An attenuator lowers the level of a signal by a precise amount without distorting it, while presenting the correct impedance to both the source and the load. The pi (π) pad is the most common resistive design: one resistor in series (R2) between two resistors to ground (R1 at the input, R3 at the output), drawn like the Greek letter π.
Attenuators are everywhere in RF and audio work: protecting a spectrum analyser or receiver input from a strong signal, setting the level into an ADC, improving the match between stages (a 6 dB pad turns a terrible mismatch into a modest one, because reflections pass through it twice), and isolating an oscillator from its load. Being purely resistive, they work from DC up to the frequency where parasitic inductance and capacitance take over.
For equal impedances – 50 Ω to 50 Ω, or 600 Ω to 600 Ω – the pad is symmetrical. For unequal impedances, such as 75 Ω to 50 Ω, the same network also transforms the impedance, but only if the attenuation is at least a minimum value (5.72 dB for 75 → 50 Ω); below that the formulas would demand a negative resistance.
How to use the Pi Attenuator Calculator
- Circuit type
- Attenuation
- Characteristic impedance (Z₀)
- Source impedance (Z_S)
- Load impedance (Z_L)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose equal or unequal impedances, enter the attenuation in dB and the impedances. The calculator converts the attenuation to the voltage factor K and applies the π-pad design equations for R1, R2 and R3.
Worked example
A 10 dB pad for a 50 Ω system has K = 10^(10/20) = 3.1623. R1 = R3 = 50 × 4.1623 ÷ 2.1623 = 96.25 Ω and R2 = 50 × (10 − 1) ÷ 6.3246 = 71.15 Ω. The output voltage is 31.6% and the output power 10% of the input. A 40 dB pad from 75 Ω to 50 Ω needs R1 = 76.9 Ω, R2 = 3,062 Ω and R3 = 50.8 Ω.
50 Ω pi attenuator values
| Attenuation | R1 = R3 | R2 |
|---|---|---|
| 3 dB | 292.4 Ω | 17.6 Ω |
| 6 dB | 150.5 Ω | 37.4 Ω |
| 10 dB | 96.2 Ω | 71.2 Ω |
| 20 dB | 61.1 Ω | 247.5 Ω |
| 30 dB | 53.3 Ω | 789.8 Ω |
Inputs explained
| Field | What to enter |
|---|---|
| Circuit type | Choose one: Equal impedances (Z_S = Z_L), Unequal impedances |
| Attenuation | In dB |
| Characteristic impedance (Z₀) | In Ω |
| Source impedance (Z_S) | In Ω |
| Load impedance (Z_L) | In Ω |
What each result means
- Voltage factor K = 10^(A/20) = 10^([Attenuation]÷20)
- Output ÷ input voltage = 1÷[Voltage factor K = 10^(A÷20)]
- Output ÷ input power = 1÷[Voltage factor K = 10^(A÷20)]^2
Formula
K = 10^(A/20) · Equal: R1 = R3 = Z₀(K + 1) ÷ (K − 1), R2 = Z₀(K² − 1) ÷ (2K) · Unequal: R1 = Z_S(K² − 1) ÷ (K² − 2K√(Z_S/Z_L) + 1), R2 = ½√(Z_S Z_L)(K² − 1) ÷ K, R3 = Z_L(K² − 1) ÷ (K² − 2K√(Z_L/Z_S) + 1)
Worked example
Inputs — Circuit type: Equal impedances (Z_S = Z_L); Attenuation: 10 dB; Characteristic impedance (Z₀): 50 Ω.
Results — Voltage factor K = 10^(A/20) = 3.16228; R1 – shunt resistor at the input = 96.24753 Ω; R2 – series resistor = 71.15125 Ω; R3 – shunt resistor at the output = 96.24753 Ω; Output ÷ input voltage = 0.316228; Output ÷ input power = 0.1; Minimum attenuation for these impedances = 0 dB; Check = Realisable with positive resistors.
Key terms
- Attenuation (dB)
- Ratio of input to output level: 20 log₁₀(V_in ÷ V_out).
- π-pad
- Attenuator with two shunt resistors and one series resistor.
- Characteristic impedance
- System impedance, typically 50 Ω (RF), 75 Ω (video) or 600 Ω (audio).
- Minimum-loss pad
- The unequal-impedance pad with the smallest possible attenuation.
Frequently asked questions
What are the resistor values for a 10 dB 50 Ω pi attenuator?
R1 = R3 = 96.25 Ω and R2 = 71.15 Ω (use 97.6 Ω and 71.5 Ω from the E96 series).
What is the difference between pi and T attenuators?
Both give the same attenuation; a π-pad has two shunt resistors and one series resistor, a T-pad two series and one shunt. Choose whichever gives more practical values.
Why is there a minimum attenuation for unequal impedances?
Matching two different impedances with resistors always costs some loss: 5.72 dB for 75 Ω to 50 Ω.
How much power can an attenuator handle?
It depends on the resistors' ratings – the input shunt resistor and the series resistor take most of the power in high-attenuation pads.
How do I build a 40 dB attenuator?
Two 20 dB pads in series usually perform better than one, because extreme resistor ratios suffer from parasitics.
Does a pi attenuator work at audio frequencies?
Yes – it is purely resistive, so it works from DC to well into the RF range.