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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
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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.
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.
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