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Fixed Pi and Tee Attenuators - Equations

See the online attenuator calculator here.

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 Z1/Z2. Attenuators with equal terminations have a minimum attenuation of 0 dB. Unequal terminations place a lower limit on the attenuation.

K = power in / power out,
      or in decibels = 10 * log (K) dB


Attenuator equation - RF Cafe, or in decibels KMIN  = 10 * log (Kmin) dB

Unbalanced Tee (T) Attenuator Attenuator equation - RF Cafe
If Z1 = Z2, then:

Attenuator equation - RF Cafe

Unbalanced T attenuator equation
Balanced Tee (T) Attenuator
 Balanced T attenuator equation - RF Cafe
Unbalanced Pi (p) Attenuator Attenuator equation - RF Cafe
If Z1 = Z2, then:

Attenuator equation - RF Cafe

 Unbalanced Pi attenuator equation - RF Cafe
Balanced Pi (p) Attenuator
 Balanced Pi attenuator equation - RF Cafe
 
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).

Attenuators with unequal terminations - RF Cafe

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