Pi-Pad Series Resistor
R2 = Z · (K² − 1) / (2K)
Quick answer
This calculator solves R2 = Z × (K² − 1) / (2K) for Series Resistor. With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, the result is 5.099 kΩ. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A Pi-pad attenuator uses two shunt resistors and one series resistor arranged like the Greek letter π. This formula gives the single series (bridging) resistor. The Pi topology is the dual of the T-pad and is often preferred when the bridging resistor value is more convenient or when matching to a transmission line whose impedance suits the shunt-heavy structure.
Variables
- R2 — Series (bridging) resistor (Ω)
- Z — Characteristic impedance (Ω)
- dB — Desired attenuation; K = 10^(dB/20)
Practical Notes
Pair with the Pi-pad shunt resistors R1 = R3 = Z(K+1)/(K−1). T and Pi pads give identical attenuation and matching; choose whichever yields nicer resistor values.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| R2 | Series Resistor | Ω | mΩ, Ω, kΩ, MΩ |
| Z | Characteristic Impedance | Ω | mΩ, Ω, kΩ, MΩ |
| dB | Attenuation | dB | dB |
Step by step
- 1. What you know: Characteristic Impedance 1.03 kΩ, Attenuation 20 dB
- 2. The relation: R2 = Z × (K² − 1) / (2K)
- 3. Substitute: Z = 1.03 kΩ, dB = 20 dB
- 4. Result: Series Resistor = 5.099 kΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 4.7 kΩ | 7.8% |
| E24 | 5.1 kΩ | 0.029% |
Worked examples
Minimum range
Given: Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB
Result: Series Resistor = 76 mΩ
Low range
Given: Characteristic Impedance 22 Ω, Attenuation 3 dB
Result: Series Resistor = 7.751 Ω
Typical
Given: Characteristic Impedance 1.03 kΩ, Attenuation 20 dB
Result: Series Resistor = 5.099 kΩ
High range
Given: Characteristic Impedance 10.3 kΩ, Attenuation 60 dB
Result: Series Resistor = 5.15 MΩ
Maximum range
Given: Characteristic Impedance 103 Ω, Attenuation 0.6 dB
Result: Series Resistor = 7.121 Ω
Solving for each variable
Solve for Series Resistor
Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB → 76 mΩ
Solve for Characteristic Impedance
Series Resistor 1 Ω, Attenuation 0.3 dB → 28.95 Ω
How Series Resistor changes with Characteristic Impedance
| Characteristic Impedance (input) | Series Resistor (result) |
|---|---|
| 103 Ω | 0.5099 kΩ |
| 0.2575 kΩ | 1.275 kΩ |
| 0.515 kΩ | 2.549 kΩ |
| 0.7725 kΩ | 3.824 kΩ |
| 1.03 kΩ | 5.099 kΩ |
| 1.545 kΩ | 7.648 kΩ |
| 2.06 kΩ | 10.2 kΩ |
| 4.12 kΩ | 20.39 kΩ |
| 7.21 kΩ | 35.69 kΩ |
| 10.3 kΩ | 50.99 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 5099000 |
| Ω | 5099 |
| kΩ | 5.099 |
| MΩ | 0.005099 |
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<p><a href="https://vbatpower.com/formulas/pi-pad-series-resistor/">Pi-Pad Series Resistor</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Pi-Pad Series Resistor?
Use R2 = Z × (K² − 1) / (2K). With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, Series Resistor works out to 5.099 kΩ.
What is the formula for Pi-Pad Series Resistor?
The formula is R2 = Z × (K² − 1) / (2K). A Pi-pad attenuator uses two shunt resistors and one series resistor arranged like the Greek letter π.
How do you find Characteristic Impedance when you know the other values?
Rearrange for Characteristic Impedance: with Series Resistor 1 Ω, Attenuation 0.3 dB, Characteristic Impedance is 28.95 Ω.
What units does Pi-Pad Series Resistor use?
Series Resistor is shown in mΩ, Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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