          



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          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.
          





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                         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



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          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.












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                       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



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          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


