T-Pad Shunt Resistor
R3 = 2 · Z · K / (K² − 1)
Quick answer
This calculator solves R3 = 2 × Z × K / (K² − 1) for Shunt Resistor. With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, the result is 0.2081 kΩ. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The shunt (middle) resistor of a symmetric T-pad attenuator connects the junction of the two series arms to ground. Together with the series arms it sets both the attenuation and the matched impedance. As attenuation rises (larger K), the shunt resistor falls, diverting more signal to ground.
Variables
- R3 — Shunt resistor to ground (Ω)
- Z — Characteristic impedance (Ω)
- dB — Desired attenuation; K = 10^(dB/20)
Practical Notes
Use together with the T-pad series arms R1 = R2 = Z(K−1)/(K+1). For very high attenuation the shunt resistor becomes small and the series arms approach Z.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| R3 | 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: R3 = 2 × Z × K / (K² − 1)
- 3. Substitute: Z = 1.03 kΩ, dB = 20 dB
- 4. Result: Shunt Resistor = 0.2081 kΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 0.22 kΩ | 5.7% |
| E24 | 0.2 kΩ | 3.9% |
Worked examples
Minimum range
Given: Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB
Result: Shunt Resistor = 63.68 Ω
Low range
Given: Characteristic Impedance 22 Ω, Attenuation 3 dB
Result: Shunt Resistor = 62.45 Ω
Typical
Given: Characteristic Impedance 1.03 kΩ, Attenuation 20 dB
Result: Shunt Resistor = 0.2081 kΩ
High range
Given: Characteristic Impedance 10.3 kΩ, Attenuation 60 dB
Result: Shunt Resistor = 20.6 Ω
Maximum range
Given: Characteristic Impedance 103 kΩ, Attenuation 600 dB
Result: Shunt Resistor = 2.06 × 10⁻²² mΩ
Solving for each variable
Solve for Shunt Resistor
Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB → 63.68 Ω
Solve for Characteristic Impedance
Shunt Resistor 1 Ω, Attenuation 0.3 dB → 34.55 mΩ
How Shunt Resistor changes with Characteristic Impedance
| Characteristic Impedance (input) | Shunt Resistor (result) |
|---|---|
| 103 Ω | 20.81 Ω |
| 0.2575 kΩ | 52.02 Ω |
| 0.515 kΩ | 104 Ω |
| 0.7725 kΩ | 156.1 Ω |
| 1.03 kΩ | 0.2081 kΩ |
| 1.545 kΩ | 0.3121 kΩ |
| 2.06 kΩ | 0.4162 kΩ |
| 4.12 kΩ | 0.8323 kΩ |
| 7.21 kΩ | 1.457 kΩ |
| 10.3 kΩ | 2.081 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 208100 |
| Ω | 208.1 |
| kΩ | 0.2081 |
| MΩ | 0.0002081 |
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<p><a href="https://vbatpower.com/formulas/t-pad-shunt-resistor/">T-Pad Shunt Resistor</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate T-Pad Shunt Resistor?
Use R3 = 2 × Z × K / (K² − 1). With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, Shunt Resistor works out to 0.2081 kΩ.
What is the formula for T-Pad Shunt Resistor?
The formula is R3 = 2 × Z × K / (K² − 1). The shunt (middle) resistor of a symmetric T-pad attenuator connects the junction of the two 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 34.55 mΩ.
What units does T-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?
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