Simultaneous conjugate match & maximum gain

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

Annotations already declare readOnly/idempotent/non-destructive, so safety is covered; the description adds real behavioral context beyond that: the K>1 and |Δ|<1 preconditions, and that design_networks triggers L-network synthesis that is self-verified by recomputing ΓS/ΓL. It does not describe return format or failure behavior, but it meaningfully enriches the annotation baseline.

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?

Two sentences, tightly written and front-loaded with the primary purpose and outputs before the conditional design_networks behavior. The heavy parenthetical nesting in the first sentence makes it dense, but every clause carries technical information rather than filler.

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 nested-object, no-output-schema tool, the description covers purpose, the exact computed quantities (effectively describing the return), validity preconditions, and the optional network-design branch. It omits any mention of error/edge-case behavior when the K/|Δ| conditions fail, leaving a small gap.

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 description coverage is 100%, so the parameters are already documented and the baseline is 3. The description adds incremental meaning for design_networks beyond the schema text ('synthesize L-section input/output networks from the system Z0, verified by recomputing ΓS/ΓL'), clarifying the role of Z0 and frequency, which justifies a bump to 4.

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?

The description names the specific operation (simultaneous conjugate match of a two-port for maximum transducer gain) and enumerates the exact deliverables (ΓS, ΓL, ZS, ZL, GT,max/MAG, MSG, U, gain error bounds), so the agent knows precisely what the tool returns. It does not name a sibling it differs from (e.g., gain_circles or design_l_match), which keeps it short of a 5.

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?

It states clear applicability conditions: 'Requires K > 1 and |Δ| < 1' tells the agent when the tool is valid, and conditionally that design_networks=true adds L-section synthesis. It does not route the agent to alternative tools or state explicit when-not cases beyond the stability constraint.

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