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<formula formulatype="inline"><tex Notation="TeX">$B$</tex></formula>-modes are special patterns in cosmic microwave background (CMB) polarization. Degree-scale <formula formulatype="inline"><tex Notation="TeX">$B$</tex></formula>-modes are smoking-gun signatures of primordial gravitational waves. The generic strategy of CMB polarization experiments is to employ a large number of polarimeters for improving the statistics. The Q/U Imaging ExperimenT-II (QUIET-II) has been proposed to detect <formula formulatype="inline"><tex Notation="TeX">$B$</tex></formula>-modes by using the world's largest coherent polarimeter array (2,000 channels). A unique detection technique using QUIET's polarimeters, which comprises a modulation/demodulation scheme, enables us to directly extract polarization signals. The extracted signals are free from unpolarized components and intrinsic <formula formulatype="inline"><tex Notation="TeX">$1/f$</tex></formula> noise. We developed a data readout system for the QUIET-II experiment. We employed a &#x201C;master&#x201D; clock strategy, on-board demodulation functions, and end-to-end Ethernet connections for logical simplicity and high-density compact electronics for physical compactness. A clock module acts as a single master and guarantees phase matching between the modulation by the polarimeters and the on-board demodulation by ADC modules. Each ADC module has 64 ADC chips in the VME-6U single slot size. Both modules have hardware processors for Ethernet TCP/UDP. All these modules and control computers are connected via end-to-end Ethernet. Physical compactness and logical simplicity enable us to easily handle a large number of polarimeters, while maintaining quality of the <formula formulatype="inline"><tex Notation="TeX">$B$</tex> </formula>-mode experiments. The developed electronics (the clock modules and the ADC modules) fulfill these requirements. Tests with a setup similar to that of the real experiment proved that the system works appropriately. The performance of all system components is validated to be suitable for <formula formulatype="inline"><tex Notation="TeX">$B$</tex></formula>-mode measurements.

Readout System With On-Board Demodulation for CMB Polarization Experiments Using Coherent Polarimeter Arrays