Quadrature mismatch shaping with a complex, tree structured DAC

Quadrature SigmaDelta ADCs require a feedback path for both the I and the Q part of the complex feedback signal. If two separated multibit feedback DACs are used, mismatch among the unit DAC elements leads to additional mismatch noise in the output spectrum as well as an unbalance between the I and Q DAC. This paper proposes a new quadrature bandpass mismatch shaping technique. In our approach the I and Q DACs are merged into one complex DAC, which leads to near-perfect I/Q balance. To select the unit DAC elements of the complex, multibit DAC, the well-known tree structured element selection logic is generalized toward a complex structure and necessary conditions for its correct operation are derived. Finally, a very efficient first-order quadrature shaper implementation is proposed and simulations show the effectiveness of the quadrature bandpass mismatch shaping technique