The effects of mismatch in complex bandpass ΔΣ modulators

Mismatch between the real and imaginary channels of a complex system is examined and equations are presented that show the relationship between mismatch and image rejection. An example is given that demonstrates the effects of mismatch on the properties of a complex filter. These results are applied to the design of a fourth-order complex bandpass ΔΣ modulator and a technique is discussed that alleviates the negative effects of mismatch on modulator performance. The technique modifies a modulator´s noise transfer function by placing a notch in its image band, giving an SNR performance improvement of approximately 15 dB (2.5 bits) over an unmodified modulator. The practical implementation of this technique is discussed