What Is the Quarter-Wave Transmission Line Impedance Transformer Calculator?
Quarter-wave matching transformers match real impedances without reactive components at a target frequency.
How Does the Quarter-Wave Transmission Line Impedance Transformer Calculator Work?
Wave reflections from the front and back interfaces of the quarter-wave section interfere destructively, cancelling reflection.
Quarter-Wave Transmission Line Impedance Transformer Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Z_t = \sqrt{Z_0 Z_L}, \quad \lambda_g = \frac{c}{f \sqrt{\varepsilon_{\text{eff}}}}, \quad \ell = \frac{\lambda_g}{4}
Quarter-wave transformer section geometric mean impedance and physical length.
How to Use the Quarter-Wave Transmission Line Impedance Transformer Calculator
- Input feedline impedance, load resistance, operating frequency, and dielectric constant.
Step-by-Step Example Calculation
2.4 GHz 50-to-100 Ohm Match
Input Values:
sourceImpedanceZ0Ohm:50
loadImpedanceZLOhm:100
designFrequencyHz:2400000000
effectivePermittivityEr:2.2
Worked Steps: Requires section impedance Z_t = 70.71 Ω and physical length ~21.06 mm.
Understanding Your Result
Provides required section impedance Z_t and physical line length in mm.
Factors That Affect the Result
- Higher dielectric constant shortens guided wavelength and physical transformer dimensions.
When Should You Use This Calculator?
- Antenna feed matching, power amplifier output networks, and Wilkinson power dividers.
Assumptions & Limitations
- Narrowband matching technique for purely resistive terminations.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Fundamental transmission line matching theorem.