The present study aims at application of the novel direct method developed by Kumar and Munjal for naturally aspirated engines [Applied Acoustics 135, 70–84 (2018)] to the turbocharged engine’s exhaust system for estimation of acoustic source characteristics. In this paper, transfer matrices of the turbine and compressor of an automotive turbocharger are derived. Mass continuity across the turbine and compressor along with the respective static pressure ratios are used for deriving their transfer matrices. The acoustic source characteristics of each cylinder for the source-load junction downstream of the exhaust valve/s is computed assuming that the cylinder discharges to the ideal pressure release boundary condition with the constant pressure being product of the turbine pressure ratio and mean pressure in the exhaust pipe downstream of the turbine. Source characteristics of each cylinder are used to estimate the source characteristics downstream of the exhaust manifold. Using the derived transfer matrix of the turbine, the source characteristics are further estimated at the source-load junction downstream of the turbine. Finally, the estimated source characteristics of the engine downstream of the turbine are used to predict the unmuffled sound pressure level (SPL) spectrum which is shown to compare reasonably well with the experimentally measured values. Importance of acoustic modelling of the turbine is highlighted by comparing the SPL spectra predicted using the estimated source characteristics with and without the turbine. The estimated source characteristics and unmuffled approximate SPL spectrum of a turbocharged engine being thus known at the engine’s inception stage, the present study can be used for the integration of design and analysis of the engine and muffler.