Pi Attenuator Calculator finds the two shunt resistors and the series resistor for a chosen loss in dB. It also checks a pad you already built and shows the heat in every resistor.
Use the same impedance on both sides for a standard pad, or two different ones for a matching pad.
Power and Standard Values
Input power sets the heat in each resistor. The series picks the nearest values you can buy.
Pi Pad Circuit
Pi Attenuator Table
| Attenuation | Each Shunt | Series |
|---|---|---|
| 1 dB | 869.5 Ω | 5.769 Ω |
| 2 dB | 436.2 Ω | 11.61 Ω |
| 3 dB | 292.4 Ω | 17.61 Ω |
| 4 dB | 221.0 Ω | 23.85 Ω |
| 5 dB | 178.5 Ω | 30.40 Ω |
| 6 dB | 150.5 Ω | 37.35 Ω |
| 8 dB | 116.1 Ω | 52.84 Ω |
| 10 dB | 96.25 Ω | 71.15 Ω |
| 12 dB | 83.54 Ω | 93.25 Ω |
| 15 dB | 71.63 Ω | 136.1 Ω |
| 20 dB | 61.11 Ω | 247.5 Ω |
| 30 dB | 53.27 Ω | 789.8 Ω |
| 40 dB | 51.01 Ω | 2.500 kΩ |
Designing a Pad With the Pi Attenuator Calculator
The Pi Attenuator Calculator takes a loss in dB and the impedance on each side of the pad. It returns the three resistors that give that loss while keeping both ports matched. With its default entries, a 10 dB pad for 50 Ω needs two 96.25 Ω shunts and a 71.15 Ω series resistor.
The circuit has the shape of the Greek letter pi. The series resistor R2 sits in the signal path. R1 runs from the input end of R2 to ground and R3 runs from the output end to ground. Open Pi Pad Circuit under the results to see the three values placed on the drawing.
Check a Built Pad works in the other direction. Enter three resistors you already have and the Pi Attenuator Calculator returns the real attenuation, the input impedance and the match. Both modes also show the heat in each resistor at the input power you set.
Pi Attenuator Formula
When source and load impedance are equal, the two shunts are equal too. The Pi Attenuator Calculator starts by turning the attenuation into a voltage ratio K, which the other two equations reuse.
A is the attenuation in dB. For 10 dB, K is 3.162. Each shunt resistor is the system impedance multiplied by a ratio of K plus one over K minus one. A small loss therefore means a large shunt.
The series resistor uses the same K. It grows quickly with attenuation, while the shunts fall toward the system impedance. At 30 dB it is nearly 800 Ω in a 50 Ω system.
For 10 dB at 50 Ω that gives 50 × 4.162 ÷ 2.162, or 96.25 Ω, for each shunt. The series resistor is 25 × 9 ÷ 3.162, or 71.15 Ω. These are the standard equal-impedance equations, and RF Cafe's attenuator reference lists them with the unequal-impedance forms.
Pi Attenuator Table for 50 Ω
The table gives the exact resistors for common steps, with the share of power and voltage that reaches the load. The Pi Attenuator Calculator builds the same table for whatever impedance you enter, under Pi Attenuator Table.
| Attenuation | Each Shunt | Series | Power Out | Voltage Out |
|---|---|---|---|---|
| 1 dB | 869.5 Ω | 5.769 Ω | 79.4% | 89.1% |
| 2 dB | 436.2 Ω | 11.61 Ω | 63.1% | 79.4% |
| 3 dB | 292.4 Ω | 17.61 Ω | 50.1% | 70.8% |
| 6 dB | 150.5 Ω | 37.35 Ω | 25.1% | 50.1% |
| 10 dB | 96.25 Ω | 71.15 Ω | 10.0% | 31.6% |
| 20 dB | 61.11 Ω | 247.5 Ω | 1.00% | 10.0% |
| 30 dB | 53.27 Ω | 789.8 Ω | 0.10% | 3.2% |
So a 10 dB attenuator passes a tenth of the power, a 20 dB pad passes a hundredth and a 30 dB pad passes a thousandth. A 1 dB pad still passes 79% of the power. A 3 dB pad halves the power and a 6 dB pad halves the voltage.
Resistor values scale directly with impedance. For 75 Ω, multiply the table by 1.5, which makes a 10 dB pad 144.4 Ω and 106.7 Ω. For a 600 Ω audio line, multiply by 12 to get 1,155 Ω shunts and an 853.8 Ω series resistor.
Standard Resistor Values
Exact values such as 96.25 Ω are not on the shelf. The first card in the Pi Attenuator Calculator picks the nearest parts in the series you choose and reports what the pad then does. The difference between series is larger than most people expect.
| Series | Shunt, Series, Shunt | Actual Loss | Return Loss |
|---|---|---|---|
| E96, 1% parts | 95.3, 71.5, 95.3 Ω | 10.07 dB | 53.8 dB |
| E24, 5% parts | 100, 68, 100 Ω | 9.63 dB | 49.6 dB |
| E12, 10% parts | 100, 68, 100 Ω | 9.63 dB | 49.6 dB |
E96 parts land within 0.07 dB of the target. E24 and E12 parts fall 0.37 dB short, though the match stays excellent. These figures use the nominal values only. The tolerance of each part adds its own spread on top.
Power in Each Resistor
A pad turns most of the input power into heat, and the three resistors do not share it evenly. Set Input Power under Power and Standard Values and the second card shows the heat in each part. With 1 W into the 10 dB pad, the input shunt takes 519.5 mW, the series resistor 328.6 mW and the output shunt 51.95 mW.
| Attenuation | Input Shunt | Series | Output Shunt |
|---|---|---|---|
| 3 dB | 17.1% | 24.2% | 8.6% |
| 6 dB | 33.2% | 33.3% | 8.4% |
| 10 dB | 51.9% | 32.9% | 5.2% |
| 20 dB | 81.8% | 16.4% | 0.8% |
| 30 dB | 93.9% | 5.9% | 0.1% |
The percentages are shares of the input power for a 50 Ω pad. Below 6 dB the series resistor runs hottest. Above it the input shunt takes over, and in a 20 dB pad it absorbs 82% of everything fed in. A 10 W signal into that pad puts 8.18 W into one resistor.
That is why a power attenuator is rated by its input side. If the signal can arrive from either port, size both shunts for the input figure. To turn a level in dBm into watts first, use the RF Power Conversion Calculator.
Matching 50 Ω to 75 Ω
Enter different source and load impedances and the Pi Attenuator Calculator designs a matching pad. The two shunts are no longer equal. A 10 dB pad from 50 Ω to 75 Ω needs a 77.11 Ω input shunt, an 87.14 Ω series resistor and a 207.4 Ω output shunt.
Resistive matching has a floor. Between 50 Ω and 75 Ω the loss cannot go below 5.72 dB, and the tool rejects anything lower. At that minimum the output shunt disappears. The pad becomes an 86.6 Ω shunt with a 43.3 Ω series resistor, the same values Mini-Circuits gives for its minimum loss pad.
The floor rises as the impedances move apart. It is 11.44 dB between 75 Ω and 300 Ω and 16.63 dB between 50 Ω and 600 Ω. When that much loss is not acceptable, a reactive network does the job without it, and the RF Impedance Matching Calculator covers that route.
Return Loss Through a Pad
A pad hides a bad load from the source. The reflected signal passes through the pad twice, so the return loss seen at the input is at least twice the attenuation. Urgent Communications describes the same rule for coaxial pads.
The last card in the Pi Attenuator Calculator gives that worst case. With a 10 dB pad the source sees 20 dB return loss, a VSWR of 1.22, even when the load is open or shorted. A 3 dB pad guarantees only 6 dB, a VSWR of 3.0. A 6 dB pad guarantees 12 dB, or 1.67. The VSWR to Return Loss Calculator converts between the two figures.
Checking a Built Pad
Switch What to Calculate to Check a Built Pad and enter the three resistors. With 150 Ω, 39 Ω and 150 Ω in a 50 Ω system, the Pi Attenuator Calculator reports 6.14 dB of attenuation and an input impedance of 50.66 Ω. That is a 6 dB pad made from common E12 parts.
The same mode shows what happens when a pad is used at the wrong impedance. Change the source and load to 75 Ω with the same three resistors and both the loss and the match move. The table then adds a row for your pad beside the exact designs.
Pi Attenuator FAQ
What is the difference between a pi and a T attenuator?
Both give the same loss and the same match. A pi pad uses two shunts and one series resistor. A T pad uses two series resistors and one shunt. The resistor values are what differ.
A 10 dB pi pad at 50 Ω needs 96.25 Ω and 71.15 Ω. At 30 dB the pi series resistor climbs to 789.8 Ω while its shunts sit near 53 Ω. Pick the form whose values are easier to buy and to lay out. The T-Pad Attenuator Calculator gives the other set.
How do I make a differential pi attenuator?
Start from the unbalanced values in the Pi Attenuator Calculator. Split the series resistor in two and put one half in each signal leg. The shunts then connect across the pair in place of going to ground. A 10 dB pad at 50 Ω becomes two 35.58 Ω series resistors with 96.25 Ω across each end.
This balanced form is often called an O pad. The loss and the impedance stay the same as the unbalanced design. The Balanced Attenuator Calculator is the tool for balanced pads.