Wide-Band Low Phase-Noise Signal Generation Using Coaxial Resonator in Cascaded Phase Locked Loop

1. Introduction

The relentless growth of data traffic in modern communication systems and radar-based sensing compels advancements in signal generation technologies. While traditional narrowband signals served past needs well, they are inadequate for the ever-expanding bandwidth requirements [1]. Modern systems often necessitate adaptability, accommodating diverse regional regulations and dynamic operating conditions [2]. This shift demands a paradigm change from simple, predetermined narrowband oscillators to sophisticated signal generation schemes. Local oscillators (LOs) now operate across a broad spectrum, often exceeding several GHz, while maintaining exceptional phase noise performance for complex digital modulations [3]. Additionally, minimizing spurious components is crucial to prevent interference with non-permissible bands. This paper presents a novel approach to LO design, specifically addressing wideband operation while overcoming the challenges associated with wideband sweeps in traditional PLL-based architectures.

Over the past four decades, extensive research has explored methodologies for generating low-noise LO signals across a wide frequency range [4,5,6,7]. While these techniques share the common goal of achieving such performance, they can be broadly classified into three distinct design approaches: analog, digital, and hybrid. Analog implementations leverage frequency mixing and doubling techniques. Digital approaches utilize high-speed digital-to-analog converters (DACs) for direct digital synthesis (DDS). Finally, hybrid methods, typically implemented as phase-locked loops, combine both analog and digital functionalities.

Purely analog designs for LO generation have become less prevalent due to their reliance on multiple mixing stages with analog filtering and signal switching. These stages increase production costs significantly. DDS systems suffer other issues. While offering programmability, their maximum achievable frequency is ultimately constrained by lithography advancements [8]. Additionally, high-speed operation often leads to significant heat dissipation challenges. For these reasons, phase-locked loops have emerged as the dominant architecture for LO generation [9]. Combining both analog and digital functionalities, PLLs offer a balance between performance and cost. Recently, advancements in lithography have enabled the integration of PLL structures and high-frequency oscillators onto a single silicon wafer [4,10]. Leveraging established chip production processes, this integration facilitates significant cost reductions.

While wideband Voltage-Controlled Oscillators (VCOs) exist, their implementation in silicon remains challenging due to the limitations of integrated varicap diodes [11]. This necessitates the use of multiple narrowband oscillators, switched digitally to achieve wideband operation, and maintain cost-effectiveness. However, this approach often requires fractional-N operation during sweeps, introducing unwanted fractional spurs [12].

Several techniques like dithering, MASH-modulators, and current balancing have been employed to reduce fractional spurs, but complete suppression remains elusive [5,13,14]. Alternatively, operating solely in integer-N mode eliminates fractional spurs, but a swept reference frequency must be implemented. However, traditional DDS circuits employed for this method struggle with heat dissipation and require complex, power-hungry digital signal processing (DSP) systems [15,16].

With advancements in PLL technology and integrated VCOs, a novel approach emerges: substituting the DDS with a fractional PLL to generate a high-frequency reference for a second PLL [17]. This configuration allows operation in a region free of fractional spurs, enabling nearly automated wideband frequency sweeps or hopping.

This research explores method to generate high-frequency signals with minimal fractional spurs, low phase noise, and reduced circuit complexity. A functional prototype covering the wide frequency range of 2-16 GHz has been developed. This two-stage PLL design can be implemented on a compact 50x20 mm footprint (four-layer PCB).

To potentially improve phase noise performance, the concept of incorporating a ceramic coaxial resonator in the first-stage oscillator is proposed. This paper presents and compares measured phase noise at 5 and 10 GHz where -102.5 dBc/Hz at 100 kHz frequency offset is achieved. Additionally, the impact of the coaxial resonator on phase noise and loop bandwidth at the first PLL stage is assessed. The design's usability is further demonstrated through measurements of fractional spurs and lock time.

The paper is organized in the following manner: Chapter 2 provides an overview of the theoretical foundation of phase-locked loop operation, with a specific emphasis on phase noise; In Chapter 3, a two-stage cascaded PLL loop structure with a high-Q coaxial resonator is proposed; In Chapter 4, measurements of phase noise, switching time, and comparisons with existing implementations are presented; Chapter 5 summarizes the main findings of the working prototype and emphasizes the benefits of the proposed solution; Lastly, Chapter 6 explores the potential for integrating the entire structure onto a single silicon wafer.

2. Phase-Locked Loop Principle and Phase Noise

2.1. Phase-Locked Loop

Modern radio systems require adjustable frequency sources with high accuracy, long-term stability, and low phase noise. While high-frequency oscillators using varicap diodes lack these qualities, crystal oscillators, known for excellent phase noise and stability, suffer from limited frequency tunability. Phase-locked loops address this challenge by combining the strengths of both oscillator types. In a PLL, a crystal oscillator acts as a highly stable reference, while a feedback loop with a frequency divider and a phase detector ensures the output signal remains synchronized (locked) to the reference in phase and frequency. The integer value of the modulo divider allows for precise adjustment of the output frequency. Figure 1 illustrates the basic structure of a PLL loop.

The behavior of a PLL can also be represented mathematically. Here, $K_{\mathsf{\Phi }}$ and $K_{VCO}$ represent the gains of the charge pump (CP) and the VCO, respectively, where:

$$K_{\mathsf{\Phi }}=\frac{\mathsf{\Delta }\mathrm{I}}{\mathsf{\Delta }\mathsf{\Phi }} \left[\frac{A}{rd}\right] and K_{VCO}=\frac{\mathsf{\Delta }{\omega }_{VCO}}{\mathsf{\Delta }\mathrm{U}} \left[\frac{A}{rd}\right] .$$

(1), (2)

Building upon the concept of individual component gains, the overall loop transfer function $H\left(\omega \right)$ of the PLL can be described as:

$$H\left(\omega \right)=\frac{{\mathsf{\Phi }}_{REF}}{\mathsf{\Delta }\mathsf{\Phi }}=K_{\mathsf{\Phi }}\cdot \frac{1}{j\omega C_1+\frac{1}{R+\frac{1}{j\omega C_2} }}{\cdot K}_{VCO}\cdot \frac{1}{N}\cdot \frac{1}{j\omega }$$

(3)

PLL filter is typically characterized by its zeros ${\tau }_2$ and poles ${\tau }_1$, represented mathematically as:

$${\tau }_2=R{C}_2 and {\tau }_1=R\frac{C_1{C}_2}{C_1+C_2} .$$

(4), (5)

Equation (3) can be rewritten in a more concise form by substituting the values derived in Equations (4) and (5):

$$H\left(\omega \right)=\frac{{-K}_{\mathsf{\Phi }}{K}_{VCO}}{{\omega }^{2}N(C_1+C_2)}\cdot \frac{1+j\omega {\tau }_2}{1+j\omega {\tau }_1}$$

(6)

When the phase error $\mathsf{\Delta }\mathsf{\Phi }$ between the reference signal and the output oscillator becomes sufficiently small, the loop achieves lock. Utilizing the PLL's transfer function, as presented in Equation (6), we can express the phase error $\mathsf{\Delta }\mathsf{\Phi }$ or the output signal phase ${\mathsf{\Phi }}_{OUT}$ as:

$$\mathsf{\Delta }\mathsf{\Phi }=\frac{{\mathsf{\Phi }}_{REF}}{1+H\left(\omega \right)} and {\mathsf{\Phi }}_{OUT}={\mathsf{\Phi }}_{REF}\cdot \frac{H\left(\omega \right)}{1+H\left(\omega \right)} .$$

(7), (8)

In many applications, output frequencies require steps smaller than the reference frequency. To achieve this fractional-N synthesis, the PLL architecture is modified by incorporating a sigma-delta modulator (Σ-∆). This modulator precisely adjusts the value of the divider between N and N+1, effectively generating a fraction of the reference frequency based on a desired percentage.

However, a crucial aspect of fractional-N PLLs is minimizing the appearance of unwanted spectral components called fractional spurs around the output frequency [18]. The switching pattern of the N divider should closely resemble ambient noise to mitigate these spurs. Unfortunately, complete elimination is not possible, especially within the loop filter's bandwidth. To address this challenge, fractional-N PLLs typically employ high-order loop filters, such as third or fourth-order designs. These filters offer a steeper transition to the stopband, resulting in greater attenuation of the Σ-∆ modulator spurs and improved overall spectral purity of the output signal.

A persistent challenge arises near fractional N-division values. In these regions, the loop bandwidth may be insufficient to adequately attenuate spurs. Additionally, traditional countermeasures, such as dithering and current balancing, can significantly degrade overall phase noise performance [19]. This work proposes a novel approach that mitigates the impact of these spurs by strategically operating the PLLs away from these critical fractional N-division values.

2.2. Phase Noise in PLL

PLLs offer a powerful technique for not only enhancing the stability and accuracy of high-frequency oscillators, but also for shaping the output noise spectrum [19]. As described by Equation (7), the output signal's phase is directly determined by the reference signal's phase and the loop transfer function. The components within the PLL architecture can either contribute additional phase noise (non-linear elements) or modify the existing noise characteristics (passive components). By carefully selecting the loop's operating conditions, significant improvements in phase noise performance can be achieved compared to a standalone high-frequency oscillator [20]. Figure 2 exemplifies the impact of non-linear components on the resulting noise spectrum.

In PLLs utilizing a high-quality reference oscillator, such as a piezoelectric resonator, the VCO and the Σ-∆ modulator become the primary contributors to the output signal's phase noise [21]. While the modulator's noise in fractional-N mode cannot be entirely eliminated, a low-pass filter following the charge pump can influence its contribution. However, for stability reasons, the loop filter's corner frequency must remain significantly lower than the phase detector (PD) operating frequency. At low frequency offsets, the PD noise, along with the reference phase noise, dominates the overall noise profile. Conversely, at higher offsets, the VCO noise becomes the primary contributor. To minimize the impact of the inherently wide VCO phase noise, a narrow loop bandwidth is desirable. Narrower filters result in longer PLL lock times, therefore there is a trade-off with this method. As shown in Equation (3), a faster PD, a higher-order narrow-band filter, and a lower VCO voltage-to-frequency gain all contribute to improved phase noise performance.

The simulation results in Figure 3 visually demonstrate the influence of different loop filter bandwidths on the output phase noise. When a narrow filter is employed, the output noise is primarily dominated by the oscillators' intrinsic noise. In contrast, wider bandwidth filters allow the Σ-∆ modulator's noise to have a more significant impact on the overall noise profile [22].

Even with exceptional PLL characteristics, the inherent phase noise of the VCO becomes the dominant factor at larger frequency offsets [21]. High-Q resonators are crucial for minimizing phase noise [23,24]. While crystal oscillators boast Q-factors in the 10⁵ range, traditional LC-VCOs typically achieve Q-factors limited to a few hundred due to the challenges associated with fabricating high-quality inductors [25]. However, crystal oscillators with fundamental frequencies above 100 MHz are unattainable, and cavity resonators become impractical below 5 GHz due to their size constraints. Ceramic coaxial resonators offer a viable alternative for the intermediate frequency range. These passive devices exhibit low loss, and their characteristics are primarily determined by their physical dimensions, making them well-suited for bandpass filter applications [26,27,28,29].

Incorporating a λ/2 or λ/4 coaxial resonator within an active loop enables the creation of a high-Q oscillator [30,31]. When coupled with a suitable varicap diode, this approach facilitates the development of a narrowband VCO [32,33]. While not a prevalent technique in existing literature, this research proposes the utilization of a coaxial resonator based VCO to achieve superior phase noise performance [34]. The phase noise measurements presented in Chapter 4 validate the rationale behind this approach and demonstrate the effectiveness of this construction method.

3. Proposed Design of Cascaded PLLs

Figure 4 illustrates the proposed wideband signal generator, which leverages a cascaded architecture employing two independent PLLs with dedicated VCOs. This design offers distinct advantages in terms of phase noise and fractional spur suppression compared to conventional approaches.

In conventional wideband signal generators, a common strategy utilizes a fractional mode of second PLL. The first PLL multiplies a relatively slow reference signal to enhance the performance of the second stage. While this approach facilitates faster sweeps, it inherently introduces fractional spurs, particularly when aiming to use the full bandwidth of the VCO. If mitigating fractional spurs is critical, a DDS can be implemented instead of the first PLL and integer-N mode selected for the second one. However, a DDS typically leads to increased power consumption and higher DSP circuit complexity. Additionally, a wideband VCO, often fabricated on non-silicon substrates and packaged in ceramic enclosures, becomes a necessity, resulting in significantly higher costs.

This work departs from conventional methods and proposes a new solution strategy for the problem. A high-frequency oscillator, comprised of multiple independent narrowband oscillators (#7), is integrated onto a single silicon die alongside the entire PLL structure, except for the loop filter (#6). This integrated circuit, designated as PLL 2 in Figure 4, can be any commercially available option. To eliminate fractional spurs in the signal spectrum, this PLL operates in integer mode. Its loop filter (#6) is designed with a reasonable bandwidth to ensure rapid lock during oscillator switching.

For optimal phase noise performance, the phase comparator within PLL 2 should operate at the highest possible frequency. Since voltage-controlled crystal oscillators (VCXOs) offer limited tuning range (typically a few kHz), a standard LC circuit is employed to create a suitable VCO (#3). This VCO is locked to the highly stable crystal oscillator (#1) using a separate, readily available IC (PLL 1). To maintain low phase noise and avoid fractional spurs, the loop filter (#2) of PLL 1 is designed to be narrowband. Here, lock time is less critical as the frequency of (#3) only varies slightly, and the phase noise of PLL 1 is the primary factor influencing the performance of the second stage.

When the output frequency (#7) surpasses the nominal crystal oscillator frequency (#1) by a factor of at least 100, PLL 1 can be configured to operate in a region sufficiently distant from integer multiples of the reference signal. This ensures that fractional spurs remain outside the loop bandwidth (#2) and are not present in the output spectrum. Since PLL 2 operates in integer mode and generates no fractional spurs, and the reference signal is also spur-free, an exceptionally clean output spectrum is achievable.

Thus, in the suggested architecture, the first PLL operates in fractional mode, replacing the commonly used DDS. It then drives the second (main) PLL, which is programmed to work in integer mode. This configuration allows for retaining low phase noise and obtaining a reasonable lock time. To further enhance the lock time of both PLLs, the loop bandwidth can be dynamically controlled through two methods: (1) by switching an additional resistor in or out of the loop (#8), and (2) by adjusting the charge pump current. Lower current values narrow the filter, while higher currents widen it. This technique has been previously demonstrated as effective, yielding good phase noise performance during narrowband and fast locking for wideband sweeps.

Figure 5 presents the selection of ICs and their corresponding operating frequencies, which serve to validate the feasibility of the proposed design. A 40 MHz temperature-controlled oscillator (TCXO) (#1) was selected due to its widespread use in GNSS receivers, offering excellent phase noise and temperature stability. The LMX2491 and MAX2609 [35,36], along with an additional buffer amplifier (#5), constitute the first PLL. Due to the LMX2491's 1/N₁ limitations with a minimum division ratio of 16 and the STuW81300 input range [37], the reference frequency is initially divided by 2. This necessitates an oscillator (#3) output frequency exceeding 320 MHz. The STuW81300 can accept reference frequencies up to 800 MHz. Therefore, it is advantageous to generate frequencies with PLL 1 as close to this limit as possible to maximize the operating frequency of the phase detector within PLL 2. Additionally, the STuW81300's 1/R₂ divider also has an upper limit, requiring an additional reference division factor of 4. This selection helps maintain low phase noise of the STuW81300's integrated oscillators (#7).

The MAX2609 with integrated varicap diodes was chosen as the VCO as its small package enables a compact design. It requires an external inductor (#4) to form a resonant circuit. While a high-quality wire-wound inductor is typically used to determine the nominal VCO frequency, our results demonstrate that it can be replaced with a ceramic coaxial resonator for enhanced performance. Additional buffer amplifiers are employed to raise the signal level and further improve isolation between the two PLL stages.

Figure 6 details the chosen frequency selection and required divider values for the implemented integrated circuits. While alternative ICs may necessitate different structure, the chosen STuW81300 offers several advantages: a wide operating frequency range exceeding a decade, integrated Low-Dropout Regulators (LDOs) for power management, and compatibility with high input frequencies. The LMX2491 complements this choice by enabling versatile automatic sweeps with minimal user intervention. This combination allows the utilization of a standard microcontroller instead of dedicated DSP hardware, simplifying design and potentially reducing cost.

For a more detailed explanation of how the sweep is achieved in the manufactured prototype based on the structure in Figure 5, please refer to Appendix A.

4. Experimental Results

To validate the proposed cascaded PLL design, a two-stage prototype was constructed and rigorously tested. Figure 7 depicts the first stage, showcasing the LDO power supply on the left, the LMX2491 integrated circuit in the center, and the oscillator circuit with a coaxial resonator on the right. An SMA connector facilitates switching between the phase noise measurement setup and the semi-rigid coaxial connection to the second stage. The first PLL is configured via Serial Peripheral Interface (SPI) control lines (left side) using an external microcontroller (not shown). Embedded code running on this microcontroller allows for parameter adjustments through a custom control interface.

The second PLL stage was fabricated on a commercially produced four-layer PCB to ensure proper thermal management and maintain the package junction temperature within operational limits. Similar connections were made for the microcontroller, and the generated reference clock was linked via a semi-rigid cable. Photographs of the final industrial-grade PCBs are provided in Appendix A (Figure 14).

Throughout the design phase, the signal spectrum, phase noise, and lock time were continuously monitored. The final measurement setup is shown in Figure 8. An Agilent E4445A served as the primary instrument for measuring frequency spectrum and phase noise. A custom Python script running on a personal computer facilitated automated phase noise measurements and data storage. Parameters of the PLL loops were monitored and adjusted through the MCUs' serial wire debug interface. A Rigol DHO1102 was utilized to observe the lock time and VCO tuning voltage behavior in both PLL loop filters. Powering and current monitoring of the prototype were achieved using Rigol DP832A and HP 34401A, respectively.

Initial investigations demonstrated significant phase noise improvements when replacing the wire-wound inductor with a coaxial resonator. As depicted in Figure 9(a), this substitution resulted in approximately 6.5 dB lower phase noise at a 10 kHz offset (8 kHz loop bandwidth) measured at the 480 MHz output of PLL 1. Notably, with a wider loop bandwidth (demonstrated with 100 kHz loop filter and inductor), the high-quality coaxial resonator within the VCO dictates the loop characteristics, leading to a narrowband response and a drastically altered phase noise profile, as seen in Figure 9(b). Consequently, the loop bandwidth was adjusted to roughly match the characteristics of the coaxial resonator, enabling a more relevant comparison of the phase noise change.

The addition of PLL 2 facilitated phase noise measurements at higher frequencies. Figure 10 presents the measured phase noise at 5 GHz and 10 GHz. The 5 GHz signal represents the fundamental frequency of the STuW81300’s oscillator, while the 10 GHz signal is internally multiplied. The positive impact of the coaxial resonator in PLL 1 on phase noise is evident here as well. Further improvements were achieved by employing a lower charge pump current in PLL 1 (approximately 30% of the nominal 3 mA). It is noteworthy that these performance changes were observed at the output of PLL 2, despite modifications being made solely to PLL 1 settings or VCO components.

Figure 11 displays the signal spectrum at 9.545 GHz, a scenario where the worst-case settings of both PLL loops could potentially generate fractional spurs. As observed from the spectrum, no significant spurs are present near the carrier signal, or they are at least 80 dBc lower.

Figure 12 depicts the lock time of the PLL 1 oscillator. This measurement represents the worst-case scenario, where the frequency is swept from its minimum to its maximum value to perform a sufficient sweep at the output of PLL 2.

5. Discussion

The realization of a cascaded PLL design where the first stage performs the actual sweep and the second acts solely as a frequency multiplier became feasible only with recent advancements in integrated circuits incorporating PLL structures. A key limitation stemmed from the use of dual-modulus dividers (e.g., 16/17) for high-frequency division. While these dividers enable contiguous N values, they limit the minimum N achievable (in our case to 16). To prevent fractional spurs, operation must occur away from integer multiples of the reference frequency. Consequently, the phase detector frequency needs to be approximately 20% higher than the desired sweep bandwidth. Because of the N divider limitation this typically translates to operation above 300 MHz, a frequency that many traditional PLL ICs cannot handle as a reference input.

As demonstrated in Chapter 4, this approach achieves a fractional spur-free spectrum. However, a trade-off between phase noise and lock time remains, as with all PLLs. Some systems prioritize exceptional phase noise as they only change frequency during channel switching. Others require fast, wideband sweeps, thus necessitating minimal lock times. Spectrum analyzers, on the other hand, demand both qualities: fast sweep times for wider spans and good phase noise for narrowband measurements. In such cases, the otherwise excellent noise performance of the coaxial resonator comes at a cost. We observed that it tends to force the loop bandwidth to be narrower. A coil is a suitable choice in these scenarios, as the loop bandwidth can be more easily influenced by adjusting the charge pump current.

Our research also revealed that PLL 2 should have a loop bandwidth exceeding 10 kHz. Values below this significantly extend lock time for large frequency steps.

Sourcing coaxial resonators presents another challenge. While high-volume manufacturing is possible upon request, they are generally difficult to obtain otherwise. Siemens B69610-G5206 was ordered for the protype design [38].

For this research, 480 MHz was chosen as the first PLL frequency to demonstrate the working principle, as this was the readily available resonator frequency during the investigation. Ideally, this frequency should be closer to 800 MHz for our PLLs. Commercially available components could readily achieve 650 MHz without requiring special VCO construction. This option was also tested; however, despite changes in lock time performance, no significant improvement in phase noise was observed.

Table 1 summarizes the performance characteristics of various published wideband PLL synthesizer architectures. Our design demonstrates exceptional fractional spur performance and achieves a reasonable lock time. It is important to acknowledge the inherent challenges in directly comparing phase noise specifications due to the significant variations in operating frequency ranges across the published works. Generally, phase noise performance improves at lower frequencies. For transparency, we have included the worst-case scenario for phase noise reported in the reviewed literature within Table 1.

6. Conclusions

This research demonstrates the feasibility of achieving wideband signal generation without the inherent complexity of DDS and dedicated DSP blocks, while preserving functional versatility. Furthermore, the proposed design offers the potential for integration onto a single silicon die, allowing both phase-locked loops to reside within a single compact package. Except for the first VCO coil, which may be challenging to integrate due to spatial constraints, and loop filters that necessitate high-value capacitors achievable only through alternative fabrication processes, most components could be implemented on-chip. This approach paves the way for a single-chip wideband signal generator, free from the limitations imposed by fractional spurs.