Multisection λ/4 Transformer
Cascading several quarter-wave sections gives a far wider matching bandwidth than a single λ/4 transformer. A binomial design makes the response maximally flat; a Chebyshev design trades a small equal-ripple mismatch for even more bandwidth. This tool returns the impedance of each section, the fractional bandwidth for your ripple spec, and a frequency sweep of the actual cascade to confirm the passband reflection.
Equations & Parameters ▸
binomial: \(\ln\dfrac{Z_{n+1}}{Z_n}=2^{-N}\binom{N}{n}\ln\dfrac{R_L}{Z_0}\)
Chebyshev: \(\Gamma(\theta)=A\,e^{-jN\theta}\,T_N(\sec\theta_m\cos\theta),\ \ A=\Gamma_m,\ \ \sec\theta_m=\cosh\!\big[\tfrac1N\cosh^{-1}\tfrac{\Gamma_0}{\Gamma_m}\big]\)
\(\dfrac{\Delta f}{f_0}=2-\dfrac{4}{\pi}\theta_m\)
Chebyshev: \(\Gamma(\theta)=A\,e^{-jN\theta}\,T_N(\sec\theta_m\cos\theta),\ \ A=\Gamma_m,\ \ \sec\theta_m=\cosh\!\big[\tfrac1N\cosh^{-1}\tfrac{\Gamma_0}{\Gamma_m}\big]\)
\(\dfrac{\Delta f}{f_0}=2-\dfrac{4}{\pi}\theta_m\)
| Z0, RL | Source impedance and (real) load resistance (Ω). |
| N | Number of quarter-wave sections (1–8). |
| Response | Binomial (maximally flat) or Chebyshev (equiripple). |
| Γm | Maximum passband reflection. For Chebyshev it is the design ripple; for binomial it is the bandwidth threshold. |
Reference: D. M. Pozar, Microwave Engineering, 4th ed., §5.6 (binomial) & §5.7 (Chebyshev).
Inputs
Ω
Feed lineΩ
Resistive1 – 8
Shape
e.g. 0.05
Results
Bandwidth
Fractional bandwidth—
Design max VSWR—
Swept passband max |Γ|—
Diagram