The T-Type Attenuator

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 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 R_4,5 is given by:

MathML formula	Formula Image	Straight text formula
$R_{4,5} = R_{4} + R_{5}$		R_4,5 = R₄ + R₅

For R₃ in parallel with the series combination of R₄ and R₅ the combined resistance R_3,4,5 is given by:

MathML formula	Formula Image	Straight text formula
$\frac{1}{R_{3,4,5}} = \frac{1}{R_{4,5}} + \frac{1}{R_{3}} = \frac{1}{R_{4} + R_{5}} + \frac{1}{R_{3}}$		1 / R_3,4,5 = ( 1 / R_4,5 ) + (1 / R₃ ) = ( 1 / ( R₄ + R₅ ) ) + ( 1 / R₃ )

Simplified, the above gives:

MathML formula	Formula Image	Straight text formula
$R_{3,4,5} = \frac{R_{3} (R_{4} + R_{5})}{R_{3} + R_{4} + R_{5}}$		R_3,4,5 = ( R₃ ( R₄ + R₅ ) ) / ( R₃ + R₄ + R₅ )