Calculator Inputs
Example Data Table
| Case | Type | Zs (Ω) | Zl (Ω) | Frequency (MHz) | Velocity Factor | Target Bandwidth (%) |
|---|---|---|---|---|---|---|
| RF Amplifier Match | Single Section | 50 | 100 | 1000 | 0.66 | 18 |
| Antenna Feed Match | Two Section | 50 | 200 | 435 | 0.80 | 28 |
| Broadband Stage | Three Section | 75 | 300 | 2400 | 0.70 | 40 |
Formula Used
Single-section quarter-wave transformer: The ideal section impedance is Zt = √(Zs × Zl). This provides an exact match at the design frequency when the section is a quarter wavelength long.
Multi-section transformer: This calculator uses geometric impedance progression. For a two-section design, section values step smoothly between source and load. For a three-section design, the progression is divided across three quarter-wave sections to improve broadband behavior.
Quarter-wave physical length: L = (c / f) × VF ÷ 4. Here, c is the speed of light, f is frequency, and VF is the line velocity factor.
Reflection coefficient: Γ = |(Z2 − Z1) / (Z2 + Z1)|. Lower reflection means better impedance transition across sections.
VSWR: VSWR = (1 + Γ) / (1 − Γ). Lower VSWR indicates better matching and reduced standing-wave stress.
Return loss: RL = −20 log10(Γ). Higher return loss means less reflected power.
Mismatch loss: ML = −10 log10(1 − Γ²). This estimates the insertion penalty caused by impedance mismatch.
How to Use This Calculator
- Choose the transformer type based on matching difficulty and desired bandwidth.
- Enter source and load impedances in ohms.
- Enter the center frequency in MHz.
- Supply the velocity factor of the chosen transmission medium.
- Set the bandwidth target and expected operating power.
- Submit the form to generate section impedances, electrical length, physical length, and matching performance estimates.
- Review the result table above the form.
- Use the CSV or PDF buttons to export the calculated design summary.
FAQs
1. What does this calculator design?
It designs quarter-wave impedance transformers for matching one impedance to another. It also estimates section lengths, reflection behavior, return loss, and expected bandwidth performance.
2. When should I use a single-section transformer?
Use a single-section transformer when you need a simple exact match at one main frequency and the impedance ratio is moderate. It is compact and easy to fabricate.
3. Why use two or three sections?
More sections create a gentler impedance transition. That usually improves broadband behavior, lowers peak reflections across a wider range, and makes the design more tolerant of frequency spread.
4. What is velocity factor?
Velocity factor is the ratio between wave speed in a transmission medium and the speed of light. It directly affects the physical quarter-wave length.
5. Does this calculator replace EM simulation?
No. It is an engineering design aid for first-pass sizing. Final hardware should still be checked with simulation, layout effects, material tolerances, and measured prototypes.
6. Can I use this for coax or microstrip?
Yes. The main requirement is using the correct effective velocity factor and then converting each target impedance into the physical line geometry required by your medium.
7. Why is my physical length different from theory?
Fringing fields, connector transitions, dielectric tolerance, and fabrication limits can shift the effective electrical length. Practical tuning is often needed after initial calculation.
8. What is the main benefit of lower VSWR?
Lower VSWR means less reflected power, better power transfer, reduced stress on amplifiers, and more predictable RF system performance around the design frequency.