MakeR (F) manual

General description The program generates dual shaped reflector antenna with a single feed using Geometrical Optics methods. The antenna radiation pattern is a high gain focused beam with a given sidelobe envelope. The sidelobe envelope is specified as a function of one coordinate, angle from the peak. The first step is synthesis of the axisymmetrical amplitude distribution over the antenna aperture which produces far field pattern with desired sidelobe envelope. As an alternative it is possible to specify a user defined amplitude distribution. Then Geometrical Optics methods are used to generate a dual reflector antenna. The antenna works as a transformer of the given feed taper into the aperture amplitude distribution.

The program generates the following antenna types:

- Axisymmetrical, where the reflector surfaces are functions of the radial coordinate only. Configuration: Cassegrian, Gregorian or double Gregorian (offset Gregorian rotated around the antenna axis). Antenna aperture: circular.
- Offset Cassegrian or Gregorian. Antenna aperture: circular or elliptical.

Program input:

- Single operating frequency (since the program is based on Geometrical Optics).
- The program starts optimisation from a conic antenna system, so some general data like aperture and sub reflector diameters, feed semi-vertex angle, etc. are required.
- The target radiation pattern is specified as a minimum value for the antenna/aperture efficiency and a sidelobe envelope, which limits the maximum sidelobe level in different angular sectors. The sidelobe envelope is a function of one coordinate only: angle from the peak.
- As an alternative it is possible to specify a user defined axisymmetrical amplitude distribution numerically (table: radius / amplitude) and use it instead of the amplitude distribution generated by the program.
- Feed is modelled as a point source with gain. The feed pattern is axisymmetrical and is a function of the angle from the feed axis only. The function can be specified using given edge taper value for cos in power n function or numerically (table: angle, deg / taper, dB).

Program output:

- Reflector surfaces or non-shaped conic surfaces. Output formats: GRASP compatible format or AutoCAD DXF Rel.12 format.
- Geometrical Optics ray structure. The output text file containes cartesian coordinates of rays as they travel from feed to the sub-reflector and main reflector.

Installation The program consists of a single executable file MakeR_F.exe for Windows 95 / Windows NT operation systems plus a few demo data files. All files are compressed in a single self extracting archive install.exe. The program does not require any special installation - simply run install.exe and extract all the files into an empty directory. You may find it useful to create a shortcut to the program and place it on the Desktop.

Notes about OpenGL dynamic link libraries (dll's) for Windows 95: The program is using OpenGL to plot 3D images. The first versions of Windows 95 do not have these dll's or have dll's with a lot of bugs (Windows NT does not have this problem). If the program does not run on your computer with Windows 95 or gives errors when you look at the "Results" page, you need to install a new version of these files.

New dll's (Opengl32.dll and Glu32.dll) can be downloaded free from Microsoft and need to be copied into Windows \ System directory. Search the web for "OpenGL on Windows 95".

Quick start The program has 5 pages: "Target envelope", "Antenna setup", "Generate amplitude", "GO synthesis" and "Results". Having started from the first page simply follow this sequence to generate an antenna.

As the first example let us generate a simple axisymmetrical Cassegrian antenna. Run the program. Press "Load" button on the left vertical panel to load a sidelobe envelope file " 27log25.env ". Now go to the next page, "Antenna setup".

Set antenna type, feed semi-vertex angle and vertical sub-reflector size as shown in the picture (fields marked with red dots). The program automatically updates the corresponding conic system data and the antenna plot. Press "Save as" button to save reflector file. Go to the next page, "Generate amplitude" (Fig.2).

Select initial amplitude distribution as Gaussian, set taper value to 10 and click small button with triangular icon to generate initial distribution (these fields are marked with red dots). You will see a picture as in Fig. 2. Note that the program automatically takes into account blockage effects in axisymmetrical systems. The normalised amplitude distribution is not shown in the blocked part, the plot starts at 0.2 value of the normalised radius. Press "Save as" button to save the amplitude file. Note that the button operation depends on the page selected.

Go to the next page, "GO synthesis" and press "Run" button on the left vertical panel. In a few seconds the program generates reflector surfaces and displays the reflector mapping picture. The picture shows how equidistantly spaced rays on the main reflector aperture map into the feed cone. In this example the feed and the aperture tapers are equal, so the circular lines are spaced at equal intervals. If the feed has higher taper than the aperture, the circles will be concentrated in the centre.

Let us go to the "Results" page (Fig. 3). You can see a 3D plot of the antenna. Point mouse at the antenna image and hold left mouse button. Keeping the button pressed you can rotate the image by moving the mouse. Use small buttons on the right vertical panel to move and scale the image. Also there are 3 pre-set views in x-z, x-y and y-z planes. Press "Save to file …" button on the right vertical panel. You can then select between GRASP compatible format or AutoCAD DXF format. Choose "GRASP" to save main and sub-reflector surfaces into two separate files in GRASP compatible format. You can specify number of data points in each file. The program also generates sub-reflector rim definition file for offset systems and the beginning of the GRASP master file with the description of antenna geometry.

At the "Results" page you can view Geometrical optics ray structure in vertical and horizontal planes (select these plots from a combo box on the right panel). The ray structure can also be saved into a file.

Target envelope page Target envelope page is used to specify the sidelobe envelope. An envelope can be specified as a set of constant, linear or log segments. Click on a line in the envelope description box to edit a segment. The segment parameters can be changed using editor boxes and a combo box under the envelope description box. The angle parameter is the end of the segment, the beginning of the segment is the angle parameter of the previous segment. It means that the first line of the envelope description does not specify a segment (it does not have a previous one), so it is used as an indication of the starting point only.

When you change the angle parameter, the envelope list is sorted automatically to put angles in increasing order. The buttons "Delete line" and "Add line" are used to delete a highlighted line or to add a copy of highlighted line to the list.

A sidelobe envelope can be saved or loaded from file using buttons on the left vertical panel. Note that you need to be in the envelope page to load or save an envelope files. When you are in the "Antenna setup" page, the program will load reflector file, not the envelope one.

Envelope file is a text file which is an exact copy of the text in the envelope description box.

Sidelobe envelope graph displays the envelope as you load or edit it. The right mouse click on the graph (and any graph in the program) gives a pop-up menu with three choices: copy graph to clipboard (as windows bitmap), run graph designer and save graph data to a text file.

Graph data can be saved into a text file in two columns (graph x / graph y), separated by tab character. Data from file can be copied directly into MS Excel (it will be formatted properly in 2 columns) to create more sophisticated plots, etc.

Graph designer

Using designer you can change graph limits and tick marks, change line style, etc.

A faster way is to use mouse to zoom in and out ( you do not need designer). To zoom in hold the left mouse button and move the mouse to select a rectangle to zoom in. When mouse button is released, the graph will be re-scaled. Double click resets the graph scale back to automatic.

To zoom out horizontal axis press and hold the left mouse button anywhere under the axis and move mouse. Imagine that you are trying to shrink the existing part of the graph by holding its corner with mouse.

To zoom out the vertical axis press the left mouse button on the right side of the graph.

It is possible to set the envelope with mouse. To do that create a new file by pressing "New" button. Then load the graph designer, un-click automatic scaling of the graph axis and set the graph limits a bit larger than the desired envelope. Close designer.

Set the starting angle of the envelope in the "Angle" edit box. Select the segment type (constant, linear or log) form the combo box. Press button "Use mouse set points". Now click on graph to set a point. All the coefficients will be computed automatically. Note that the mouse position is displayed in the bottom left corner of the program window. The x-coordinate (angle) must be larger than the last point in the envelope list in order to set a new point, so the points are recorded in increasing order. Un-click the "Use mouse set points" button when finished. You can use "Delete" button to remove points from the list.

Tip. The first segment usually does not come right when you are using linear or log segments, so when you finished setting the envelope you can change the first segment (i.e. the second line) to const. See example files: "const_segments.env", "lin_segments.env", "log_segments.env".

Antenna setup page The program is using a conic reflector system as a starting point for the synthesis. On the antenna setup page you need to define the conic system parameters plus some extra data: frequency and the feed radiation pattern. The antenna setup page is shown in Fig.10.

All parameters are listed on the right. The top combo box allows to select 5 antenna types: 3 axisymmetrical (Cassegrian, Gregorian and Double Gregorian) and 2 offset (Cassegrian, Gregorian). Below you can select the feed taper (cos power n or user defined) and the frequency.

The program can compute conic system data from some general parameters like antenna length or sub-reflector size (you type these parameters in the top panel "General antenna data"). If you wish you can enter the conic system data in the bottom panel "Conic system data". To load a number press Enter key or move cursor to a different edit box. All parameters and the antenna plot will be updated. It is possible to toggle automatic update of the antenna parameters by clicking the button with two red arrows. To update parameters in manual mode use buttons with calculator icon (they are disabled in auto mode). Press the top button with calculator icon to compute conic system parameters from the general antenna data. Press the bottom button to update general data from conic parameters.

Antenna parameters definition

We use Cartesian coordinate system for the main reflector, z is the horizontal axis, x is the vertical axis and the y axis is rectangular to the picture plane. For plots we are using the feed position as the origin (shown as small red square on the plot). The other red square indicates the main reflector focus.

Sub-reflector is defined in the spherical coordinate system centred at the feed. The surface is specified inside the feed cone. Feed semi-vertex angle is measured between the axis of the feed cone and its edge.

Vertical aperture size and horizontal/vertical aperture size ratio define the size of circular or elliptical aperture on the x-y plane. Size ratio edit box is disabled for axisymmetrical antennas.

Vertical sub-reflector size is the length of the sub-reflector projection on the vertical axis.

Antenna length is measured between the bottom edge of the main reflector and the top edge of the sub-reflector. This parameter may not be exactly equal to the actual antenna length in some cases.

Vertical clearance is the distance between projections of two points on the vertical axis: bottom of the main reflector and top of the sub-reflector. This edit box is disabled for axisymmetrical antennas.

F/D ratio is the ratio of the main reflector focal length to its vertical size (the main reflector has parabolic surface). The sub-reflector surface is an ellipse or hyperbola which are defined by eccentricity, half-distance between focii (i.e. between the feed and the main reflector focus indicated by two red squares) and the sub-reflector axis angle. The sub-reflector axis is the line connecting the feed and the main reflector focus. The angle is measured between this line and the z-axis. The feed tilt angle is measured between the feed axis and the z-axis.

For the offset system the program is using formulae from [1] to find the conic parameters. The formulae are approximate, so the parameters you see are not exactly the values you typed, but are very close. Please refer to [1] for more information.

User feed window

It is possible to choose between a cos power n feed taper or specify the feed taper as a table (angle, deg / power, dB). Select Feed taper "User defined" and press small button next to feed combo box to set the feed pattern (Fig. 11).

You can type numbers in the editor window, load data from a text file or paste it from clipboard. The data interpretation depends on the option selected in "Load as" menu item. It does not matter if the data is not arranged in 2 or 3 columns in your source file. What is important is the order of numbers. The numbers can be separated by spaces, tabs or end-of-line characters. Press OK or Update plot button to check and re-arrange the data in columns. Use Plot menu to switch between feed power or feed phase plots. Feed phase information is not used in this program since the feed can be modelled as a point source only with Geometrical Optics methods. If the feed phase pattern is constant, it will not be displayed next time you open the window.

You must have more than 2 lines (2 data points) in the user pattern and the pattern angular range must be equal or larger than the feed semi-vertex angle.

The dialogue window size and the editor horizontal size can be changed by dragging its edges with mouse. The graph can be saved into clipboard (right mouse click to see menu).

The program is using second order interpolation to generate the feed pattern used for the synthesis from the user data.

Generate amplitude page Generate amplitude page (Fig.12) is used to synthesize an axisymmetrical distribution over the antenna aperture which satisfies the target sidelobe envelope and given value of the minimum aperture efficiency. The antenna works as a transformer of the given feed taper into the optimised aperture amplitude distribution.

To illustrate how the amplitude optimiser works let us try the following example. We are going to design an axisymmetrical Cassegrian antenna working at 14.2 GHz with main reflector diameter 3.7 m and sub diameter 0.56 m. The sidelobe envelope is 27 + 25log(angle), which is 2 dB below a standard 29+25log(angle) envelope used for satellite communications. The envelope starts from the second sidelobe, the value of the first sidelobe has to be limited at 10 dB below the main peak.

Please go to "Target envelope" page and load "27log25_limit 1st.env" file. In "Antenna setup" page load reflector file "D3.7 Sub 0.56 Cass.rfl". Now proceed to "Generate amplitude" page and load "D3.7 Sub 0.56 run1.amp". You will see a picture as in Fig.12.

Fig.12 shows the initial uniform amplitude distribution. To set initial distribution select "Uniform" or "Gaussian" from the combo box on the top panel, enter the edge taper for the Gaussian distribution and press small button with triangular icon next the the edit box. In this example we are using uniform taper to start.

The normalized amplitude distribution and the corresponding far-field radiation pattern is shown in the top and bottom graphs. The radiation pattern is computed in the horizontal plane (y-z plane) and the angle is measured from the direction of the z-axis. This remark is relevant to antennas with elliptical apertures since the radiation pattern is different in vertical and horizontal planes.

The radiation pattern graph can be scaled as the envelope graph, so you can zoom in with mouse to inspect parts on the pattern and restore graph scale with double click. The amplitude distribution graph is very simple, so the scaling feature is disabled.

Aperture distribution optimisation is a two stage process. First the distribution is computed as a sum of cosine function with some coefficients c:

If all coefficient are zero we have a constant distribution. We are using Powell optimisation procedure to find an optimum set of coefficients. This is called "Initial optimisation". Click "Run" button to run the optimisation procedure. At the bottom of the program window you can see the iteration number and the value of the penalty function , which should decrease to zero as the radiation pattern fits the desired envelope and if the aperture efficiency is higher than the required minimum value. You can update plots after each iteration to see changes to the pattern. To do that toggle the "Auto update plots" button. This slows the procedure, so it is recommended to toggle this button on and off to update the pattern instead of using this feature all the time.

When the program runs, the "Run" button is disabled, and the "Stop" button is enabled. To terminate the program press "Stop" button and wait until the program finished, it takes a few iterations. When program stops, "Run" button become enabled again. If the program stops and the value of the penalty function is not zero, it means that the procedure can not find the solution which satisfies the envelope.

Now we can try the feature to move down the sidelobe envelope automatically until the program can not find the solution. From "Decrease automatically" combo box select "SL envelope", and press "Run" button. You can see that the sidelobe envelope is now pushed down in 1 dB steps until the program stops. This amplitude distribution is stored in "D3.7 Sub 0.56 run2.amp" file.

Now let us proceed to the final stage of the optimisation. It is based on an extremely powerful analytical gradient optimisation procedure, which optimise the whole continuous curve (references [2]-[4]). Select "Final (whole curve)" from "Optimisation" combo box. The procedure needs a good starting point so if you far from the solution it may give some unusable answers. Also it requires a smoothness parameter (values from -10 to 10) which control the smoothness of the aperture distribution. The default value is 4. The larger parameter the smoother the curve, but you can achieve less since the curve become less flexible.

Please press "Run" button to start the procedure. As you notice the procedure stops after couple iterations. Now decrease the smoothness parameter to 3 and run the procedure again. This way you can move sidelobe envelope by a dB down. If you set smoothness parameter to -10 you can go much further, but the distribution become unusable. It is recommended to save "good" results under different names, so you can reload them back again and proceed with the optimisation after altering some parameters. This amplitude distribution is stored in "D3.7 Sub 0.56 run3.amp" file.

It is possible to make the adjustment to the sidelobe envelope, so you do not need to change the envelope file each time. You can specify min and max values for the envelope (in degrees). If the envelope is smaller the limits, it will be extended using constant segments to the min and max values. You may find it useful to make the max value smaller at the initial stage of the optimisation (10-15 degrees) and reset it back during the final stage of the optimisation. This make the optimisation much faster, since the procedure puts about 8 testing points per sidelobe. The more sidelobes the more points it has to use.

Also you can move the whole envelope up and down and set the minimum sidelobe limit required (say, -20 dBi), so envelope values below -20 dBi will be set to -20 dBi.

User amplitude distribution

To use a user defined amplitude distribution select "User defined" from the initial distribution combo box. Press a small button next to the combo box to set the distribution. The input window is similar to the user feed input window. There are a few "Load as" options (Normalised radius / Amplitude; Normalised radius / Power and Normalised radius / Amplitude, dB). Note that the aperture radius must be normalised to 1.0. The amplitude does not need to be normalised. When you press "Update plot" button the input data will be converted to amplitude (if you selected "Load as" Power or Amplitude, dB) and plotted.

When you press "OK" button, the amplitude plot in the main program window will be updated. The program is using second order interpolation to generate the amplitude distribution from the user data. This is the amplitude distribution which will be used for the reflector synthesis. Note that the amplitude synthesis is disabled when you use user defined amplitude distribution.

Remarks about the initial distribution. The general recommendation is to start from uniform distribution (zero taper) for antennas with blockage. For antennas without blockage and low sidelobe use high tapers since they give low sidelobe level. But watch the aperture efficiency parameter , since high tapers has low aperture efficiency. If you need to meet a given aperture efficiency, start with a taper which has a bit higher efficiency and move sidelobes down, instead of trying to pull the efficiency up. Note that the final optimisation does not optimise the aperture efficiency, it makes just the final tuning to the radiation pattern!

Remarks about the amplitude and reflector files. The information stored in the amplitude file is used to reconstruct the shape of the amplitude distribution. Other important parameter is the size of the reflector aperture, which is stored in the reflector file. It means that if you change the antenna parameters or load a different reflector file, the radiation pattern from the same amplitude distribution may be different. We recommend to store files for different antenna designs in different directories or give long self-explanatory names to the files, so you can identify which amplitude file corresponds to a given reflector file. This probably seems inconvenient, but offers flexibility of using an amplitude file from one design as a starting point for a different design.

GO synthesis page The program using separate synthesis procedures for axisymmetrical and offset antennas. The axisymmetrical synthesis procedure is much simpler that the offset one and is using a standard Runge-Kutta method for solving a first order differential equation to create reflector profiles. Information about similar GO synthesis formulae can be found in [5] for example.

Axisymmetrical system synthesis does not require any parameters to specify and always converge. Simply press "Run" button to generate reflector surfaces. Note that the operation of the "Run" button depends on the page you are in. "Load" and the other file operation buttons work with the reflector files in this page (since the GO generated reflector profiles are stored in the reflector file).

When the program finished it displays the reflector mapping picture. The picture shows how equidistantly spaced rays on the main reflector aperture map into the feed cone. What you see is the projection of the feed cone on a plane rectangular to the central ray.

General offset synthesis procedures for antennas with elliptical apertures are more complicated. We are using a very efficient Monge-Ampere equation method [6]. The required parameters can be set on the right vertical panel and are explained below (see Fig. 13).

The offset procedure is using non equidistant rectangular grid defined on the antenna aperture. The first parameters is the number of grid lines along the x-axis. The larger this number the more accurate the solution, but the slower the program. Recommended value - 14...18. This parameter has to be even.

The idea of the reflector GO synthesis procedure is to transform gradually the initial conic system into a system with elliptical aperture and desired aperture power distribution. This transformation has to be done slowly, otherwise the procedure does not converge. The speed of the transformation is controlled by the number of steps to perform power shaping and the aperture shaping. If the procedure does not converge, you have to make these values larger. General rule is the bigger the difference between the final system and the initial conic system - the larger the numbers. If the final system has circular aperture as the conic system you can skip aperture shaping and set number of aperture shaping steps to one. The same relates to the power shaping. If the procedure does not converge you can also increase number of grid lines.

The last parameter is the correction constant which is a number close to 1.0. This parameter is used to improve the convergence. As example load file "D3 Sub 0.4 Offset Cass.rfl". The correction constant is set to 0.98 in this example. Change the number to 1.0 and run the program again. You will notice that the plot lines in the centre become jammed. This kind of distortion may prevent the program from convergence. If you see this kind of picture and the program does not converge (make sure that "Auto update plots" button is pressed to animate the plot), try to make the correction constant a bit smaller. If you have a different kind of distortion - lines are spread away from the centre - try to make the constant a bit bigger to get convergence. A kind of ideal mapping picture is shown in Fig.13.

On "Results" page you can see a 3D plot of the antenna. If you do not see an antenna image it means that the antenna has not been generated yet, so you need to run GO synthesis procedure (i.e. go back to GO synthesis page). You need to run GO synthesis each time you change reflector or amplitude file, or load a different amplitude file (since the program assumes that are going to design a different antenna). A "safe" way to keep the GO solution is to load an amplitude file, then reflector file.

Point mouse at the antenna image and hold left mouse button. Keeping the button pressed you can rotate the image by moving the mouse. Use small buttons on the right vertical panel to move and scale the image. Also there are 3 pre-set views in x-z, x-y and y-z planes.

To save reflector surfaces set the number of data points in each file (along radius or along y). For an elliptical aperture antenna the number of points along x (vertical axis) will be computed from the number of points along y and the aperture size ratio. Press "Save to file …" button on the right vertical panel. You can then select between GRASP compatible format or AutoCAD DXF format. If you select GRASP format the program saves main and sub-reflector surfaces into two separate files. The program also generates sub-reflector rim definition file for offset systems and the draft of the GRASP master file with the description of antenna geometry. If you select AutoCAD format the program generates a single *.dxf file. It is assumed that the feed is located in the origin. All dimentions are in metres.

As an option you can view and save non-shaped refelctor surfaces. To do that select "Conic surfaces" from "Plot" combo box. To save surfaces press "Save to file …" button. Note that the operation of "Save to file …" button depends on the type of plot you view on screen, you save the data that you view. Note also that you do not need to generate shaped reflector surfaces to view and save conic reflector surfaces.

You can view Geometrical optics ray structure in vertical and horizontal planes (select these plots from a combo box on the right panel). The ray structure in vertical and horizontal planes can also be saved into a file (x, y, z coordinates of rays as they travel from the feed to the sub and main reflector).

Ctrl-O	Load (open) file
Ctrl-S	Save file
Ctrl-R	Run or Stop the program
Ctrl-1	Select Target envelope page
Ctrl-2	Select Antenna setup page
Ctrl-3	Select Generate amplitude page
Ctrl-4	Select GO synthesis page
Ctrl-5	Select Results page

Note that you can use standard Windows keys (as Ctrl-C or Ctrl-Insert) to copy, cut and paste text.

References 1. Brown K.W. and Prata A. "A design procedure for classical offset dual reflector antennas with circular apertures", IEEE Trans. on Antennas and Propagation, Vol.42, No 8, August 1994, pp.1145-1153.

2. Westcott B.S. and Zaporozhets A.A.: "Fast synthesis of aperture distributions for contoured beam reflector antennas", Electronics Letters, 1993, Vol 29, No 20, pp.1735-1737.

3. Westcott B.S. and Zaporozhets A.A. "Dual-reflector synthesis based on analytical gradient-iteration procedures", IEE Proc., Part H, Vol. 142, No 2 April 1995, pp 129-135.

4. Westcott B.S. and Zaporozhets A.A.: "Single reflector synthesis using an analytical gradient procedure", Electronics Letters, 1994, Vol 30, No 18, pp.1462-1463.

5. Lee J.J., Parad L.I. and Chu R.S. "A shaped offset-fed dual reflector antenna", IEEE Trans. on Antennas and Propagation, Vol.27, No 2, March 1979, pp.165 - 171.

6. Westcott B.S., Graham R.K. and Wolton I.C. "Synthesis of dual-offset, shaped reflectors for arbitrary aperture shapes using coninuous domain deformation", IEE Proc., Part H, Vol. 133, pp 57-64.

User manual

MakeR (F)

Focused beam dual shaped reflector antenna synthesis

Version 2.0