Pi-Pad Shunt Resistor
R1 = Z · (K + 1)/(K − 1)
Quick answer
This calculator solves R1 = R3 = Z × (K + 1)/(K − 1) for Shunt Resistor. With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, the result is 1.259 kΩ. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The two equal shunt resistors of a symmetric Pi-pad attenuator connect each port to ground. This formula gives each shunt arm. As attenuation increases the shunt resistors fall toward Z, while the series resistor rises—the opposite trend to the T-pad and a useful way to keep resistor values in a practical range.
Variables
- R1 — Each shunt resistor to ground (Ω)
- Z — Characteristic impedance (Ω)
- dB — Desired attenuation; K = 10^(dB/20)
Practical Notes
Combine with the Pi-pad series resistor R2 = Z(K²−1)/(2K). For low attenuation the shunt arms become large (near open) and the pad approaches a through connection.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| R1 | Shunt 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: R1 = R3 = Z × (K + 1)/(K − 1)
- 3. Substitute: Z = 1.03 kΩ, dB = 20 dB
- 4. Result: Shunt Resistor = 1.259 kΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 1.2 kΩ | 4.7% |
| E24 | 1.3 kΩ | 3.3% |
Worked examples
Minimum range
Given: Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB
Result: Shunt Resistor = 127.4 Ω
Low range
Given: Characteristic Impedance 22 Ω, Attenuation 3 dB
Result: Shunt Resistor = 128.7 Ω
Typical
Given: Characteristic Impedance 1.03 kΩ, Attenuation 20 dB
Result: Shunt Resistor = 1.259 kΩ
High range
Given: Characteristic Impedance 10.3 kΩ, Attenuation 60 dB
Result: Shunt Resistor = 10.32 kΩ
Maximum range
Given: Characteristic Impedance 103 kΩ, Attenuation 600 dB
Result: Shunt Resistor = 103 kΩ
Solving for each variable
Solve for Shunt Resistor
Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB → 127.4 Ω
Solve for Characteristic Impedance
Shunt Resistor 1 Ω, Attenuation 0.3 dB → 17.27 mΩ
How Shunt Resistor changes with Characteristic Impedance
| Characteristic Impedance (input) | Shunt Resistor (result) |
|---|---|
| 0.227 kΩ | 0.23 kΩ |
| 0.5675 kΩ | 0.5749 kΩ |
| 1.135 kΩ | 1.15 kΩ |
| 1.703 kΩ | 1.725 kΩ |
| 2.27 kΩ | 2.3 kΩ |
| 3.405 kΩ | 3.449 kΩ |
| 4.54 kΩ | 4.599 kΩ |
| 9.08 kΩ | 9.198 kΩ |
| 15.89 kΩ | 16.1 kΩ |
| 22.7 kΩ | 23 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 1259000 |
| Ω | 1259 |
| kΩ | 1.259 |
| MΩ | 0.001259 |
Embed this calculator
Paste this into any page. It keeps working when this page updates, and credits the source.
<iframe src="https://vbatpower.com/embed/pi-pad-shunt-resistor/" width="100%" height="460" style="border:1px solid #1f2a37;border-radius:12px" loading="lazy" title="Pi-Pad Shunt Resistor"></iframe>
<p><a href="https://vbatpower.com/formulas/pi-pad-shunt-resistor/">Pi-Pad Shunt Resistor</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Pi-Pad Shunt Resistor?
Use R1 = R3 = Z × (K + 1)/(K − 1). With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, Shunt Resistor works out to 1.259 kΩ.
What is the formula for Pi-Pad Shunt Resistor?
The formula is R1 = R3 = Z × (K + 1)/(K − 1). The two equal shunt resistors of a symmetric Pi-pad attenuator connect each port to ground.
How do you find Characteristic Impedance when you know the other values?
Rearrange for Characteristic Impedance: with Shunt Resistor 1 Ω, Attenuation 0.3 dB, Characteristic Impedance is 17.27 mΩ.
What units does Pi-Pad Shunt Resistor use?
Shunt 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
All Attenuators & Pads formulas →Need more features?
Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.
Try the App