# On High-Speed Digital-to-Analog Converters and Semi-Digital FIR Filters

Abstract: High-speed and high-resolution digital-to-analog converters (DACs) are vital components in all telecommunication systems. Radio-frequency digital-to-analog converter (RFDAC) provides high-speed and high-resolution conversion from digital domain to an analog signal. RFDACs can be employed in direct-conversion radio transmitter architectures. The idea of RFDAC is to utilize an oscillatory pulse-amplitude modulation instead of the conventional zero-order hold pulse amplitude modulation, which results in DAC output spectrum to have high energy high-frequency lobe, other than the Nyquist main lobe. The frequency of the oscillatory pulse can be chosen, with respect to the sample frequency, such that the aliasing images of the signal at integer multiples of the sample frequency are landed in the high-energy high-frequency lobes of the DAC frequency response. Therefore the high-frequency images of the signal can be used as the output of the DAC, i.e., no need to the mixing stage for frequency up-conversion after the DAC in the radio transmitter. The mixing stage however is not eliminated but it is rather moved into the DAC elements and therefore the local oscillator (LO) signal with high frequency should be delivered to each individual DAC element.In direct-conversion architecture of IQ modulators which utilize the RFDAC technique, however, there is a problem of finite image rejection. The origin of this problem is the different polarity of the spectral response of the oscillatory pulse-amplitude modulation in I and Q branches. The conditions where this problem can be alleviated in IQ modulator employing RFDACs is also discussed in this work.?? modulators are used preceding the DAC in the transmitter chain to reduce the digital signal’s number of bits, still maintain the same resolution. By utilizing the ?? modulator now the total number of DAC elements has decreased and therefore the delivery of the high-frequency LO signal to each DAC element is practical. One of the costs of employing ?? modulator, however, is a higher quantization noise power at the output of the DAC. The quantization noise is ideally spectrally shaped to out-of-band frequencies by the ?? modulator. The shaped noise which usually has comparatively high power must be filtered out to fulfill the radio transmission spectral mask requirement.Semi-digital FIR filter can be used in the context of digital-to-analog conversion, cascaded with ?? modulator to filter the out-of-band noise by the modulator. In the same time it converts the signal from digital domain to an analog quantity. In general case, we can have a multi-bit, semi-digital FIR filter where each tap of the filter is realized with a sub-DAC of M bits. The delay elements are also realized with M-bit shift registers. If the output of the modulator is given by a single bit, the semi-digital FIR filter taps are simply controlled by a single switch assuming a current-steering architecture DAC. One of the major advantages is that the static linearity of the DAC is optimum. Since there are only two output levels available in the DAC, the static transfer function, regardless of the mismatch errors, is always given by a straight line.In this work, the design of SDFIR filter is done through an optimization procedure where the ?? noise transfer function is also taken into account. Different constraints are defined for different applications in formulation of the SDFIR optimization problem. For a given radio transmitter application the objective function can be defined as, e.g., the hardware cost for SDFIR implementation while the constraint can be set to fulfill the radio transmitter spectral emission mask.

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