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 R_{2}, R_{3} and R_{4} form what is known as a "T-type attenuator" inserted between a given sinusoidal voltage generating source of internal resistance R_{1} and a load resistance R_{5}.

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

For R_{4} and R_{5} in series the combined resistance R_{4,5} is given by:

MathML formula | Formula Image | Straight text formula |
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${R}_{\mathrm{4,5}}={R}_{4}+{R}_{5}$ | R_{4,5} = R_{4} + R_{5} |

For R_{3} in parallel with the series combination of R_{4} and R_{5} the combined resistance R_{3,4,5} is given by:

MathML formula | Formula Image | Straight text formula |
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$\frac{1}{{R}_{\mathrm{3,4,5}}}=\frac{1}{{R}_{\mathrm{4,5}}}+\frac{1}{{R}_{3}}=\frac{1}{{R}_{4}+{R}_{5}}+\frac{1}{{R}_{3}}$ | 1 / R_{3,4,5} = ( 1 / R_{4,5} ) + (1 / R_{3} ) = ( 1 / ( R_{4} + R_{5} ) ) + ( 1 / R_{3} ) |

Simplified, the above gives:

MathML formula | Formula Image | Straight text formula |
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${R}_{\mathrm{3,4,5}}=\frac{{R}_{3}\left({R}_{4}+{R}_{5}\right)}{{R}_{3}+{R}_{4}+{R}_{5}}$ | R_{3,4,5} = ( R_{3} ( R_{4} + R_{5} ) ) / ( R_{3} + R_{4} + R_{5} ) |