Digital Background Calibration Algorithm for "Split ADC ... - CiteSeerX
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Digital Background Calibration Algorithm for "Split ADC ... - CiteSeerX
digital domain whenever possible. The desired architecture should implement all calibration and error correction digitally, while relaxing required performance ...
> 3354 3354 3354 3354 3354 3354 SDKB4 " SDKB3 always, even for DC inputs. Behavioral simulations have indicated that for a wide range of input signal conditions (for example: DC, random noise, periodic signals at multiples of the conversion frequency) the activity in matrix coefficients enabled by choosing different residue modes is sufficient to prevent singularity in the matrix coefficients corresponding to εA and εB. V. ITERATIVE MATRIX SOLUTION PROCEDURE A. Jacobi iteration method review As mentioned previously, matrix inversion is avoided to simplify the digital hardware implementation. It will be seen that the procedure used has the additional advantage of dealing gracefully with matrix singularity. The procedure is based on the Jacobi iteration method [17, 18], which is now briefly reviewed: Suppose we are trying to solve a linear system $S11 & S " e = d # &S21 &%S31
in which the di are observations of a system (in our case the ∆x differences), ei are unknown parameters (the estimate errors) we are trying to determine based on the observations, and the Sij are known coefficients in (27) describing how the various parameters ei affect the observations di . Expanding the matrix product for the first row gives (29)
S11e1 + S12e2 + S13e3 = d1
!
If we already knew e2 and e3, we could solve for e1 . In the Jacobi iteration procedure, we develop the next (new) iteration for e1 using the previous (old) values of e2 and e3: e1(new) =
!
(28)
1 d1 " S12e2 (old ) " S13e3 (old ) S11
(
)
Analogous expressions can be derived for e2 and e3 using the other rows of the S matrix. Expressing the iteration in matrix form gives
