Understanding Characteristic Impedance: Definition, Formulas, and Transmission Line Types

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This page explains the basics of characteristic impedance and provides equations for calculating it for various transmission lines. These include parallel lines, coaxial lines, shielded parallel lines, striplines, and more.

When the reflected wave in a transmission line is zero, the ratio of V(z)/I(z) in the direction of propagation (z) is called the characteristic impedance. It’s denoted by the symbol Z₀.

Characteristic impedance (Z₀) is defined as:

Z0=ZY=R+jωLG+jωCZ_0 = \sqrt{\frac{Z}{Y}} = \sqrt{\frac{R + j\omega L}{G + j\omega C}}

Where:

  • Z is the impedance per unit length
  • Y is the admittance per unit length
  • R is the resistance per unit length
  • L is the inductance per unit length
  • G is the conductance per unit length
  • C is the capacitance per unit length
  • ω\omega is the angular frequency (2πf2\pi f)
  • jj is the imaginary unit

Characteristic Impedance of Different Transmission Lines

Characteristic Impedance of a Lossy Transmission Line

Zo=R+jωLG+jωCZ_o = \sqrt{\frac{R + j\omega L}{G + j\omega C}}

Characteristic Impedance of a Lossless Transmission Line

Zo=LCZ_o = \sqrt{\frac{L}{C}}

Characteristic Impedance Equations for Specific Transmission Line Types

Parallel Line

Zo=276ϵrlog(2Sd)Z_o = \frac{276}{\sqrt{\epsilon_r}} * log(\frac{2S}{d})

Where:

  • S is the spacing between the two conductors.
  • d is the diameter of the conductor.
  • ϵr\epsilon_r is the relative dielectric constant (dielectric constant) between the conductors.

Coaxial Line

Zo=138ϵrlog(Dd)Z_o = \frac{138}{\sqrt{\epsilon_r}} * log(\frac{D}{d})

Where:

  • D is the diameter of the outer conductor.
  • d is the diameter of the inner conductor.
  • ϵr\epsilon_r is the relative dielectric constant (dielectric constant) of the insulator between the conductors.

Shielded Parallel Line

Zo=276ϵrlog(2A(1B2)1+B2)Z_o = \frac{276}{\sqrt{\epsilon_r}} * log (\frac{2A *(1-B^2)}{1+B^2})

Where:

  • A = s/d
  • B = s/D
  • s is the center-to-center spacing of the parallel conductors
  • d is the diameter of the conductors
  • D is the inner diameter of the shield
  • ϵr\epsilon_r is the relative dielectric constant (dielectric constant) of the medium between the conductors

Stripline

Zo=377ϵr(TW)Z_o = \frac{377}{\sqrt{\epsilon_r}} * (\frac{T}{W})

Where:

  • T is the thickness of the dielectric material (e.g., PCB substrate).
  • W is the width of the etched line (the signal trace).
  • ϵr\epsilon_r is the relative dielectric constant (dielectric constant) of the dielectric material.
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