{ "openapi": "3.1.1", "info": { "title": "Ohmforge Impedance Calculator API", "version": "1.0.0", "summary": "Complex impedance of R, L, C series/parallel networks: |Z|, phase, admittance, resonance.", "description": "Every endpoint performs the same calculation as the human page and returns inputs, result, units, assumptions, sources, warnings and computedAt. MCP endpoint: /mcp." }, "servers": [ { "url": "https://ohmforgeimpedancecalculator.usefulweb.app" } ], "paths": { "/api/v1/calculate": { "post": { "operationId": "calculate", "summary": "Complex impedance of R, L, C series/parallel networks: |Z|, phase, admittance, resonance.", "description": "Type a small network such as R100 + (L10m || C1u) and a frequency. The calculator returns the complex impedance (R + jX), magnitude and phase, the admittance G + jB, the equivalent inductance or capacitance at that frequency, Q, every resonance of the network, an |Z| and phase plot over frequency and the reactance of each part – checked against Ohmforge's AC simulator.\n\nMethodology:\n- Each element becomes a complex impedance: Z_R = R, Z_L = jωL, Z_C = 1/(jωC) with ω = 2πf. Series groups add impedances, parallel groups add admittances (Y = 1/Z). Complex division uses Smith's algorithm for numerical robustness.\n- Admittance Y = 1/Z = G + jB. The equivalent part at the frequency is L = X/ω for X > 0 or C = −1/(ωX) for X < 0; Q = |X| / R of the series equivalent.\n- Resonances are frequencies where the reactance X changes sign (zero phase): found on a 50-points-per-decade scan from 1 mHz to 100 GHz and refined by bisection. A minimum of |Z| (X from − to +) is a series resonance, a maximum (X from + to −) a parallel resonance.\n- Cross-check: the network is driven by a 1 A AC current source in Ohmforge's AC analysis, so the simulated node voltage equals Z; the relative difference is reported.\n\nIdeal parts: real inductors have winding resistance and self-resonance, capacitors have ESR and ESL, and both change with frequency, temperature and (for ceramics) DC bias.", "tags": [ "apps" ], "x-mcp-tool": "ohmforge_impedance_calculator", "x-owner-app": "ohmforge", "requestBody": { "required": true, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/OhmforgeImpedanceCalculatorInput" }, "examples": { "example1": { "summary": "R100 + (L10m || C1u) at 1 kHz", "value": { "network": "R100 + (L10m || C1u)", "frequency": 1000 } }, "example2": { "summary": "Series RLC at resonance (≈ 5.03 kHz)", "value": { "network": "R10 + L1m + C1u", "frequency": 5033 } }, "example3": { "summary": "Speaker crossover branch at 3 kHz", "value": { "network": "(R8 + L0.42m) || (C6.6u + R2.2)", "frequency": 3000 } } } } } }, "responses": { "200": { "description": "Calculation result envelope.", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/OhmforgeImpedanceCalculatorResult" } } } }, "400": { "description": "Malformed JSON body.", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "422": { "description": "Invalid input (see errors[]).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "429": { "description": "Rate limit exceeded (see Retry-After).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } } } } }, "/api/v1/tool": { "get": { "operationId": "getToolDefinition", "summary": "Inputs, output schema and examples for this tool", "responses": { "200": { "description": "Tool definition.", "content": { "application/json": { "schema": { "type": "object" } } } } } } } }, "components": { "schemas": { "Problem": { "type": "object", "description": "RFC 9457 problem details. 422 responses include per-field `errors`.", "required": [ "type", "title", "status", "detail" ], "properties": { "type": { "type": "string" }, "title": { "type": "string" }, "status": { "type": "integer" }, "detail": { "type": "string" }, "code": { "type": "string" }, "errors": { "type": "array", "items": { "type": "object", "required": [ "field", "message" ], "properties": { "field": { "type": "string" }, "message": { "type": "string" } } } } } }, "OhmforgeImpedanceCalculatorInput": { "type": "object", "additionalProperties": false, "properties": { "network": { "title": "Network", "description": "Elements R, L, C; + = series, || (or //) = parallel, parentheses group. || binds tighter than +.", "type": "string", "maxLength": 2000, "default": "R100 + (L10m || C1u)" }, "frequency": { "title": "Frequency", "type": "number", "minimum": 0.000001, "maximum": 1000000000000, "default": 1000, "x-unit": "Hz" } }, "required": [] }, "OhmforgeImpedanceCalculatorResult": { "type": "object", "additionalProperties": false, "required": [ "schemaVersion", "tool", "computedAt", "inputs", "summary", "result", "units", "assumptions", "sources", "warnings", "presentation", "links" ], "properties": { "schemaVersion": { "type": "string", "const": "1.0" }, "tool": { "type": "object", "additionalProperties": false, "required": [ "id", "name", "version" ], "properties": { "id": { "type": "string" }, "name": { "type": "string" }, "version": { "type": "string" } } }, "computedAt": { "type": "string", "format": "date-time" }, "inputs": { "type": "object", "description": "Normalised inputs actually used, including applied defaults." }, "summary": { "type": "string" }, "result": { "type": "object", "required": [ "network", "frequency", "real", "imaginary", "magnitude", "phaseDeg", "resonances", "simulatorCheck" ], "additionalProperties": false, "properties": { "network": { "type": "string", "description": "Canonical form of the network with element names." }, "expression": { "type": "string" }, "frequency": { "type": "number" }, "real": { "type": "number" }, "imaginary": { "type": "number" }, "magnitude": { "type": "number" }, "phaseDeg": { "type": "number" }, "conductance": { "type": "number" }, "susceptance": { "type": "number" }, "admittanceMagnitude": { "type": "number" }, "equivalent": { "type": "object", "additionalProperties": false, "properties": { "kind": { "type": "string" }, "value": { "type": "number" } } }, "q": { "type": [ "number", "null" ] }, "elements": { "type": "array", "items": { "type": "object", "additionalProperties": false, "properties": { "name": { "type": "string" }, "kind": { "type": "string" }, "value": { "type": "number" }, "reactance": { "type": "number" } } } }, "resonances": { "type": "array", "items": { "type": "object", "additionalProperties": false, "properties": { "frequency": { "type": "number" }, "type": { "type": "string" }, "magnitude": { "type": [ "number", "null" ], "description": "null = unbounded (parallel resonance of ideal, lossless L and C)." } } } }, "sweep": { "type": "object", "additionalProperties": false, "properties": { "frequencies": { "type": "array", "items": { "type": "number" } }, "magnitude": { "type": "array", "items": { "type": "number" } }, "phaseDeg": { "type": "array", "items": { "type": "number" } } } }, "simulatorCheck": { "type": "object", "additionalProperties": false, "properties": { "simulatedMagnitude": { "type": "number" }, "simulatedPhaseDeg": { "type": "number" }, "relativeError": { "type": "number" } } }, "netlist": { "type": "string" } } }, "units": { "type": "object", "additionalProperties": { "type": "string" } }, "assumptions": { "type": "array", "items": { "type": "string" } }, "sources": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "title" ], "properties": { "title": { "type": "string" }, "url": { "type": "string" }, "publisher": { "type": "string" }, "retrievedAt": { "type": "string" }, "note": { "type": "string" } } } }, "warnings": { "type": "array", "items": { "type": "string" } }, "presentation": { "type": "array", "items": { "type": "object" }, "description": "Display blocks used by the human page (same data)." }, "links": { "type": "object", "additionalProperties": false, "required": [ "human", "api", "openapi", "methodology" ], "properties": { "human": { "type": "string", "format": "uri" }, "api": { "type": "string", "format": "uri" }, "openapi": { "type": "string", "format": "uri" }, "methodology": { "type": "string", "format": "uri" } } } } } } } }