Compensation of mismatch errors in a time-interleaved analog-to-digital converter
A method for the compensation of frequency-response mismatch errors in M-channel time-interleaved ADCs. The compensation is done utilizing a technique that makes use of a number of fixed filters, that approximate differentiators of different orders, and a few variable multipliers that directly correspond to parameters in polynomial models of the M channel frequency responses. A compensated M-channel time-interleaved ADC is based on and can perform the method.
1. A method for compensating frequency response mismatch errors in an M-channel interleaved analog-to-digital converter (TI-ADC) comprising M ADCs (1 1 −1 M ) in an array and a filter structure connected to the output of the TI-ADC, the method comprising:
selecting M frequency functions of order P,
determining M (P+1) coefficients ε pr ; p=0,1, . . . , P; r=0,1, . . . M−1 of said frequency functions,
choosing an approximation order K, and
computing a compensated output sequence by applying the TI-ADC output to said filter structure containing multipliers with said coefficients ε pr and M fixed filters G p (z), p=1,2, . . . , M.
2. The method according to claim 1 , further comprising:
denoting the channel responses by Q r (jω),
determining the polynomial models of the frequency functions of the channel responses Q r (jω), r=0,1, . . . , M−1 given as
Q r ( jω )=ε 0r (1+ε 1r ×( jω )+ε 2r ×( jω ) 2 + . . . +ε Pr ×( jω ) P ).
3. The method according to claim 1 , further comprising:
choosing a reference channel r ref ,
denoting the channel responses by Q r (jω),
determining polynomial models of the frequency functions Q r (jω)/Q r ref (jω), r=0,1, . . . , M−1 given as:
Q r ( jω )/Q r ref ( jω )=ε 0r (1+ε 1r ×( jω )+ε 2r ×( jω ) 2 + . . . +ε Pr ×( jω ) P ),
wherein p=0,1, . . . , P; r=0,1, . . . , M−1; r≠r ref and ε pr ref is set to ε 0r ref =1 and further ε pr ref =0 for p=1,2, . . . , P.
4. The method according to claim 1 , further comprising:
approximating pth order differentiators G p (z).
5. The method according to claim 1 , further comprising:
optimizing G p (z) simultaneously.
6. A compensated analog-to-digital time-interleaved converter, comprising:
a number of M channels,
each channel including an ADC (1 1 −1 M ), and
a filter structure (2) connected to the output of the M channel TI-ADC,
wherein the converter is configured to carry out a method for compensating frequency response mismatch errors in the converter, the method comprising
selecting M frequency functions of order P,
determining M (P+1) coefficients ε pr ; p=0,1, . . . , P; r=0,1, . . . M−1 of said frequency functions,
choosing an approximation order K, and
computing a compensated output sequence by applying the TI-ADC output to said filter structure containing multipliers with said coefficients ε pr and M fixed filters G p (z), p=1,2, . . . , M.
7. The compensated analog-to-digital converter according to claim 6 , wherein said filter structure comprises a number of fixed filters G p (z) and variable multipliers.
8. The compensated analog-to-digital converter according to claim 6 , wherein the filter structure has G p (z) filters corresponding to pth order differentiators.
9. The compensated analog-to-digital converter according to claim 6 , wherein said filter structure has variable multipliers corresponding to the coefficients ε pr .