Why Do All Node Voltages Calculate as Zero in My AC Nodal Analysis Equations?

The discussion addresses a problem in AC nodal analysis where all node voltages (V1, V2, V3) calculate as zero. The original poster provided nodal equations involving complex impedances and an AC source with a complex value of 0 + 60i (60∠90°). Respondents highlighted issues such as missing schematic details, incorrect or inconsistent node definitions, and algebraic errors in the equations. Key points include the necessity of correctly setting up the nodal admittance (Y) matrix with the AC source terms properly included on the right-hand side to avoid trivial zero solutions. The importance of verifying complex algebra, converting between polar and rectangular forms, and ensuring the reference node is correctly assigned despite reactive components (inductors and capacitors) was emphasized. It was suggested to check branch currents and node voltages by combining impedances in series/parallel and to use software tools for matrix solving once equations are correctly formulated. The zero voltage result likely stems from an incorrect matrix setup where the source term was not properly isolated, leading to a zero Y matrix and thus trivial solutions. Correcting the matrix to include the source voltage as a nonzero entry in the excitation vector enables solving for nonzero node voltages.
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