What is Characteristic Impedance: Formulas, Transmission Line Types

Characteristic impedance is the ratio of voltage to current in a transmission line when a signal propagates without reflections. It is a key parameter in RF, microwave and communication systems, ensuring proper impedance matching, minimizing signal loss and maximizing power transfer efficiency. This page explains the basics of characteristic impedance and provides formulas 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:

$Z_0 = \sqrt{\frac{Z}{Y}} = \sqrt{\frac{R + j\omega L}{G + j\omega C}}$

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
• $\omega$ is the angular frequency ($2\pi f$)
• $j$ is the imaginary unit

Characteristic Impedance of Different Transmission Lines

Characteristic Impedance of a Lossy Transmission Line

$Z_o = \sqrt{\frac{R + j\omega L}{G + j\omega C}}$

Characteristic Impedance of a Lossless Transmission Line

$Z_o = \sqrt{\frac{L}{C}}$

Characteristic Impedance Equations for Specific Transmission Line Types

Parallel Line

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

Where:

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

Coaxial Line

$Z_o = \frac{138}{\sqrt{\epsilon_r}} * log(\frac{D}{d})$

Where:

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

Shielded Parallel Line

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

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
• $\epsilon_r$ is the relative dielectric constant (dielectric constant) of the medium between the conductors

Stripline

$Z_o = \frac{377}{\sqrt{\epsilon_r}} * (\frac{T}{W})$

Where:

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

Continue Learning RF Technology

• What is RF Signal : Radio Frequency Fundamentals
• RF Related Terminologies
• RF Components & Their Basic Functions, Manufacturers
• What is RF Radiation: Safety, Uses & Health Concerns

Compare RF (Radio Frequency) with The Rest

• RF Vs. Microwave : Key Comparison
• RF Vs. Baseband : Key Differences Explained
• RF Vs. IF: Difference Between RF and IF Signals
• RF Vs. PHYSICAL LAYER : Key differences explained

Continue Learning VSWR, Return Loss & Reflection Coefficients

Essential reading on impedance matching and signal reflection. Learn how to calculate and minimize the power lost when signals hit a mismatched load or antenna.

• Reflection and Transmission Coefficients
• Reflection Coefficient vs Return Loss vs VSWR
• VSWR & Return Loss Formulas and Conversion
• Optical Return Loss vs Optical Insertion Loss

Troubleshooting & Tools

• High VSWR: Reasons and Resolutions
• VSWR Calculator and Formula
• Reflection Coefficient to SWR Converter