Transforming Input Reflection Coefficient

The Input reflection coefficient GI can, before displaying, be subject to a user-defined transformation, accounting, e.g., for a two-port network connected at the Homer Autotuner input. A typical example for its use is a magnetron Rieke diagram measurement (Fig. 63a). A Rieke diagram is usually defined for a waveguide different from that of the Homer. In such situation, we need an adapter between the launcher waveguide (LWG) and the Homer waveguide (HWG). To arrive at the Rieke diagram-related reflection coefficient GR and the net power PR delivered by the magnetron we need to use the formulas

where D = S11S22 – S12S21 is the determinant of the S-matrix, PL is the power absorbed in the matched load, and Sij are (frequency-dependent) scattering parameters of the two-port network (Fig. 63b) between plane R (where GR is defined) and the tuner Stub 1 axis plane A (where GI is defined). The equation is a conformal mapping, also called a bilinear transform.

Fig. 63.  a) Rieke diagram measurement setup example. b) Substitution of the two-port network between the GR reference plane R and the GI measurement plane A by its scattering matrix S.

The Homer can perform this transform in real-time, after an appropriate text file with tabulated frequency dependence of Sij is loaded. The necessary actions can be carried out via the following submenu items of the Homer|Transform menu.

Active

Switching the bilinear transform ON (YES) and OFF (NO), provided that the transformation data have been loaded. (otherwise, the menu item is disabled).

Load

Load a text file containing the tabulated frequency dependence of the network scattering parameters. The parameters are interpolated if the actual frequency is between the tabulated values. For an actual frequency below the lowest tabulated frequency, the lowest tabulated frequency values are used. For an actual frequency above the highest tabulated frequency, the highest tabulated frequency values are used.

Once the file is successfully loaded, the bilinear transform is both enabled and activated.

Clear

Disables the transform permanently. It can be enabled again only by a new Load.

Format of S-Parameters Text Files

An example of a scattering parameters text file is shown below:

! Lines starting with exclamation mark are ignored

{ Lines between braces are ignored.

  Empty lines are also ignored }

*    Info =    This is a comment associated with the file

#   MHz   S11_Re  S11_Im  S21_Mag  S21_Deg  S22_Log  S22_Rad

    2420  0.2     -0.3    0.8      50       -20      1.7453

    2425  0.21    -0.25   0.79     40       -21      1.3963

    2430  0.22    -0.2    0.78     30       -22      1.0472

    2435  0.23    -0.15   0.77     20       -23      0.6981

    2440  0.24    -0.1    0.76     10       -24      0.3491

    2445  0.25    -0.05   0.75     0        -25      0.0000

    2450  0.26    0       0.74     -10      -23      -0.3491

    2455  0.27    0.05    0.73     -20      -21      -0.6981

    2460  0.28    0.1     0.72     -30      -19      -1.0472

    2465  0.29    0.15    0.71     -40      -17      -1.3963

    2470  0.3     0.2     0.7      -50      -15      -1.7453

    2475  0.31    0.25    0.69     -60      -13      -2.0944

End                            

The file is terminated by a line containing the string END.

The files are case-insensitive.

Four line types are distinguished:

  • Comments and blank lines.

  • Info line.

  • Header line.

  • Data lines.

Comment Lines

Comment lines are those starting with the exclamation mark (!). They can appear anywhere in the text and will be ignored.

If a line starts with the left brace ({), this line and all following lines will be ignored until the right brace (}) is found. (The line with the right brace will also be ignored.)

Empty lines will also be ignored.

Info Line

The Info line starts with an asterisk (*). The line is not mandatory. The structure of the Info line is

* INFO = <Text>

<Text> symbolizes an arbitrary comment (up to the end of the line). The asterisk as well as the equality sign can be surrounded by whitespaces, such as Space (ASCII 32) or Tab (ASCII 9).

Header Line

The Header line starts with the # character. It can be optionally followed by whitespaces.

Exactly one Header line must precede the Data lines.

The Header line consists of substrings, mutually separated by at least one Space (ASCII 32) or Tab character (ASCII 9). The substrings are of two types:

  • Frequency unit substring.

  • Data type substrings.

Frequency Unit

Accepted frequency unit substrings are (the letter case is irrelevant)

Hz, kHz, MHz, GHz

The substring is mandatory and must be the first item in the Header line. The frequency values in Data lines (the first item in each line) are interpreted according to the specified frequency unit.

Data type

The form, quantity and arrangement of the data type substrings in the header line provide information about the type of data, their format, number and order in the data lines.

Each substring consists of two parts, separated by the underscore character (e.g., S11_RE).

The first part identifies the data type: it can be S11, S12, S21, or S22.

The second part denotes the data format:

RE: real part

IM: imaginary part

MAG: linear magnitude

LOG: logarithmic magnitude (dB)

SWR: standing wave ratio

DEG: phase angle in degrees

RAD: phase angle in radians

The existence of a header term indicates the existence of the corresponding data item in the data lines.

The order of the terms indicates the order of the corresponding data items in the data lines.

Rules for Header Substrings

The following data type terms must be present in the header: S11, S22, and one or both of S12, S21. If S12 or S21 is missing, the two-port network is considered reciprocal, i.e., S12 = S21.

Each scattering parameter must have two components, which can be:

  • Real and imaginary parts (e.g., S11_RE & S11_IM).

  • Magnitude and phase (e.g., S11_LOG & S11_DEG, S21_MAG & S21_RAD, etc.).

Invalid combinations are, for instance, S22_RE & S22_DEG, or S12_MAG & S12_IM.

The substrings can be in arbitrary order, e.g.,

S11_MAG  S21_MAG  S22_MAG  S11_DEG  S21_DEG  S22_DEG

Data Lines

Data lines follow the Header line. There must be at least one Data line.

A Data line consists of numeric terms separated by at least one Space (ASCII 32) or Tab character (ASCII 9).

The first data item is frequency in units specified in the header frequency unit term.

The frequencies must be ordered in ascending order.