A Class of Quantizers With DC-Free Quantization Noise and Optimal Immunity to Nonlinearity-Induced Spurious Tones

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phase-locked loops (PLLs) typically use noise-shaping coarse quantizers to control their instantaneous output frequency. The resulting quantization noise and its running sum inevitably get distorted by non-ideal analog components within the PLL, which induces undesirable spurious tones in the PLL's output signal. A recently proposed quantizer, called a successive requantizer, has been shown to mitigate this problem. Its quantization noise and the running sum of its quantization noise can be subjected to up to fifth-order and third-order nonlinear distortion, respectively, without inducing spurious tones. This paper extends the previously published successive requantizer results to enable the design of successive requantizers whose quantization noise running sum sequences attain such immunity to nonlinearity-induced spurious tones up to arbitrarily high orders of distortion. The extended results are used to design example successive requantizers whose quantization noise and quantization noise running sum sequences have optimally reduced susceptibility to nonlinearity-induced spurious tones.