I cannot directly convert files, but here's your free, exclusive method to convert JPG to DWG without paid software:

Manual tracing workflow (recommended for accuracy)

1. Import JPG into a CAD program supporting image underlays (AutoCAD, LibreCAD via plugins, QCAD).
2. Lock the raster image layer and set it to a dim opacity.
3. Create a new layer for traced geometry.
4. Use polyline, line, arc, circle tools to manually trace over the image, snapping endpoints.
5. Dimension and scale using a known reference length on the image.
6. Clean up and organize layers, add hatches, annotations as required.

Summary Recommendation

• If you need editable lines and have a complex drawing: Use Inkscape or the Scan2CAD trial.
• If you just need the image inside a DWG file: Use an online converter like AnyPDFtoDwg.

Method 1: Inkscape (Best for accurate conversion)

1. Download Inkscape (free)
2. Import your JPG: File → Import
3. Trace bitmap: Path → Trace Bitmap
4. Adjust threshold → click Update → OK
5. Save as DXF: File → Save As → select Desktop Cutting Plotter (AutoCAD DXF R14)
6. Use Free DXF to DWG Converter (online, free)

Recommended workflow (automated → refine)

1. Prepare the JPG
   • Crop to relevant area.
   • Increase contrast and remove background noise (use free editors: GIMP, Paint.NET).
   • Resize to maintain detail (avoid heavy downscaling).
2. Convert raster to vector (use Inkscape auto-trace or an online tracer)
   • Open Inkscape → File → Import → select JPG.
   • Select the image → Path → Trace Bitmap.
   • Choose "Brightness cutoff" (for solid lines) or "Edge detection" (for outlines); preview and adjust threshold.
   • Click OK → close dialog → move the traced vector aside and delete original bitmap.
   • Clean up vectors: remove stray nodes, simplify paths (Path → Simplify), join segments.
3. Export to DXF
   • In Inkscape: File → Save As → choose "Desktop Cutting Plotter (AutoCAD DXF R14)".
   • In export dialog, set units and base scale (match intended CAD units), and enable "Use LWPOLYLINE" if available.
4. Convert DXF → DWG (if DWG required)
   • Use ODA File Converter to convert DXF to desired DWG version, or use a free trial of a CAD app that exports DWG.
   • Alternatively, open DXF in LibreCAD/QCAD and save/export as DXF in appropriate version; to get DWG, use an online DXF→DWG converter (watch for privacy/watermarks).
5. Import into CAD and refine
   • Open DWG/DXF in AutoCAD, BricsCAD, LibreCAD, or QCAD.
   • Snap/scale the drawing to correct dimensions (use a known dimension on the JPG to scale).
   • Convert curves to polylines, join segments, set layers, set line types.
   • Recreate or snap architectural/engineering entities as needed for precision.

Method 2: Free Desktop Software (More Control)