In a wide-band RF system, the RF channel is located within 50 MHz to 9 GHz. A high-frequency resolution phase-locked loop (PLL) with 100$\%$ tuning range oscillator is the core to generate the RF carrier frequency which covers such a wide range. The phase noise and spurs of the PLL are required to be low to avoid degrading RF system performance. A PLL applies $\Sigma \Delta$ modulation to increases its resolution and is known as a fractional-N PLL, but $\Sigma \Delta$ modulation introduces considerable quantization noise into the loop. The nonlinearity of the PLL also converts part of the noise into fractional-N spurs. Noise cancellation is usually applied to eliminate this quantization noise. Calibration, often with long settling time, is necessary to maintain cancellation efficiency. Power intensive calibration is also required to notch spurious tones.

In this thesis, we first investigate the delay-locked loop (DLL) and attempt to use DLL to replace PLL as an RF frequency synthesizer. An LTI model of DLL is established, which indicates the limitation of DLL as a high-performance synthesizer. Then, the thesis focuses on PLL again. A calibration-free triple-loop PLL is introduced. The merits of heterodyne PLL are rediscovered, which applies a mixer in the loop to translate the VCO frequency to a low-frequency feedback signal. By implementing the harmonic mixing concept, the designed prototype effectively reduces the pulling risk of a traditional heterodyne PLL, allowing it to be integrated on a single chip. This PLL provides higher-order noise filtering and can naturally reduce fractional-N PLL noise and spurs. An analytical model for this PLL is also presented, which allows us to fully appreciate this PLL and optimize the loop design. After this, a sub-sampling PLL-based low-noise frequency extender is introduced, which increases the tuning range of an oscillator from 30$\%$ to 100$\%$, and requires only a small chip area. By combining the triple-loop PLL and the frequency extender, a synthesizer which can support a wideband radio system is achieved.

We study the jitter performance of multiplying delay locked loops (MDLLs) and provide an effective approach to derive the phase noise of open loop MDLLs. We demonstrate that the ring oscillator phase noise models from Abidi and Hajimiri are essentially the same. Based on the analysis for MDLL jitter performance, new system models for Edge Combining DLLs and Recirculating DLLs are proposed which are accurate and simple for stability and noise analysis. Moreover, spurs caused by mismatch errors in Edge Combining DLLs are studied based on the new system model.