Introduction

Cable television integrated circuits are usually designed to interface with 75Ω inputs and outputs, while most RF test equipment use 50Ω impedance. In most cases, minimum-loss pads are used to convert the input and output impedances from 75Ω to 50Ω, and vice-versa. Although convenient, minimum-loss pads should be avoided when measuring S-parameters.

This application note presents an easy way to perform S-parameter measurements by treating the input and output impedance of the cable device as 50Ω, performing the test, and making a mathematical conversion. We provide the equations and a handy Excel spreadsheet to convert 50Ω-referenced S-parameters back to 75Ω.

S-Parameter to Impedance

The conversion of a 50Ω-referenced S-parameter to 75Ω begins with equation 1. Both the S-parameter and input impedance are complex numbers (R + jX), where R represents the real component, and the X represents the imaginary component. Z_O is usually a real impedance. For the sake of simplicity, input return loss (S₁₁) will be considered throughout this application note.


Rearrange Eq. 1 to obtain an input impedance (Z_IN) expression Eq. 2,


Replace the S₁₁ with R + jX,


Multiply the denominator of Eq. 3 with its complex conjugate to separate the real and imaginary components,


Eq. 6 is the real component of the input impedance,


Eq. 7 is the imaginary component of the input impedance,

Impedance to S-Parameter

Once the complex input impedance is obtained, Eq. 1 is used once again to convert the impedance back to a 75Ω-referenced S-parameter.

Eq. 8 is the same expression as Eq. 1, except Z_IN is replaced with R + jX,


Multiply the denominator of Eq. 8 with its complex conjugate to separate the real and imaginary components,


Eq. 11 is the real component of the input return loss (S₁₁),


Eq. 12 is the imaginary component of the input return loss (S₁₁),


Example

Excel Spreadsheet

Table 1 shows the Excel spreadsheet that allows fast conversion of 50Ω S-parameter data to 75Ω.


Download Table as an Excel Spreadsheet (XLS, 16kB)