Batch Bayesian Optimization for Minimizing IPN in RF PLLs

Minimizing integrated phase noise (IPN) in RF phase-locked loops (PLLs) is critical to spectral purity and system-level performance, yet post-fabrication tuning relies on expensive measurements over discrete trimming codes, making exhaustive search impractical. Therefore, sample-efficient optimization is essential, especially when instrumentation time is limited and the configuration space is large. This study investigates batch Bayesian optimization (BO) with batch expected improvement for minimizing IPN of RF PLLs under discrete trimming codes and expensive measurements. Although parallel test resources typically drive batch BO, we considered a single-device-under-test setup in which q candidates were queued and sequentially measured. We evaluated performance as a function of the total number of physical measurements B, comparing it against sequential BO and genetic algorithms across three PLL boards. For small B, a moderate batch size accelerated IPN reduction and improved tail behavior. At larger B, the mean performance of batch BO was comparable to that of sequential BO. However, batch BO retained a tail-performance advantage on certain boards. Additionally, within batch BO, we observed a non-monotonic effect of the batch size q. Specifically, moderate batch sizes improved early progress, whereas excessively large q degraded performance due to selecting all batch candidates simultaneously without using intermediate measurement feedback. These results suggest that appropriate batch-size selection can reduce the number of measurements required to achieve a target IPN, making batch BO particularly attractive under constrained measurement budgets.