Note that before trying to understand the T-type attenuator circuit it may be helpful to read Efficient Power Transfer (links to http://www.mw0llo.com/efficient-power-transfer.aspx).

In the circuit diagram below the components R2, R3 and R4 form what is known as a "T-type attenuator" inserted between a given sinusoidal voltage generating source of internal resistance R1 and a load resistance R5.

The T-Type Attenuator

The same circuit diagram is repeated below with some additional labels to assist with the calculations:

The T-Type Attenuator

For R4 and R5 in series the combined resistance R4,5 is given by:

MathML formulaFormula ImageStraight text formula
R 4,5 = R 4 + R 5 t-type-attenuator-formula-01 R4,5 = R4 + R5

For R3 in parallel with the series combination of R4 and R5 the combined resistance R3,4,5 is given by:

MathML formulaFormula ImageStraight text formula
1 R 3,4,5 = 1 R 4,5 + 1 R 3 = 1 R 4 + R 5 + 1 R 3 t-type-attenuator-formula-02 1 / R3,4,5 = ( 1 / R4,5 ) + (1 / R3 ) = ( 1 / ( R4 + R5 ) ) + ( 1 / R3 )

Simplified, the above gives:

MathML formulaFormula ImageStraight text formula
R 3,4,5 = R 3 R 4 + R 5 R 3 + R 4 + R 5 t-type-attenuator-formula-02 R3,4,5 = ( R3 ( R4 + R5 ) ) / ( R3 + R4 + R5 )
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