1. PLL Structure

Fig. 1 illustrates the block diagram of the RF PLL system, which consists of several key blocks. The main blocks include the phase frequency detector (PFD), charge pump (CP), loop filter (LF), voltage controlled oscillator (VCO), and multi-modulus divider (MMD). These blocks work together to ensure the proper functioning of the PLL ^[2,3].

Fig. 1. RF PLL structure used for measurement.

The PFD compares the external reference (REF) signal with the DIV which is the VCO output divided by N.Frac. It then generates UP and DN signals, which correspond to positive and negative frequency phase differences, respectively.

The UP and DN signals are then fed into the charge pump circuit (CPC), which converts them into the corresponding currents. The CPC adjusts the input voltage of the VCO based on the voltage from the LF. Then, the VCO generates a voltage-controlled oscillating signal. The MMD component divides the VCO output signal by a division ratio specified by N.Frac. This division is necessary to produce the desired output frequency.

Fig. 2 illustrates the structure of CPC. In this figure, we see that CPC consists of 63 UP current sources (UCS) and 63 DN current sources (DCS). Each of them has charge pump circuit bias (CPCB) value which determines its current amount. Thus, we can generate the current amounts of the UCS and the DCS by combinations of the switch positions and the CPCB.

Fig. 2. CPC structure used for measurement.

In this paper, we focus on finding the optimal integrated phase noise (IPN) value of the PLL. The control variables that significantly impact the performance of the CPC are charge pump circuit whole bias (CPCB), UP current (VBP), and DN current (VBN). CPCB adjusts the bias current of the bandgap circuit that supplies the CPC, while VBP and VBN control the ratio of PMOS and NMOS currents in the CPC ^[2].

In such a fractional-N PLL, the out-band quantization noise of delta-sigma modulation (DSM) is folded into the in-band region due to nonlinearity of PFD-CP circuits. A simple and effective way to block the effect of noise folding is to move the lock point to a more linear region on the transfer function. So, we measured the optimal IPN by adjusting the CP offset current ^[4].

The IPN is an integrated measure of phase noise and is commonly used to assess the performance of a PLL. Phase noise (PN) is a frequency domain measurement that quantifies the undesirable fluctuations or noise in the phase of a signal. It is crucial for the PN to have a low value as it can adversely affect signal modulation.

3. IPN Data Acquisition

The IPN data of the RF PLL was obtained using automated measurement techniques. The measurement automation setup is illustrated in Fig. 3. A DC power supply provides a constant voltage to the motherboard, which in turn supplies a constant voltage to both the device under test (DUT) board and the serial peripheral interface (SPI) module.

Fig. 3. Proposed automatic measurement structure for PLL.

By establishing SPI communication between the personal computer (PC) and the SPI module, the dominant variables of the RF PLL on the DUT board can be controlled. Once the desired parameters are set, the IPN of the RF PLL is measured using a Phase Noise Analyzer. To facilitate the measurement process, the general-purpose interface bus (GPIB) is employed. The IPN data obtained through the Phase Noise Analyzer is then saved in comma-separated values (CSV) format using the PC as a storage medium.

4. Exhaustive Search

Exhaustive search (ES), also known as brute-force search, is a simple and straightforward algorithmic technique used to solve problems by systematically checking all possible solutions. It involves considering every possible candidate solution and evaluating each one to determine if it meets the problem requirements.

The ES method was initially employed to obtain the IPN values for three different RF PLL chips. The search method involved sequentially varying each control variable, namely CPCB, VBP, and VBN, and recording the resulting performance values. Since each control variable could have an N-bit variation, the total number of measurements required would be $2^{3N}$ to cover all possible IPN values. However, considering the need to reduce measurement time, we imposed an limitation of only allowing 20 points of variables for each control variable. Consequently, a total of 8000 measurements were performed, covering a subset of IPN values, to identify the most optimal IPN value among them.

Fig. 4-6 illustrate the IPN values obtained by varying the three control variables for the A3, A5, and A15 boards, respectively. As anticipated, the figures demonstrated that the optimal combination of control variables exists for each circuit. Nonetheless, utilizing the ES to determine the optimal combination of the control variables would be extremely time-consuming.

Fig. 4. IPN characteristics of A3 board.

Fig. 5. IPN characteristics of A5 board.

Fig. 6. IPN characteristics of A15 board.

To address this challenge, we introduce the application of the BO, which enables the identification of sub-optimal control variable combinations with only a small number of measurements. By leveraging BO, the search process becomes more efficient, allowing for a quicker identification of promising regions in the control variable combination space. Consequently, we achieve a significant reduction in the overall measurement time while still obtaining satisfactory results.

5. Bayesian Optimization

In the previous section, the ES method was utilized to perform a comprehensive analysis of IPN values for different control variable combinations. However, due to the time-intensive nature of the ES, we need to consider the optimization method to achieve faster and more efficient measurements, focusing on identifying sub-optimal control variable combinations with a reduced number of experiments.

In the vast landscape of global optimization, BO and genetic algorithms (GA) are two techniques that often take center stage. Each boasts its unique strengths and operational characteristics, making them suitable for diverse challenges. BO, using its probabilistic model-based approach, excels in efficiently finding the maximum of intricate functions with minimal evaluations ^[5]. In contrast, GA operates on a generational paradigm, often requiring multiple evaluations for each generation ^[6]. This becomes particularly challenging when optimizing parameters like IPN, where each evaluation bears substantial time and cost implications. In such contexts, the frequent evaluations of GA can escalate expenses quickly. Meanwhile, BO, with its capacity to leverage prior data, ensures fewer, more strategic evaluations. Especially when the cost of evaluations is a crucial factor, BO often stands out as a more economical option over GA.

Specifically, BO aims to solve

(1)

where an objective function is an expensive-to-evaluate function and is a feasible set [5, 7, 8]. If the problem we aim to solve in this paper is interpreted from the perspective of BO, the notations , , and in (1) can be seen as a 3-dimenstional vector representing the combination of control variables, a set comprising all possible 8000 combinations of these control variables, and a function that produces the IPN value multiplied by ‘ ’ for a given combination of control variables, respectively. The reason for employing this type of objective function is because BO aims to discover a solution that maximizes the objective function.

Because the objective function is not an analytical function, the key idea of BO is to build a probabilistic surrogate model of the objective function using N observations as

(2)

which is then used to select the next candidate point of by balancing exploration and exploitation. This balance is often achieved via an acquisition function. Furthermore, this process is repeated until either a specified number of iterations has been reached, or the difference between the objective function value of the newly chosen candidate point and that of the preceding point falls below a predetermined threshold. Fig. 7 illustrates the flow chart of BO process.

Fig. 7. Flow chart of Bayesian optimization.

Because the IPN measurement requires a relatively long time, we expect that a suboptimal solution can be found with a small number of measurements through the BO.