MMANA appendix

First version 1999.11.01 by JE3HHT Makoto Mori
Updated version 2000.05.31 by JE3HHT Makoto Mori
English MMANA.EXE version 0.5 released on 2001.06.25 by DL2KQ (also EU1TT) Gontcharenko Gary
English manual version 0.5 released on 2001.06.25 by JA7UDE Nob Oba

This document describes the following topics.

- Equation
- Segmentation and tapering
- Pulse assignment
- S parameter of lumped constant
- Tips for the optimization
- All elements button of the optimization
- Antenna stacking
- Ground permittivity and conductivity
- Association of the document file
- Resonance frequency of the element
- Height of the vertical antenna
- Combination of plural pipes
- Adjustment if the radius of the wire is changed
- Use of isolation wire (R=0)
- "Change the coordinate proportionally" in Element edit


-----
Equation
-----

You can use an equation instead of a number.  The numeric operators MMANA supports are +, -, *, and /.  You can use () to specify the calculation order.

	5*2+1 = 11
	1+5*2 = 11
	(1+5)*2 = 12
	5*(2+1) = 15
	20/(3+7) = 2

Special constant below can also be used.

	R	Wavelength (meter)
	I	1 inch (meter)		1 inch = 2.54 cm
	F	1 foot (meter)		1 ft = 12 inches

[Example]
	R/4	1/4 lambda (wavelength)
	5*R/8	5/8 lambda
	30*F	30 feet
	15*I	15 inches

The equation is calculated immediately.  MMANA does not memorize the equation itself in the wire definition.



-----
Segmentation and tapering
-----

The moment method divides a wire into pieces, called segments, and calculates the current flow on each segment.  Thus, the calculation accuracy strongly depends on how the wire is divided into segments.

It is said that the dipole or yagi antenna, which consists of simple straight wires, can successfully be modeled with simple equal segmentation.  If the wire is bended (e.g., loop antenna), you should segment the wire into fine pieces; otherwise you will not get an accurate result.

Tapering is one of the methods that improve the calculation accuracy.  It divides the wire section near the bending point into small segments, but divides the other sections (straight sections) into large segments.  If all the wires were divided into small segments, the computation time would become intolerably large.
Tapering sometimes allows you to keep the calculation accuracy for the straight wire with small number of segments.

To improve the calculation accuracy, it needs to have small segments, but the calculation would become unstable for too small segments (less than 0.001 lambda).  It also is said that a thick wire (radius:segment > 4:1) cannot be calculated in good accuracy.

The table blow shows the typical values for segmentation.  Keep in mind, however, this table gives just typical examples, and you may have to get it smaller in accordance with the antenna shape and feeding method. 

Antenna			Seg		DM1		DM2
Dipole, yagi		0 or -1		200 - 400	40
Square loop		-1		200-400		40
Triangle loop		-1		400-600		40
Rectangle loop		-1		400-600		60
Henntenna		-1		400-600		60

(If Seg = 0, DM1 is don't care)

If the calculation speed is regarded important, for example in the optimization, DM1 and DM2 can be set to the values smaller than those show above.  It is a good idea to observe the margin beforehand.  With small DM1 and DM2, the calculation error tends to be small in the gain and F/B ratio, but is relatively large in the impedance (jX).

There is no exact criterion to judge the calculation accuracy.  You could, however, checks how the impedance is affected by increasing or decreasing the number of segments.  If the impedance does not change much, your modeling should be fine.  You should see the current distribution in the antenna view window.  If the current does not traverse smoothly, check your modeling again.

Generally speaking, you cannot expect accurate results for the wires that closely placed or for the wire that is tightly bended.
Some sample models I put in the ANT directory have a matching section defined with the combination of short wires.  They are only experimental; you may not trust the absolute dimension of them.


+++++   Pulse assignment

The pluses are assigned to the wires in the order of the wire definition.  The pulse is not assigned to the dead end of an independent wire.  If the wire, on the other hand, is connected to the other wire, a pulse is assigned to the end point.
As for the special case, if the wire has its Z value 0, a pulse is assigned to that point (a vertical antenna is a typical example).

Be careful for the point at which three or more wires are connected together.  The pulse is not assigned to the point of the firstly defined wire.  For example, think of a GP antenna with four radials, that is, five wires are connected at the one point.  Even if you set the source at the end of the first wire, the actual feeding point is one segment inner of the wire, as shown below.  To avoid this, set the source at the end point of second wire or afterward one.



          Source = w1b                       Source = w3b
               (1)                               (3)
                |                                 |
                |                                 |
                |                                 |
                *                                 |
                |                                 |
      (2)-------+-------(3)             (1)-------*-------(2)
      Fed at one segment inner           Fed at the bottom


Care also should be taken for the current direction at the source.  See the example of four wires below.  This is the case of the feeding scheme for the double doublet or twin delta loop.  It is a good idea to insert a short wire between two sets of wires, and to feed at the center of the inserted wire, as shown in the right figure.  Refer to DlbDp.maa and TwinD.maa as examples.

           source = w2b                source = w1c
               (2)                                  (2)
                |A			             |A
                ||			             ||
                |			             |   ->
     (1)--------+--------(3)		             +--------(3)
           ->   |   <-			         (1)/
                |A			(4)--------+
                ||			      ->   |
               	|		           	   |A
		(4)			           ||
                 			          (5)
          Invalid feeding                    Valid feeding


+++++   S parameter of the lumped-constant circuit

The S parameter can be obtained by applying the Laplace transformation to the lumped-constant circuit (S = jw). The coefficients of the numerators are A0 - An and those of the denominator are B0 - Bn.  The LC type built in the MMANA cannot compose a serial resonance circuit.


                                        R+LS+(1/CS)     1 + RC*S + CL*S^2
 Z = R+jwL+(1/jwC)  -->  R+SL+(1/SC) = ----------- =  ------------------------------------------
                                         1               0 + C*S + 0*S^2

Therefore, you can simulate it with A0=1, A1=RC, A2=CL, B0=0, B1=C, B2=0 (or A0=1/C, A1=R, A2=L, B0=0, B1=1, B2=0).
The units for R, C and L are ohm, F, and H, respectively.  The absolute values of this system tend to be very small, and therefore the exponential notation is recommended.  For instance, 20pF is 20 * 10^-12 = 20e-12.

The antenna definition file, MCQM.MMA, has an example of the complicated circuit.  You could see the explanation in the comment field.

You have the same results using S parameter or R+jX because they represent exactly the same lumped-constant load.  However, R+jX must be adjusted its value according to the frequency.  For this reason, it is hard to analyze a multi-band antenna using R+jX.  The LC type of load is modeled with the fixed circuit configuration in MMANA, so MMANA automatically changes its notation to R+jX.

Comments by DL2KQ, Good freeware program RFSimm99 for calculation S-parameters is on www.hydesign.co.uk.

+++++   Tips on the optimization

I have tried various optimization algorithms.  I have figured out that the algorithm similar to the practical antenna adjustment, that is, changing one parameter at a time to maximize the target value and repeating it for other parameters as well, gives fast convergence and good results.
This procedure, however, would not always give the real optimized solution that the one-by-one method gives.  It could terminate the optimization just after finding a local minimum.  If you are not satisfied with the result, change the parameter manually and retry the optimization.
The result could depend on the parameter order.  MMANA attempts the optimization by changing No. 1 parameter first and then does No.2 parameter.  It is a good idea to put the most effective parameter in the first place of the variable parameter list.

Pursuing the gain often results in the low impedance.  The very low impedance makes the sustainable bandwidth narrow, and the wire loss cannot be ignored.  It is difficult to implement the very low impedance antenna in the real world.  Consider SWR in the optimization for obtaining reasonable results. 

If you put two or more bands, MMANA attempts the optimization in each band and sums up the evaluation rates.  Only the first feeding information is displayed.
To keep the performance even in the band edge, put the band edge frequency as well.  However, it increases the calculation time for the convergence.  I am not sure if you could achieve good results.

In case of Yagi antenna, the moment method is weak in the calculation speed, so I recommend you use another analyzing tool that uses the electromotive force method.


----------
Optimization goals
----------

- If your goal is Z
Push Options menu, select Options and setup, click on the Setup tab, and input R and jX in the Standard SWR pane.  Set the target to the SWR minimization and start the optimization.
Another way to this is: push Options menu, select Optimization, push Advance button, select Goal tab, check Optional Z, and put your R and jX.  Set the target to the matching circuit and star the optimization.  Do not set the target to SWR or jX.

- If your goal is R
Push Options menu, select Optimization, push Advance button, select Goal tab, check Optional Z, and put your R.  Put * to jX.  Set the target to the matching circuit and star the optimization.  Do not set the target to SWR or jX.

- If your goal is jX
Push Options menu, select Optimization, push Advance button, select Goal tab, check Optional Z, and put your jX.  Put * to R.  Set the target to the matching circuit and star the optimization.  Do not set the target to SWR or jX.

- If your goal is to get the voltage fed antenna resonant
Push Options menu, select Optimization, push Advance button, select Goal tab, check Optional Z, and put 10000 to R.  Put 0 to jX.  Set the target to the matching circuit and star the optimization.  You may put a little value to jX.  In case of the end-fed antenna, put * to jX.

- If your goal is beam pattern
Push Options menu, select Optimization, push Advance button, select Environment tab, put 180 to Azimuth, and put 90 to Vertical.  Set the slider bars of the Gain and F/B rates around the center, input your SWR, and start the optimization. 

- If your goal is a broad band antenna
Set two or three frequency spots as the bands.  It is recommended to minimize SWR rather than jX because R will not vary much (set SWR to the target beforehand).

- If you want to keep the boom length
Use the element position as a variable.  Bear in mind that you have to keep the front-end and back-end elements fixed.  In other words, you use the positions of the elements except for these two elements.
To automatically register the element position as a variable, you should uncheck the Distance from the active element box in the Edit element window.

If you put * in R or jX, the marked value are not taken into consideration in the evaluation.



+++++   All elements button in the optimization

When you push the All elements button in the optimization window, MMANA automatically uses the following parameters as variables.

Loop		Loop length, space (or position)
Others		Width, length, X-width, space (or position)

MMANA analyzes the relative positions of the elements and assigns the variables in the order of the radiator, reflector, and directors (d1-dn).
If two or more elements have the identical X-axis value, they are assumed to be connected.  MMANA makes them associated.  If an element has two or more variables in the width, length, and X-width, MMANA asks the user how they should be treated (a dialog box appears).

MMANA does not automatically make association between the elements that have different X values.  In such a case, right click on the optimization window to get the pop-up menu, select the element association.  You can make association the element with the other element that have different X value.
This technique would be useful for the antennas, such as a surface antenna, which has many elements in the same size and space.

When you push the All elements button, MMANA puts a typical value to the pitch.  You may change the value as you like.  The pop-up menu provides a means to give the identical pitch to the all variables.


+++++   Stack

The Stack button gets you the horizontally/vertically-stacked antennas based on the original antenna you designed.  The design of the original antenna is unchanged, so you can easily make up various formation.

To make your stacked design permanent, push the Use this stack as the new antenna definition button in the Stack window.  If you have done this once, you no longer get it back to the original design, that is, a single antenna.  This is used to implement a phased driven or a unbalanced driven antenna.

In either case, the number of antennas N is given by [number of horizontal] multiplied by [number of vertical].  This means that:
Number of pulses:		*N
Number of wires:		*N
Number of sources:	*N (voltage = 1/N, identical phase)
Number of lumped-constant:	*N

MMANA checks if these numbers, except the number of pulses, are affordable in the computation.  In case you see the message "PULSE NUMBER EXCEEDS DIMENSION," you have reached the maximum limit.  You have to increase the maximum limit of the pulse number in the Options menu.

When making a vertical stack, you can select one of the three ways to set the reference height.  It is not taken into consideration in the free space calculation, but is used to define the antenna height in the calculation with ground.


+++++  Dielectric constant and conductivity of the ground

The table below shows typical values, which I refer to the Antenna Handbook Edition 20, 1976 (comment by JA7UDE: this is Japanese book, and no longer selling).

			Dielectric constant		Conductivity (mS/m)
Sea water			81			4000
Fresh water			80			1 - 10
Wet ground			5 - 15			1 - 10
Dry field, forest		13			5
Sandy field			12			2
Suburb, industrial		5			1
Arid field			2 - 6			0.1

The conductivity widely varies according to the field.  To get the values in your region, consult "Wire antenna" or "Antenna design using PC" published by CQ publishing of Japan (comment by JA7UDE: these books are written in Japanese and available in Japan only).


+++++   MMANA files
MMANA never touches the Windows registry, and therefore it does not make an association for the file types.  If you want to open the MMANA by clicking a MMANA file in the Windows file manager, do it manually.  You could use the icons for MAA, MAB, and MAO files provided in the MMANA.EXE.


+++++   How to get the resonance frequency of the element

It is extensively used to measure and set the resonance frequency of the element with the grid-dip meter (GDM).  It should be useful for the antenna construction to have the resonance frequency of each element by using the antenna simulation.

MMANA offers two methods to get the resonance frequency of the element.

1. By optimization
Put the source to the target element.  Set the frequency as the variable and set jX to the goad.  jX = 0 indicates the resonance, so the obtained frequency is the resonance frequency.

2. By frequency characteristics
Put the source to the target element.  Calculate once at the appropriate frequency in the band.   Push the Resonance button in the Frequency characteristic window.  fo in the Z chart is the resonance frequency.

In either case, you should make the antenna definition equivalent to the practical GDM measurement.  For example, if you measure each element independently (no other element exists around it), you should make a model of a single element.  If you measure each element after you put up the whole antenna, you should make a model of the whole antenna.

In the real situation, it is impossible to completely avoid the effect of surroundings (including yourself).  Take the effect into consideration.


+++++   Height of the vertical antenna

You must put zero to the Z-axis value of the source and set the ground height zero; otherwise, you would model an end-fed antenna and result in an incorrect calculation of the impedance.

You may want to calculate the beam pattern of the antenna that is set up on the housetop of an apartment house.  In such a case, put a minus value to the media setting window in the real ground option.


+++++   Wire tapering

Yagi antennas for HF commonly compose an element with two or more pipes in different radiuses.  In MMANA version 1.55 or earlier, the user had to define the parameters of each pipe.  In MMANA version 1.56 or later, you can define the combination with one shot using the predefined parameters.
First, put a minus value to the R (radius) of the pipe.  Next, define the following parameters.

R (mm)		Pointer to the definition - must be minus
Type		Type of combination (e.g., center point, starting point)
L0 - L9		Length of each pipe
R0 - R9		Radius of each pipe

When MMANA finds a minus value in the R field, it looks for the definition of R in the combination wire list.  If two or more definitions have the same R, MMANA uses the first one.  The R used here is just a pointer and is not the real radius value.

[Type <> or <> *] 
      L4    L3    L2    L1     L0     L1    L2    L3    L4
  -----+-----+-----+-----+------+-----+------+-----+------ 
      R4    R3    R2    R1     R0     R1    R2    R3    R4

Example 
                              ----		   Short element
                         ---+------+---
                   ---+-----+------+-----+---
               -+-----+-----+------+-----+------+- Long element

[Type -> or -> *]

     L0    L1    L2    L3    L4
  ------+-----+------+-----+------ 
     R0    R1    R2    R3    R4

Example
  ----				Short element
  ------+---
  ------+-----+----
  ------+-----+------+----	Long element

You can use "<>" or "<> *" for Yagi antennas, and "->" or "-> *" for vertical antennas.

For instance, when you compose three pipes:
Diameter	Length
30 mm		2 m
25 mm		1.8m
20 mm		Variable (toward the end)

Use the following parameters
L0=2		R0=15
L1=1.8		R1=12.5
L2=99999.9	R2=10

L2=99999.9 makes the L3 unused, and uses the L2 toward the end (if you put 0 to L3, L2 automatically becomes 99999.9).



[Type <> or <> *]

	2.2m   1.8m   2m    1.8m   2.2m
       ------+-----+------+-----+-------
        20mm   25mm  30mm   25mm   20mm

[Type -> or -> *]

	2m     1.8m         6.2m
       ------+-----+--------------------
        30mm   25mm       20mm

In the antenna view window, you can observe how the element is composed of the pipes.  The connecting points are marked with a blue square.  Right click on the element to verify the combination.

You should pay attention to the segmentation for the combination of pipes.  Even if you specify the equal segmentation, the actual segmentation will not follow it because of the element decomposition.  You have to adjust the DM2 value using the antenna view (increase it to 50 or 60).
When the segment tapering is specified and define "<> *" or "->*" the tapering is applied only to the end of the element.  Even in this case, the inner pipes are divided into the segments of the same length, and therefore you have to adjust the DM2 value.

Since MMANA is not wise, unfortunately, it would generate unbalanced segmentation if the combination and tapering are applied at the same time.  Be sure that see how the element is segmented using the antenna viewer.

The samples of the combination pipes are given in:
	3el20.maa 4el20.maa 4el20hm.maa 5el20.maa 6el10.maa 2delta20.maa in directory ...\ANT\HF beams
	8el6mW.maa in directory ...\ANT\VHF beams


+++++   Adjustment when the wire radius is changed

It is common for an antenna to have very different characteristics when the wires' radius is changed.  Particularly in Yagi or Quad antenna, the radius affects not only the impedance but also the gain and F/B ratio.
However, you may want to change the radius of the antenna which you are very happy with.  You may want to change the combination of the pipes.

Here is the commendable procedure to keep the original characteristics.
1. Change the radius and calculate once. **
2. Push the Resonance button in the Frequency characteristics window, and get the fo.
3. Use the fo as the design frequency in the antenna definition window.
4. Calculate the model again.  If the antenna characteristics are close to the original's, step forward.  If not, give up, hi.
5. In the antenna size window of the Edit menu, check Y-axis and Z-axis (uncheck X-axis to keep the boom length).  Resize the antenna so that it matches the original frequency.
6. Calculate the model again.
7. Repeat 1 to 6 if needed.

** A broad band Yagi antenna would have two or more frequencies that give jX=0.  The resonance frequency derived the frequency characteristics window is only one of them, and therefore the derived frequency is not always same as the original fo.  Keep the following tendency in mind. 
- When you enlarge the pipe radius, the resonance frequency is likely to decrease.  When you shorten the pipe radius, the resonance frequency is likely to increase.  It should be noted that this tendency is reversed in loop antennas.
- When you get the element tapered, the resonance frequency is likely to increase.  When you use a straight single pipe, the resonance frequency is likely to decrease.
Following this procedure, I believe you get the original characteristics back, but you could optimize the antenna again.  This procedure, however, presumes that the original antenna is resonant at the design frequency.  If your element is a little bit capacitive with a hairpin match, adjust the element length first to be resonant and follows the procedure above.  After you are finished, tune again the element with the hairpin match.


+++++   Using an insulated wire (R=0)

The element consisting of two or more wires must be connected together if it is edited or if it is treated as the element variable in the optimization.  However, you may want to treat separated wires as one element.  MMANA version 1.63 or later accepts zero radium (R=0) in the wire definition, and does not calculate the wire.

MMANA assumes in the Element edit (variables) that the element is symmetrical with respect to X-, Y-, or Z-axis, and determines the changing points of the elements.  Thus, the elements that are not targets will not be changed as you expected.  In such a case, the insulated wire helps.

Example1:

    -Y                 0                  Y
    --------------           --------------
In the Element edit, the element is divided into two wires.

    -Y                 0                  Y
    --------------===========--------------
If you define the insulated wire "=====", it behaves as one element.  When you change the width of the element in the Element edit, only the outmost points are moved.

Example 2:
    -Y                 0                  Y
    --------------
If you change the width of this element, both end points are moved.  You want to fix the right end point.

    -Y                 0                  Y
    --------------=========================
Add the insulated wire "=====" at the right end of the element.  When you change the width of the element in the Element edit, both end points are moved, but the right edge of the original element is fixed.

Be sure:
- You cannot connect a source to the insulated wire.
- You cannot insert a lumped-constant load.

MMANA does not check if these conditions are met.



+++++   Change all coordinates proportionally in the Element edit

Let me assume that L1=L2=L3=L4 in the example below.  If you have checked "Change only end points box," L1 and L4 are changed, but L2 or L3 is not changed.

	+----------+----------+----------+----------+
	|          |          |          |          |
	|          |          |          |          |
	|          |          |          |          |
	+----------+----------+----------+----------+
	     L1         L2         L3         L4

In such a case, be sure to check the "Change all coordinates proportionally box," for keeping L1=L2=L3=L4.

The variables in the optimization are selected as follows:
Change only end points:		Width, length and loop length
Change all coordinates proportionally:		Width (all coordinates), length (all coordinates), and loop length (all coordinates)



73 JE3HHT Makoto Mori
