De-embedded S-Matrices

De-embedding allows you to shift the reference plane of the S-matrix for any port by adding (or subtracting) a length of lossless transmission line to (or from) a port. The following figure illustrates such a case.

The S-matrix, S_1, describes the behavior of the structure that was modeled.

The de-embedded S-matrix, D_1, describes the behavior of a structure created by subtracting or adding a length of lossless transmission line to the structure that was modeled. It is computed by phase rotating the S-matrix inward toward or outward away on the structure by the specified length at each port.

To shift the reference plane of the structure, the S-matrix of the modified structure can be calculated using the following relationship:

Where:

is a diagonal matrix with the following entries:

• g = a + jb is the complex propagation constant, where a is the attenuation constant of the current and b is the phase constant associated with the uniform transmission line at port i.
• l_i is the length of the reference plane shift. A positive value indicates a shift toward the structure by a length l.

The value of gfor each port is automatically calculated by Electronics Desktop. However, when performing de-embedding, the attenuation constant, a, at each edge port is ignored. Therefore, only the phase of the S-parameter is affected.