Bridged-T Bridge Resistor

Rb = Z · (K − 1)

Quick answer

This calculator solves Rb = Z × (K − 1) for Bridge Resistor. With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, the result is 9.27 kΩ. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Bridge Resistor (Ω)
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Formula

Rb = Z × (K − 1)

Description

A bridged-T attenuator keeps the two series arms equal to the characteristic impedance Z and varies only two resistors—the bridge resistor across the top and the shunt resistor to ground—to set the attenuation while staying matched. This formula gives the bridge resistor. Because only two resistors change with attenuation, the bridged-T is the basis of constant-impedance variable (stepped) attenuators.

Variables

  • Rb — Bridge resistor across the series arms (Ω)
  • Z — Characteristic impedance = series-arm value (Ω)
  • dB — Desired attenuation; K = 10^(dB/20)

Practical Notes

The matching shunt resistor is Rs = Z/(K−1), so Rb × Rs = Z². Switching just these two resistors gives calibrated step attenuators with constant input/output impedance.

Symbols and units

Symbol Meaning Default unit Accepted units
Rb Bridge Resistor Ω mΩ, Ω, kΩ, MΩ
Z Characteristic Impedance Ω mΩ, Ω, kΩ, MΩ
dB Attenuation dB dB

Step by step

  1. 1. What you know: Characteristic Impedance 1.03 kΩ, Attenuation 20 dB
  2. 2. The relation: Rb = Z × (K − 1)
  3. 3. Substitute: Z = 1.03 kΩ, dB = 20 dB
  4. 4. Result: Bridge Resistor = 9.27 kΩ

Nearest standard component values

Series Nearest value Error
E12 10 kΩ 7.9%
E24 9.1 kΩ 1.8%

Worked examples

Minimum range

Given: Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB

Result: Bridge Resistor = 77.31 mΩ

Low range

Given: Characteristic Impedance 22 Ω, Attenuation 3 dB

Result: Bridge Resistor = 9.076 Ω

Typical

Given: Characteristic Impedance 1.03 kΩ, Attenuation 20 dB

Result: Bridge Resistor = 9.27 kΩ

High range

Given: Characteristic Impedance 10.3 kΩ, Attenuation 60 dB

Result: Bridge Resistor = 10.29 MΩ

Maximum range

Given: Characteristic Impedance 103 Ω, Attenuation 0.6 dB

Result: Bridge Resistor = 7.366 Ω

Solving for each variable

Solve for Bridge Resistor

Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB → 77.31 mΩ

Solve for Characteristic Impedance

Bridge Resistor 1 Ω, Attenuation 0.3 dB → 28.46 Ω

How Bridge Resistor changes with Characteristic Impedance

Characteristic Impedance (input) Bridge Resistor (result)
103 Ω 0.927 kΩ
0.2575 kΩ 2.318 kΩ
0.515 kΩ 4.635 kΩ
0.7725 kΩ 6.953 kΩ
1.03 kΩ 9.27 kΩ
1.545 kΩ 13.91 kΩ
2.06 kΩ 18.54 kΩ
4.12 kΩ 37.08 kΩ
7.21 kΩ 64.89 kΩ
10.3 kΩ 92.7 kΩ

The same result in other units

Unit Value
mΩ 9270000
Ω 9270
kΩ 9.27
MΩ 0.00927

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Frequently asked questions

How do you calculate Bridged-T Bridge Resistor?

Use Rb = Z × (K − 1). With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, Bridge Resistor works out to 9.27 kΩ.

What is the formula for Bridged-T Bridge Resistor?

The formula is Rb = Z × (K − 1). A bridged-T attenuator keeps the two series arms equal to the characteristic impedance Z and varies only two resistors—the bridge resistor across the top and the shunt resistor to ground—to set the attenuation while staying matched.

How do you find Characteristic Impedance when you know the other values?

Rearrange for Characteristic Impedance: with Bridge Resistor 1 Ω, Attenuation 0.3 dB, Characteristic Impedance is 28.46 Ω.

What units does Bridged-T Bridge Resistor use?

Bridge 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 →
Attenuation Factor (K) T-Pad Series Resistor T-Pad Shunt Resistor Pi-Pad Series Resistor Pi-Pad Shunt Resistor Bridged-T Bridge Resistor Bridged-T Shunt Resistor

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