T-Pad Series Resistor

R1 = Z · (K−1)/(K+1)

Quick answer

This calculator solves R1 = R2 = Z × (K − 1)/(K + 1) for Series Resistor. With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, the result is 0.8427 kΩ. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Series Resistor (Ω)
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Formula

R1 = R2 = Z × (K − 1)/(K + 1)

Description

A symmetric T-pad attenuator uses two equal series resistors and one shunt resistor to provide a set attenuation while presenting the characteristic impedance Z to both the source and the load. This formula gives the value of each series arm. The T-pad is the standard matched attenuator for equal source and load impedances, used throughout RF and audio test gear.

Variables

  • R1 — Each series arm resistor (Ω)
  • Z — Characteristic (source = load) impedance (Ω)
  • dB — Desired attenuation; K = 10^(dB/20)

Practical Notes

Pair this with the T-pad shunt resistor R3 = 2ZK/(K²−1). Because the pad is matched, it both attenuates and maintains impedance, avoiding reflections on transmission lines.

Symbols and units

Symbol Meaning Default unit Accepted units
R1 Series 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: R1 = R2 = Z × (K − 1)/(K + 1)
  3. 3. Substitute: Z = 1.03 kΩ, dB = 20 dB
  4. 4. Result: Series Resistor = 0.8427 kΩ

Nearest standard component values

Series Nearest value Error
E12 0.82 kΩ 2.7%
E24 0.82 kΩ 2.7%

Worked examples

Minimum range

Given: Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB

Result: Series Resistor = 37.99 mΩ

Low range

Given: Characteristic Impedance 22 Ω, Attenuation 3 dB

Result: Series Resistor = 3.762 Ω

Typical

Given: Characteristic Impedance 1.03 kΩ, Attenuation 20 dB

Result: Series Resistor = 0.8427 kΩ

High range

Given: Characteristic Impedance 10.3 kΩ, Attenuation 60 dB

Result: Series Resistor = 10.28 kΩ

Maximum range

Given: Characteristic Impedance 103 kΩ, Attenuation 600 dB

Result: Series Resistor = 103 kΩ

Solving for each variable

Solve for Series Resistor

Characteristic Impedance 2.2 Ω, Attenuation 0.3 dB → 37.99 mΩ

Solve for Characteristic Impedance

Series Resistor 1 Ω, Attenuation 0.3 dB → 57.91 Ω

How Series Resistor changes with Characteristic Impedance

Characteristic Impedance (input) Series Resistor (result)
103 Ω 84.27 Ω
0.2575 kΩ 0.2107 kΩ
0.515 kΩ 0.4214 kΩ
0.7725 kΩ 0.632 kΩ
1.03 kΩ 0.8427 kΩ
1.545 kΩ 1.264 kΩ
2.06 kΩ 1.685 kΩ
4.12 kΩ 3.371 kΩ
7.21 kΩ 5.899 kΩ
10.3 kΩ 8.427 kΩ

The same result in other units

Unit Value
mΩ 842700
Ω 842.7
kΩ 0.8427
MΩ 0.0008427

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Frequently asked questions

How do you calculate T-Pad Series Resistor?

Use R1 = R2 = Z × (K − 1)/(K + 1). With Characteristic Impedance 1.03 kΩ, Attenuation 20 dB, Series Resistor works out to 0.8427 kΩ.

What is the formula for T-Pad Series Resistor?

The formula is R1 = R2 = Z × (K − 1)/(K + 1). A symmetric T-pad attenuator uses two equal series resistors and one shunt resistor to provide a set attenuation while presenting the characteristic impedance Z to both the source and the load.

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 57.91 Ω.

What units does T-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

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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