Resistive Attenuator (Pad) Calculator
Enter the attenuation in dB and the impedance (the same for source and load) to get the resistor values of a T-pad and a pi-pad.
Which circuits are covered
This calculator covers only symmetric resistive attenuators where the source impedance and the load impedance are equal (Z₀). It shows the T-pad and the pi-pad together. Both are designed so that the impedance seen from the input and from the output is Z₀. The impedance is treated as pure resistance.
Not covered: L-pads (the minimum-loss pad for different input and output impedances), bridged-T pads, balanced pads (H and O types), cases where the source and load impedances differ, and complex impedances (which change with frequency).
Formulas
Let K = 10^(attenuation ÷ 20) (the voltage ratio). Because the source and load impedances are equal, the power ratio in dB is the same number (the power ratio is K²).
| Circuit | Resistor | Formula |
|---|---|---|
| T pad | Series R₁ (two, equal) | Z₀ × (K − 1) ÷ (K + 1) |
| T pad | Shunt R₂ (middle) | 2 × Z₀ × K ÷ (K² − 1) |
| Pi pad | Shunt R₃ (two, equal) | Z₀ × (K + 1) ÷ (K − 1) |
| Pi pad | Series R₄ (middle) | Z₀ × (K² − 1) ÷ (2 × K) |
These match the formulas in an explanatory reference (Wikipedia, "Attenuator (electronics)"), which writes them with A = 10^(−Loss/20), if you set K = 1 ÷ A. The book that the reference cites for the pads was not checked.
K is found with floating-point arithmetic and then turned into a fraction with 15 significant digits; the resistor values are then calculated exactly from that fraction (when the attenuation is a multiple of 20 dB, K is a power of 10 and is exact). The attenuation must be from 0.01 to 100 dB, because for small attenuations K − 1 becomes tiny and digits are lost. Values are shown with 7 significant digits. The values are not rounded to standard resistor series (such as E24). In practice you pick resistors with nearby values, and the attenuation and impedance then drift slightly from the design.
Example
For Z₀ = 50 Ω and 10 dB (K ≈ 3.1623):
| Resistor | Value |
|---|---|
| T pad R₁ (series) | about 25.97 Ω |
| T pad R₂ (shunt) | about 35.14 Ω |
| Pi pad R₃ (shunt) | about 96.25 Ω |
| Pi pad R₄ (series) | about 71.15 Ω |
Notes
- These are theoretical values for pure resistance. Tolerance, power rating, temperature and frequency behavior are not considered, and the power rating is not calculated.
- Safety and operation when connected to an amplifier, speaker or power supply are not guaranteed. Follow the equipment manual and the manufacturer's instructions.
- Electrical safety: there is a risk of electric shock, fire and short circuits. Have a qualified person do any work that involves high voltage, large currents, mains power or amplifier outputs.
- To convert between a ratio and dB, see the Decibel Calculator. For the relation between voltage, current, power and resistance, see the Ohm's Law Calculator. To combine speaker impedances, see the Speaker Impedance Calculator.
Frequently asked questions
Should I use a T pad or a pi pad?
Both are designs for the same attenuation and the same impedance. Choose the one whose resistor values are easier to make from the parts you have.
Are the resistors rounded to standard values?
No. The calculated values are shown as they are. In practice you pick resistors with nearby values, which moves the attenuation and the impedance slightly from the design.
Is the attenuation a voltage ratio or a power ratio?
Because the source and load impedances are equal, the dB value is the same. The voltage ratio is K and the power ratio is K².