Automating radio frequency (RF) amplifier design remains challenging because existing methods suffer from the curse of dimensionality, weak use of domain knowledge, and poor transferability, leading to low data efficiency. Meanwhile, although large language models (LLMs) have shown promise in many scientific domains, applying them directly to RF sizing is nontrivial due to the numerical nature of circuit optimization and the reliance on domain-specific design flows. To address this, this paper proposes RFAmpDesigner, a multi-agent framework that automates RF amplifier sizing. It introduces a resource-allocation middleware that reframes high-dimensional parameter tuning as a low-dimensional resource distribution problem, making it easier to inject sizing knowledge into general-purpose LLMs. The framework also follows standard design practice, enabling LLMs to distinguish between high- and low-cost actions and search in parallel. To realize a self-evolving optimization process, the framework employs retrieval-augmented generation (RAG) to reuse past knowledge and experience from memory base. As a proof of concept, we apply RFAmpDesigner to low noise amplifiers of varying complexity. The experimental results show that it can automatically synthesize designs with fractional bandwidths ranging from 10\% to 80\% and center frequencies from 10 GHz to 50 GHz. To the best of our knowledge, this work develops the first LLM-driven approach for RF amplifier sizing that operates on design concepts instead of treating netlists as text, offering a novel solution to mitigate data scarcity in RF design.

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