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This work presents a 2nd-order, multi-bit Continuous-time Quadrature Bandpass Delta-Sigma (CT QBP ΔΣ) modulator with a Pseudo-random Quadrature Mismatch Shaping (PQMS) algorithm for GSM-EDGE/Bluetooth Low-IF receiver. CT QBP ΔΣ modulator is vulnerable to mismatches between its in-phase and quadrature (I/Q) paths that can dramatically degrade its Signal to Noise-plus-Distortion Ratio (SNDR) and image-rejection ratio (IRR). This modulator incorporates a proposed PQMS to mitigate the main I/Q mismatch source from multi-bit I/Q DAC units to improve IRR The CT QBP ΔΣ modulator is fabricated in a 0.18-μm CMOS process. With the proposed PQMS, the modulator achieves a dynamic range of 82/69 dB in 200 kHz/1 MHz, respectively. The IRR is better than 65 dB with -4 dBFS input level and the whole CT QBP ΔΣ modulator consumes less than 8.5 mW in both modes from a 1.8-V supply voltage.