Design a quarter-wave (λ/4) transformer
design_quarter_waveDesign a quarter-wave impedance transformer to match real or complex loads to a source, returning offset length, transformer impedance, physical lengths, and matched bandwidth.
Instructions
Design a λ/4 impedance transformer Z1 = √(Z0·R). Real loads are matched directly; complex loads first get a section of Z0 line that rotates them to the nearest voltage maximum (R = Z0·VSWR) or minimum (R = Z0/VSWR) on the real axis. Returns the offset length, transformer impedance, physical lengths (if frequency is given), verification and matched bandwidth. Elements are listed load → source.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| z0 | No | Reference (system) characteristic impedance Z0 in Ω. Default 50. | |
| load | Yes | The load (termination) at the far end of the circuit. Give exactly one of: z, gamma, table, or a 1-port Touchstone (.s1p) via touchstone_path / touchstone_content (e.g. a measured antenna). | |
| source | No | Source impedance (default = z0, purely resistive). Complex sources are conjugately matched. | |
| eps_eff | No | Effective permittivity of the lines (default 1). | |
| language | No | Language of the human-readable summary: 'en' (English) or 'tr' (Türkçe). Defaults to the server setting. | |
| frequency | No | Optional: needed for physical lengths and frequency-dependent loads. | |
| bandwidth_vswr | No | VSWR limit used to report the matched bandwidth of each solution (default 2 ≈ 9.5 dB return loss). | |
| velocity_factor | No | Velocity factor; overrides eps_eff. |