{ "openapi": "3.1.1", "info": { "title": "Ohmforge L-Network Impedance Matching (Smith Chart) API", "version": "1.0.0", "summary": "Match a load to 50 Ω with two parts: every L-network solution, part values, Q and a Smith chart.", "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://ohmforgeimpedancematching.usefulweb.site" } ], "paths": { "/api/v1/calculate": { "post": { "operationId": "calculate", "summary": "Match a load to 50 Ω with two parts: every L-network solution, part values, Q and a Smith chart.", "description": "Enter a load impedance R + jX, the source or line impedance and the frequency. The tool returns every lossless two-element L-network that matches them — shunt-first and series-first, with inductor and capacitor values — the nodal Q, the VSWR ≤ 2 bandwidth and a Smith chart that shows each match path from the load to the centre. Each solution is verified by evaluating the network's input impedance.\n\nMethodology:\n- Analytic L-section design after Pozar §5.1. Shunt-first (shunt part across the load, series part towards the source): B = (X_L ± √(R_L/Z0)·√(R_L² + X_L² − Z0·R_L)) / (R_L² + X_L²), then the series reactance cancels what is left; possible when |Z_L|² ≥ Z0·R_L (always for R_L > Z0). Series-first (series part next to the load, shunt part towards the source): X = ±√(R_L(Z0 − R_L)) − X_L, B = ±√((Z0 − R_L)/R_L)/Z0; possible when R_L < Z0.\n- Parts at f: X > 0 → L = X/ω, X < 0 → C = −1/(ωX); B > 0 → C = B/ω, B < 0 → L = −1/(ωB).\n- Each solution is checked by computing the input impedance of the finished network with complex arithmetic and once more by parsing its network expression with Ohmforge's impedance calculator.\n- Nodal Q = |X|/R at the node between the two parts. The VSWR ≤ 2 band is found by bisection on |Γin(f)| = 1/3, with the load modelled as R_L plus the inductor or capacitor that has X_L at the design frequency.\n- The Smith chart is normalised to Z0; series parts move along circles of constant resistance, shunt parts along circles of constant conductance.\n\nIdeal, lossless parts: real inductors have resistance and self-resonance, capacitors have ESR and ESL, and PCB pads add parasitics that matter above a few hundred MHz. A real load's impedance changes with frequency differently from the simple R + L or R + C model used for the bandwidth. Tune on the bench with a VNA.", "tags": [ "apps" ], "x-mcp-tool": "ohmforge_impedance_matching", "x-owner-app": "ohmforge", "requestBody": { "required": true, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/OhmforgeImpedanceMatchingInput" }, "examples": { "example1": { "summary": "Pozar example 5.1: 200 − j100 Ω to 100 Ω at 500 MHz", "value": { "loadR": 200, "loadX": -100, "z0": 100, "frequencyMHz": 500 } }, "example2": { "summary": "Low-impedance load 10 + j5 Ω to 50 Ω at 100 MHz", "value": { "loadR": 10, "loadX": 5, "z0": 50, "frequencyMHz": 100 } }, "example3": { "summary": "Short 433 MHz antenna 12.5 − j60 Ω to 50 Ω", "value": { "loadR": 12.5, "loadX": -60, "z0": 50, "frequencyMHz": 433.92 } } } } } }, "responses": { "200": { "description": "Calculation result envelope.", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/OhmforgeImpedanceMatchingResult" } } } }, "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" } } } } } }, "OhmforgeImpedanceMatchingInput": { "type": "object", "additionalProperties": false, "properties": { "loadR": { "title": "Load resistance R", "type": "number", "minimum": 0.000001, "maximum": 1000000000, "default": 200, "x-unit": "Ω" }, "loadX": { "title": "Load reactance X", "description": "Positive = inductive, negative = capacitive.", "type": "number", "minimum": -1000000000, "maximum": 1000000000, "default": -100, "x-unit": "Ω" }, "z0": { "title": "Source / line impedance Z0", "description": "Real impedance to match to, usually 50 Ω.", "type": "number", "minimum": 0.001, "maximum": 1000000, "default": 100, "x-unit": "Ω" }, "frequencyMHz": { "title": "Frequency", "type": "number", "minimum": 0.000001, "maximum": 1000000, "default": 500, "x-unit": "MHz" } }, "required": [] }, "OhmforgeImpedanceMatchingResult": { "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": [ "loadR", "loadX", "z0", "frequencyHz", "solutions" ], "additionalProperties": false, "properties": { "loadR": { "type": "number" }, "loadX": { "type": "number" }, "z0": { "type": "number" }, "frequencyHz": { "type": "number" }, "gammaLoad": { "type": "number" }, "vswrLoad": { "type": [ "number", "null" ] }, "loadModel": { "type": "object", "additionalProperties": false, "properties": { "kind": { "type": "string" }, "value": { "type": "number" } } }, "solutions": { "type": "array", "items": { "type": "object", "additionalProperties": false, "properties": { "topology": { "type": "string", "enum": [ "shunt-first", "series-first" ] }, "series": { "type": "object", "additionalProperties": false, "properties": { "kind": { "type": "string", "enum": [ "L", "C", "none" ] }, "value": { "type": "number", "description": "H or F." }, "reactance": { "type": "number", "description": "Series: X in Ω. Shunt: B in S." } } }, "shunt": { "type": "object", "additionalProperties": false, "properties": { "kind": { "type": "string", "enum": [ "L", "C", "none" ] }, "value": { "type": "number", "description": "H or F." }, "reactance": { "type": "number", "description": "Series: X in Ω. Shunt: B in S." } } }, "q": { "type": "number" }, "zInReal": { "type": "number" }, "zInImag": { "type": "number" }, "bandLowHz": { "type": [ "number", "null" ] }, "bandHighHz": { "type": [ "number", "null" ] }, "expression": { "type": "string", "description": "Network for the Ohmforge impedance calculator (load modelled as R plus L or C)." } } } }, "notes": { "type": "array", "items": { "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" } } } } } } } }