What is a Pi attenuator?
A Pi attenuator, or Pi pad, is two shunt resistors to ground joined by one series resistor. It reduces the signal level by a fixed amount while presenting the system impedance at both ports.
FREE TOOL
Pi attenuator calculator (and T pad)
Give this Pi attenuator calculator any attenuation and impedance, and it returns the three resistors of a Pi pad or a T pad. See the nearest standard values, the loss and return loss they really give, and how much power each one dissipates.
Topology
Examples
dB
Ω
Source and load are both this value.
Resistor series
Enter input power in
W
Optional: gives the dissipation in each resistor.
Pi pad, 10 dB at 50 Ω
Shunt 96.25 Ω, series 71.15 Ω
- Shunt resistors (2)
- 96.25 Ω exact
- Series resistor
- 71.15 Ω exact
- Nearest E96 shunt
- 95.3 Ω
- Nearest E96 series
- 71.5 Ω
- Attenuation with E96 parts
- 10.07 dB
- Input return loss with E96 parts
- 53.8 dB
- Power reaching the load
- 98.5 mW
- Hottest resistor
- Input shunt, 523 mW
Equal source and load impedance, ideal resistors. Above a few hundred MHz, resistor parasitics and layout set the real loss and match.
Dissipation is for the parts listed, driven from a matched source. Derate each resistor for its pulse and temperature limits.
ShuntSeries
Pi pad parts, source to load
| Position | Exact | E96 | Error | Dissipation |
|---|---|---|---|---|
| Input shunt | 96.25 Ω | 95.3 Ω | -0.98% | 523 mW |
| Series | 71.15 Ω | 71.5 Ω | 0.49% | 327 mW |
| Output shunt | 96.25 Ω | 95.3 Ω | -0.98% | 51.7 mW |
How to calculate attenuator resistor values
Let K = 10^(dB ÷ 20). For a Pi pad, each shunt resistor is Z0 × (K + 1) ÷ (K − 1) and the series resistor is Z0 × (K² − 1) ÷ (2K). A 10 dB, 50 Ω Pi pad has K = 3.162, so the shunt arms are 96.25 Ω and the series arm is 71.15 Ω.
Attenuator formula for Pi and T pads
Both pads present Z0 at each port when the other port is terminated in Z0. These forms are for equal source and load impedance.
Pi: Rshunt = Z0 × (K + 1) ÷ (K − 1) Rseries = Z0 × (K² − 1) ÷ (2K)
- K
- voltage ratio, 10^(dB / 20)
- Z0
- system impedance in Ω
- dB
- attenuation
T: Rseries = Z0 × (K − 1) ÷ (K + 1) Rshunt = 2 × Z0 × K ÷ (K² − 1)
The Pi attenuator formula sizes two equal shunt arms and one series arm; the T attenuator formula sizes two equal series arms and one shunt arm. Once the parts are rounded, the attenuator calculator treats the pad as a two-port and computes the loss and return loss from the actual values, which is why the real numbers below are not simply the target.
Worked examples
Example 1: 10 dB, 50 Ω Pi pad with E96 parts
K = 3.162. Rshunt = 50 × (4.162 ÷ 2.162) = 96.25 Ω and Rseries = 71.15 Ω. The nearest E96 values are 95.3 Ω and 71.5 Ω, giving 10.07 dB of attenuation and 53.8 dB of input return loss.
Example 2: 6 dB, 75 Ω T pad
Rseries = 24.92 Ω and Rshunt = 100.4 Ω. Rounded to E96, that is 24.9 Ω and 100 Ω, which gives 6.01 dB and 61.6 dB of return loss.
Example 3: where 1 W goes in a 20 dB Pi pad
With 1 W from a matched source into the exact design, the input shunt (61.11 Ω) takes 818 mW, the series resistor (247.5 Ω) takes 164 mW, the output shunt takes 8.18 mW, and 10 mW reaches the load. The input shunt is the part to size.
Attenuator table: Pi and T resistor values, 1 to 20 dB at 50 Ω
Exact values. Scale every resistor by Z0 ÷ 50 for another impedance.
| Attenuation | Pi shunt | Pi series | T series | T shunt |
|---|---|---|---|---|
| 1 dB | 869.5 Ω | 5.769 Ω | 2.875 Ω | 433.3 Ω |
| 2 dB | 436.2 Ω | 11.61 Ω | 5.731 Ω | 215.2 Ω |
| 3 dB | 292.4 Ω | 17.61 Ω | 8.55 Ω | 141.9 Ω |
| 4 dB | 221 Ω | 23.85 Ω | 11.31 Ω | 104.8 Ω |
| 5 dB | 178.5 Ω | 30.4 Ω | 14.01 Ω | 82.24 Ω |
| 6 dB | 150.5 Ω | 37.35 Ω | 16.61 Ω | 66.93 Ω |
| 7 dB | 130.7 Ω | 44.8 Ω | 19.12 Ω | 55.8 Ω |
| 8 dB | 116.1 Ω | 52.84 Ω | 21.53 Ω | 47.31 Ω |
| 9 dB | 105 Ω | 61.59 Ω | 23.81 Ω | 40.59 Ω |
| 10 dB | 96.25 Ω | 71.15 Ω | 25.97 Ω | 35.14 Ω |
| 11 dB | 89.24 Ω | 81.66 Ω | 28.01 Ω | 30.62 Ω |
| 12 dB | 83.54 Ω | 93.25 Ω | 29.92 Ω | 26.81 Ω |
| 13 dB | 78.84 Ω | 106.1 Ω | 31.71 Ω | 23.57 Ω |
| 14 dB | 74.93 Ω | 120.3 Ω | 33.37 Ω | 20.78 Ω |
| 15 dB | 71.63 Ω | 136.1 Ω | 34.9 Ω | 18.36 Ω |
| 16 dB | 68.83 Ω | 153.8 Ω | 36.32 Ω | 16.26 Ω |
| 17 dB | 66.45 Ω | 173.5 Ω | 37.62 Ω | 14.41 Ω |
| 18 dB | 64.4 Ω | 195.4 Ω | 38.82 Ω | 12.79 Ω |
| 19 dB | 62.64 Ω | 220 Ω | 39.91 Ω | 11.36 Ω |
| 20 dB | 61.11 Ω | 247.5 Ω | 40.91 Ω | 10.1 Ω |
Real loss with nearest E96 parts, Pi pad at 50 Ω
Rounding the resistors moves the attenuation slightly and limits the match. These are the computed values for ideal parts of exactly those resistances.
| Target | Shunt (E96) | Series (E96) | Real loss | Return loss |
|---|---|---|---|---|
| 1 dB | 866 Ω | 5.76 Ω | 1.00 dB | 70.7 dB |
| 2 dB | 432 Ω | 11.5 Ω | 2.00 dB | 54.8 dB |
| 3 dB | 294 Ω | 17.8 Ω | 3.01 dB | 54.1 dB |
| 6 dB | 150 Ω | 37.4 Ω | 6.01 dB | 67.0 dB |
| 10 dB | 95.3 Ω | 71.5 Ω | 10.07 dB | 53.8 dB |
| 15 dB | 71.5 Ω | 137 Ω | 15.05 dB | 77.7 dB |
| 20 dB | 60.4 Ω | 249 Ω | 20.13 dB | 47.2 dB |
Building a pad that behaves
At audio and low RF, any resistor works. Above a few hundred MHz, the capacitance across a series resistor and the inductance of a shunt resistor’s via start to set the response, so keep the parts small, close to the signal line and tied to ground with short paths. Check dissipation against the resistor’s rating at the temperature it will actually see, and remember that high-voltage peaks matter separately from average power. A pad ahead of a receiver stage raises the noise figure by its loss, so put attenuation after the first gain stage in a sensitive receiver.
Glossary
- Attenuator pad
- A resistive network that reduces signal level by a fixed amount while presenting the system impedance at both ports.
- Pi pad
- Two shunt resistors to ground, joined by one series resistor.
- T pad
- Two series resistors in line, with one shunt resistor to ground between them.
- Return loss
- How far the reflected power is below the incident power, in dB. Higher is a better match.
- Insertion loss
- The drop in power to the load caused by inserting the network between matched source and load.
- Z0
- The system impedance, the value seen looking into each port with the other port terminated.
Related guides
- VSWR calculator: relate return loss to VSWR and mismatch loss.
- dBm to watts converter: turn a level in dBm into the watts each resistor sees.
- Resistor power rating calculator: size the resistor for the dissipation.
Frequently asked questions
What resistors make a 3 dB 50 Ω attenuator?
A 3 dB Pi pad uses 292.4 Ω shunt resistors with a 17.61 Ω series resistor. A 3 dB T pad uses 8.55 Ω series resistors with a 141.9 Ω shunt resistor.
What resistors make a 6 dB or 10 dB 50 Ω Pi pad attenuator?
6 dB: shunt 150.5 Ω, series 37.35 Ω. 10 dB: shunt 96.25 Ω, series 71.15 Ω. A 6 dB T pad is 16.61 Ω series with a 66.93 Ω shunt.
Should I use a Pi or a T pad?
Ideal Pi and T pads behave identically at a single impedance, so choose by the resistor values you can buy and lay out. High attenuation shows the difference: a 40 dB T pad needs a 1 Ω shunt resistor, while a 40 dB Pi pad needs a 2.5 kΩ series resistor.
Is this only a Pi pad calculator, or also a T attenuator calculator?
It covers both. Choose the T pad tab and the same attenuation and impedance give two equal series resistors and one shunt resistor, with the same standard-value rounding and power figures.
How much power does an attenuator resistor dissipate?
It depends on the resistor’s position and the attenuation, so enter the input power to get each one. In a 20 dB Pi pad with 1 W in, the input shunt takes 818 mW, the series resistor 164 mW and the output shunt 8.18 mW, with 10 mW reaching the load.
Does an attenuator improve impedance match?
Yes. A reflection from the load passes through a matched pad twice, so the return loss at its input is the load’s return loss plus twice the attenuation: a 6 dB pad turns a 6 dB return loss into 18 dB. The cost is the same loss on the signal, and a pad ahead of a receiver raises its noise figure by the same number of dB.
Can I scale a 50 Ω attenuator to another impedance?
Yes. Every resistor scales in proportion to the impedance, since the equations are linear in Z0. To convert a 50 Ω design to 75 Ω, multiply every resistor by 1.5.
How much attenuation can one pad give?
The equations have no limit, but at RF, above about 40 dB, the signal coupling around the pad through parasitic capacitance and ground currents starts to dominate. Use a cascade of smaller pads with shielding between them instead.
More free PCB tools
See all free electronics tools →
- Antenna length calculatorWavelength, half-wave dipole and quarter-wave monopole lengths for any frequency, with an end-effect factor.
- Free-space path loss calculatorFree-space path loss between two antennas from distance and frequency, in dB, with the distance for a given loss.
- Frequency to wavelength calculatorWavelength from frequency and back, in free space or in a cable or PCB with a velocity factor or dielectric constant.
- VSWR calculatorConvert between VSWR, return loss, reflection coefficient and mismatch loss, or compute them from a load impedance.
- Cascaded noise figure calculatorTotal noise figure and gain of up to six cascaded stages with the Friis formula, noise temperature and receiver sensitivity.
- dBm to watts converterConvert dBm, dBW, watts and milliwatts, plus the RMS and peak-to-peak voltage in 50 Ω or any impedance.
Sources
Design the whole board, not one number
ProtoFlow is free AI PCB design software: describe a circuit and get a schematic with real parts, PCB layout with an autorouter, SPICE simulation and Gerber files. Native KiCad, Altium and EAGLE import and export. Free on macOS, Windows and Linux.
Get for Mac
Free to start. No card required.
