Bridged-T Shunt Resistor
Rs = Z / (K − 1)
Quick answer
This calculator solves Rs = Z / (K − 1) for Shunt Resistor. With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, the result is 114.4 Ω. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The shunt resistor of a bridged-T attenuator connects the centre of the two Z-valued series arms to ground. Together with the bridge resistor it sets the attenuation while keeping the input and output impedance equal to Z. This formula gives that shunt value; it falls as attenuation increases.
Variables
- Rs — Shunt resistor to ground (Ω)
- Z — Characteristic impedance (Ω)
- dB — Desired attenuation; K = 10^(dB/20)
Practical Notes
The companion bridge resistor is Rb = Z(K−1); their product equals Z². The two series arms stay fixed at Z, which is what makes the bridged-T a constant-impedance design.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Rs | 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: Rs = Z / (K − 1)
- 3. Substitute: Z = 1.03 kΩ, dB = 20 dB
- 4. Result: Shunt Resistor = 114.4 Ω
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 120 Ω | 4.9% |
| E24 | 110 Ω | 3.9% |
Worked examples
Minimum range
Given: Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB
Result: Shunt Resistor = 62.6 Ω
Low range
Given: Characteristic Impedance 22 Ω, Attenuation 3 dB
Result: Shunt Resistor = 53.33 Ω
Typical
Given: Characteristic Impedance 1.03 kΩ, Attenuation 20 dB
Result: Shunt Resistor = 114.4 Ω
High range
Given: Characteristic Impedance 10.3 kΩ, Attenuation 60 dB
Result: Shunt Resistor = 10.31 Ω
Maximum range
Given: Characteristic Impedance 103 kΩ, Attenuation 600 dB
Result: Shunt Resistor = 1.03 × 10⁻²² mΩ
Solving for each variable
Solve for Shunt Resistor
Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB → 62.6 Ω
Solve for Characteristic Impedance
Shunt Resistor 1 Ω, Attenuation 0.3 dB → 35.14 mΩ
How Shunt Resistor changes with Characteristic Impedance
| Characteristic Impedance (input) | Shunt Resistor (result) |
|---|---|
| 103 Ω | 11.44 Ω |
| 0.2575 kΩ | 28.61 Ω |
| 0.515 kΩ | 57.22 Ω |
| 0.7725 kΩ | 85.83 Ω |
| 1.03 kΩ | 114.4 Ω |
| 1.545 kΩ | 0.1717 kΩ |
| 2.06 kΩ | 0.2289 kΩ |
| 4.12 kΩ | 0.4578 kΩ |
| 7.21 kΩ | 0.8011 kΩ |
| 10.3 kΩ | 1.144 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 114400 |
| Ω | 114.4 |
| kΩ | 0.1144 |
| MΩ | 0.0001144 |
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<p><a href="https://vbatpower.com/formulas/bridged-t-shunt-resistor/">Bridged-T Shunt Resistor</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Bridged-T Shunt Resistor?
Use Rs = Z / (K − 1). With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, Shunt Resistor works out to 114.4 Ω.
What is the formula for Bridged-T Shunt Resistor?
The formula is Rs = Z / (K − 1). The shunt resistor of a bridged-T attenuator connects the centre of the two Z-valued series arms 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 35.14 mΩ.
What units does Bridged-T 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
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