RF Cascade Workbook

Copyright

1996 -
2016

Webmaster:

Kirt
Blattenberger,

BSEE - KB3UON

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Fixed attenuators can be designed to have either equal or unequal impedances and to provide any amount
of attenuation (theoretically) equal to or greater than the configuration's minimum attenuation - depending
on the ratio of Z_{1}/Z_{2}. Attenuators with equal terminations have a minimum attenuation
of 0 dB. Unequal terminations place a lower limit on the attenuation as follows:

Express in decibels as:

In the attenuator formulas below:

, which is the linear attenuation ratio of
the two powers (note above that k has a minimum value if Z_{1} and Z_{2}.are
not equal).

If, as is typical, the attenuation is given in decibels (* K dB vs. k*),
then convert to a ratio as follows:

<———>

An online attenuator calculator is provided at the bottom of the page.

Unbalanced Tee (T) Attenuator |
If Z |

Balanced Tee (T) Attenuator | |

Unbalanced Pi (π) Attenuator |
If Z |

Balanced Pi (π) Attenuator | |

Note: Only enter values in the yellow cells or risk overwriting formulas! |

An RF Cafe visitor wrote to say that he thought the above equations might be in error when unequal source and load termination resistances are used. The image below shows the mathematical steps that prove the equations are correct. It uses a source resistance of 50 ohms and a load resistance of 100 ohms, with an attenuation of 10 dB. Resistor values for both the "T" and ""Pi" attenuators were determined using the attenuator calculator on RF Cafe (which uses these equations).