AnalogCoder is a novel training-free LLM-based agent designed to automate analog circuit design through Python code generation. The system addresses the challenges of analog circuit design, such as complexity, abstraction level, and data scarcity, by incorporating a feedback-enhanced design flow, a circuit tool library, and domain-specific prompt engineering. AnalogCoder can automatically generate Python code for functional analog circuits, leveraging the LLM's strong Python programming capabilities. Extensive experiments on a comprehensive benchmark show that AnalogCoder outperforms other LLM-based methods, successfully designing 20 out of 24 analog circuits, surpassing the performance of standard GPT-4o. The benchmark, which includes 24 unique circuits, is the largest and most diverse set of analog circuit design tasks evaluated to date. AnalogCoder's success rate is further enhanced by the circuit tool library, which stores and reuses modular sub-circuits, facilitating the design of more complex circuits. The work provides an open-source benchmark and code to enable future research and applications in analog circuit design.AnalogCoder is a novel training-free LLM-based agent designed to automate analog circuit design through Python code generation. The system addresses the challenges of analog circuit design, such as complexity, abstraction level, and data scarcity, by incorporating a feedback-enhanced design flow, a circuit tool library, and domain-specific prompt engineering. AnalogCoder can automatically generate Python code for functional analog circuits, leveraging the LLM's strong Python programming capabilities. Extensive experiments on a comprehensive benchmark show that AnalogCoder outperforms other LLM-based methods, successfully designing 20 out of 24 analog circuits, surpassing the performance of standard GPT-4o. The benchmark, which includes 24 unique circuits, is the largest and most diverse set of analog circuit design tasks evaluated to date. AnalogCoder's success rate is further enhanced by the circuit tool library, which stores and reuses modular sub-circuits, facilitating the design of more complex circuits. The work provides an open-source benchmark and code to enable future research and applications in analog circuit design.