Design Pi / T matching networks with a target Q

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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), so the lower bar applies. The description adds real value beyond them: it discloses the mathematical validity constraint on Q and enumerates what is returned (all low-pass/high-pass/mixed variants with component values, virtual resistance, verification, bandwidth). No output schema exists, so this return-value disclosure matters.

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

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

Four tight sentences, front-loaded with the verb and resource, then the constraint, the return content, and finally use cases. Every sentence adds distinct information; nothing is redundant with the title or schema.

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

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

For a 10-parameter tool with nested load objects and no output schema, the description covers purpose, validity constraint, return contents, and use cases adequately. It does not describe failure/error behavior beyond the Q constraint or the effect of ordering options like preference, but nothing essential for a correct call is missing.

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

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

Schema coverage is 100%, so the baseline is 3. The description goes beyond the schema by explaining that Q sets the loaded bandwidth (≈ f0/Q) and that the required minimum Q derives from the impedance ratio, which gives the agent a semantic grasp of the key parameter's role.

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

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

States a specific verb ('Synthesize') and resource (three-element Pi/T lumped matching networks) and even spells out the topology element order. It explicitly contrasts itself with the L-network sibling (design_l_match), so an agent can route between them without opening either schema.

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

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

Gives concrete use cases (PA output networks, harmonic filtering, 'match 10 Ω to 50 Ω with Q = 5') and a hard precondition (Q must exceed √(Rhigh/Rlow − 1)). It implies the L-network as the alternative when that constraint fails, but never names the sibling or states explicitly when NOT to use this tool, so it stops short of a 5.

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