A script to calculate the design paramters of an RF power divider
2012-03-27 2012-04-07

In the last period I was designing multiple microstrip (unequal) power dividers. There, I have to optimize all alternative solutions repeatedly in order to control the overall tolerance and to match the circuit layout. To estimate the rough initial parameters for the required transmission lines and lumped elements, the following simple script has been created.

A new kind of power divider (see the this paper) is used in my circuit and therefore, it is also considered in this script. That one has a low bandwidth, but it is able to create a large power ratio more reliably.

Example output:

```\$ cc divider.c -lm -o divider
\$ ./divider
Frequency (in GHz) = 5.9
Relative epsilon = 2.2
Height of the substrat (in mm) = 0.79
Z0 (in Ohm) = 50
P2      |S21|
k^2 = ---- = (-------) ^ 2 = 5
P3      |S31|

========================================

>>> Numerical tolerance of calculation for Z0 is 0.854769%
>>> Width for 50.000000 Ohm = 2.424016 mm
>>> Lambda for 50.000000 Ohm at 5.900000 GHz is 37.175866 mm
>>> Lambda / 2 is 18.587933 mm
>>> Lambda / 4 is 9.293966 mm

========================================

>>> Branchline:

Port 1                     Port 2
o-----+-----[Zh]-----+-----o
|              |
|              |
[Zv]           [Zv]
|              |
|              |
*---+-----[Zh]-----+-----o
|                     Port 3
^
Z0
v
|
---
-

>>> Zh = 45.643546 Ohm ,	W = 2.772481 mm ,	 Length = 9.257762 mm
>>> Zv = 111.803399 Ohm ,	W = 0.545679 mm ,	 Length = 9.630547 mm

========================================

>>> Wilkinson:

+------+----[Z2t]-----o
/       |
[Z2]      |           Port 2
/         ^
o---+          R
Port 1   \         v
[Z3]      |           Port 3
\       |
+------+----[Z3t]-----o

>>> Z2 = 36.628415 Ohm ,	W = 3.771446 mm ,	 Length = 9.173780 mm
>>> Z3 = 183.142075 Ohm ,	W = 0.119482 mm ,	 Length = 9.795098 mm
>>> Lumped Resistor: R = 134.164079 Ohm
>>> Z2t = 33.437015 Ohm ,	W = 4.260057 mm ,	 Length = 9.140518 mm
>>> Z3t = 74.767439 Ohm ,	W = 1.261895 mm ,	 Length = 9.460037 mm

========================================

>>> A novel loop:

+-----------[Z,L2]-------------+
|                              |   Port 2
o-------+                              +------o
Port 1     |                              |
|                             <R>
|                              |
+----[Z,L3]----+----[Z,L3']----+
|
|
|
Port 3    o

>>> R = 100 Ohm ,	 Z = 70.710678 Ohm ,	 W = 1.393964 mm
>>> L2 = 16.086952mm ,	 L3 = 9.436088 mm ,	 L3' = 6.650864mm

========================================
```