calc.engineer

lc resonance

lc_resonance

Calculates the resonant frequency of an LC circuit, along with optional Q factor and bandwidth when series resistance is provided. The resonant frequency f0 = 1/(2pisqrt(L*C)) is where inductive and capacitive reactances cancel. Used for designing tank circuits, oscillators, bandpass filters, and antenna matching networks. If resistance R is given, computes quality factor Q = (1/R)*sqrt(L/C) and 3 dB bandwidth = f0/Q. Chain into impedance_match to design matching networks at the resonant frequency.

Input Schema

TableJSON Schema

Name	Required	Description
`inductance_h`	Yes	Inductance in henries (H). The inductive element of the LC circuit.
`capacitance_f`	Yes	Capacitance in farads (F). The capacitive element of the LC circuit.
`resistance_ohm`	No	Optional series resistance in ohms for Q factor and bandwidth calculation. Omit for ideal LC analysis.

Output Schema

TableJSON Schema

Name	Required	Description
`q_factor`	Yes	Quality factor Q = (1/R)*sqrt(L/C). Null if no resistance provided.
`bandwidth_hz`	Yes	3 dB bandwidth in hertz (f0/Q). Null if no resistance provided.
`angular_freq_rad`	Yes	Angular resonant frequency in radians per second (omega_0 = 2pif0).
`resonant_freq_hz`	Yes	Resonant frequency in hertz.
`resonant_freq_mhz`	Yes	Resonant frequency in megahertz for convenience.
`impedance_at_resonance_ohm`	Yes	Impedance at resonance in ohms. Equals the series resistance R if provided; null if ideal (no R).

TDQS

A4.3/5.0

Behavior4/5

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

No annotations provided, so description carries full burden. It explains that optional resistance yields Q factor and bandwidth, mentions the formula, and implies the behavior of the tool when resistance is omitted. However, it does not discuss edge cases like extreme values or precision.

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?

Four sentences covering purpose, formula, applications, and optional feature. Front-loaded with the main action. Could be slightly tighter, but no wasted words.

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?

Given the presence of an output schema (assumed to define return values), the description adequately explains inputs and outputs. It also provides chaining context. For a calculation tool with moderate complexity, this is sufficiently complete.

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

Parameters4/5

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

Schema coverage is 100%, so baseline is 3. Description adds value by explaining how each parameter contributes to the calculation (e.g., 'series resistance for Q factor and bandwidth') and provides formulas, going beyond schema descriptions.

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?

The description clearly states the tool calculates resonant frequency, Q factor, and bandwidth for an LC circuit. It uses a specific verb ('calculates') and resource ('LC circuit'), and distinguishes itself from siblings by mentioning chaining with impedance_match.

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

Usage Guidelines4/5

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

The description provides explicit use cases (tank circuits, oscillators, filters, antenna matching) and suggests chaining to impedance_match. It lacks explicit 'when not to use' guidance, but the context is clear enough.

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

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TDQS

A3.9/5.0

Disambiguation4/5

Despite 89 tools, each has a clearly distinct purpose with detailed descriptions that often reference related tools. Overlap exists (e.g., multiple LoRa/RF tools), but the descriptions are sufficient to distinguish them. Some confusion possible among similar-sounding tools like attenuator_pi and attenuator_tee, but the descriptions explicitly compare them.

Naming Consistency4/5

Consistent underscore-separated lowercase naming. Most tools follow a verb_noun pattern (e.g., capacitor_charge, wire_gauge) or noun_noun (power_cost). Minor inconsistencies such as 'bmi_calculator' vs 'solar_sizing' but overall predictable.

Tool Count2/5

89 tools is far too many for a single MCP server. This scope is more appropriate for multiple specialized servers. The sheer number will slow agent selection and increase cognitive load, reducing coherence.

Completeness3/5

Covers many domains (RF, solar, PCB, networking, math, etc.) but lacks depth in some areas (e.g., no three-phase power, no airflow calculations). Some domains have comprehensive coverage (LoRa/Meshtastic), but others feel incomplete for the tool count.

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