What a resistive attenuator does
An attenuator, or "pad", drops a signal by a fixed number of decibels while keeping the impedance seen at both ports equal to the system impedance — 50 Ω for most RF work, 75 Ω for video and cable, 600 Ω for legacy audio lines. Matching matters: a plain series resistor would attenuate, but it would also spoil the match and cause reflections. The Pi and T networks use three resistors arranged so that the input looks like z when the output is terminated in z, and vice versa.
Pi and T formulas
Let K = 10dB/20 be the voltage attenuation ratio and z the matched impedance. For the Pi pad (two shunt resistors R1, R3 and a series R2):
R1 = R3 = z·(K+1)/(K−1) R2 = z·(K²−1)/(2K)
For the T pad (two series resistors R1, R3 and a shunt R2):
R1 = R3 = z·(K−1)/(K+1) R2 = 2z·K/(K²−1)
Worked example: 3 dB at 50 Ω
K = 103/20 = 1.4125. The Pi pad wants R1 = R3 = 50·(2.4125/0.4125) = 292.4 Ω and R2 = 50·(0.9953/2.8251) = 17.6 Ω. Snap those to the E24 series and you get 300 Ω and 18 Ω, which this calculator then feeds back through the actual network equations: the real attenuation lands at about 3.0 dB with an input impedance near 50.6 Ω — close enough for most work, and exactly the kind of check the "nearest standard values" section gives you for free.
Common pads at 50 Ω
| dB | Pi shunt | Pi series | T series | T shunt |
|---|---|---|---|---|
| 1 dB | 870 Ω | 5.8 Ω | 2.9 Ω | 433 Ω |
| 2 dB | 436 Ω | 11.6 Ω | 5.7 Ω | 215 Ω |
| 3 dB | 292 Ω | 17.6 Ω | 8.5 Ω | 142 Ω |
| 6 dB | 150 Ω | 37.4 Ω | 16.6 Ω | 66.9 Ω |
| 10 dB | 96.2 Ω | 71.2 Ω | 26.0 Ω | 35.1 Ω |
| 20 dB | 61.1 Ω | 247.5 Ω | 40.9 Ω | 10.1 Ω |
Practical notes
The resistor that dissipates the most power is the one nearest the source — in a Pi pad that is the input shunt, in a T pad the first series resistor. For a 1 W signal into a 10 dB pad, most of that watt is burned in the first element, so size its wattage accordingly. Pads also cascade cleanly: put a 3 dB and a 6 dB pad in series and you have 9 dB, because decibels add.
Related tools: the decibel calculator converts between dB and power or voltage ratios, and the antenna length calculator covers the other end of an RF bench.