## Series to Parallel Conversion

Convert a series connected impedance and reactance into a parallel circuit or vice versa.

Exact | Approximate | |||
---|---|---|---|---|

R = |
≈ | Ω | ||

X = |
≈ | Ω |

Please note that approximations are valid if *R _{s}*

^{2}<< |

*X*|

_{s}^{2}or

*R*

_{p}^{2}>> |

*X*|

_{p}^{2}.

*Fill out the fields, you can use SI suffixes in your numbers e.g. 10k would be 10 kilo. Capitalization matters, as 1m would be 1 milli and 1M would be 1 mega. Finally, press the "Convert" button to get the answer.*

### Description:

In some cases it is convenient to deal with series circuits, in some other - with parallel. Series-to-Parallel Conversion allows to transform one circuit into another one keeping the total impedance of the circuit constant.

*Series to parallel conversion.*

The circuits are interchangeable if

- for series to parallel conversion
*R*= (_{p}*R*_{s}^{2}+*X*_{s}^{2}) /*R*≈_{s}*X*_{s}^{2}/*R*, and_{s }*X*= (_{p}*R*_{s}^{2}+*X*_{s}^{2}) /*X*≈_{s}*X*,_{s} - for parallel to series conversion
*R*=_{s}*R*·_{p}*X*_{p}^{2}/ (*R*_{p}^{2}+*X*_{p}^{2}) ≈*X*_{p}^{2}/*R*, and_{p }*X*=_{s}*X*·_{p}*R*_{p}^{2}/ (*R*_{p}^{2}+*X*_{p}^{2}) ≈*X*_{s}

Remember, that the approximations are valid only if *R _{s}*

^{2}<< |

*X*|

_{s}^{2}or

*R*

_{p}^{2}>> |

*X*|

_{p}^{2}.