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Design a quarter-wave (λ/4) transformer

design_quarter_wave
Read-onlyIdempotent

Design 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

TableJSON Schema
NameRequiredDescriptionDefault
z0NoReference (system) characteristic impedance Z0 in Ω. Default 50.
loadYesThe 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).
sourceNoSource impedance (default = z0, purely resistive). Complex sources are conjugately matched.
eps_effNoEffective permittivity of the lines (default 1).
languageNoLanguage of the human-readable summary: 'en' (English) or 'tr' (Türkçe). Defaults to the server setting.
frequencyNoOptional: needed for physical lengths and frequency-dependent loads.
bandwidth_vswrNoVSWR limit used to report the matched bandwidth of each solution (default 2 ≈ 9.5 dB return loss).
velocity_factorNoVelocity factor; overrides eps_eff.

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

A3.9/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already carry the safety profile (readOnly, idempotent, non-destructive), and the description adds genuine behavioral context: the offset-line step for complex loads, the VSWR-based real-axis targets, and the conditional physical-length output tied to frequency. It also discloses return content and element ordering, which matters since no output schema exists.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with the formula and purpose, followed by conditional behavior and the return-content sentence. Four sentences, each informative, though the algorithm detail is dense relative to the routing guidance an agent most needs.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description correctly enumerates what is returned (offset length, transformer impedance, physical lengths, verification, matched bandwidth) and notes the load→source ordering. Given the nested load object and eight parameters, this is nearly complete, missing only error/edge-case behavior.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the schema already documents all eight parameters, including the complex vs real load handling and defaults. The description adds conceptual context (the rotation step, conjugate source matching) but no per-parameter syntax or format details beyond what the schema provides.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource (design a λ/4 impedance transformer) and even gives the governing formula Z1 = √(Z0·R). An agent can distinguish this immediately from siblings like design_l_match, design_pi_t_match, and design_stub_match.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description explains the internal approach (real loads matched directly, complex loads get a rotating Z0 section) but never states when to choose this topology over the sibling matching tools. Usage is implied by the matching context rather than compared against alternatives.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.