Mathematical proof of errors in Capasso's excess noise factor formula for an n-step staircase multiplier
Solid-state devices such as multistep staircase avalanche photodiodes (APDs) are analogues to the photomultiplier tubes and are considered as a cascade-amplifier. The major source of internal noise in these APDs is due to the randomness in their stepwise impact ionization. Recent literature on staircase APDs by research groups such as Campbell and co-workers have reported the theoretical estimates of total excess noise factors using Capasso's excess noise factor formula. This formula is based on Friis' total noise factor formula for cascade networks. This article proves that Capasso's formula for a staircase APD, erroneously considers the power gains in Friis' total noise factor formula as the gains.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Mechanic: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving
Recent advances in large language models (LLMs) and LLM-based agents have substantially improved the capabilities of automated theorem proving. However, for problems requiring complex mathematical reasoning, current syst…
Automated Theorem ProvingMathematical ReasoningExistence of Equilibrium Prices: A Pedagogical Proof
Under the same assumptions made by Mas-Colell et al. (1995), I develop a short, simple, and complete proof of existence of equilibrium prices based on excess demand functions. The result is obtained by applying the Brouw…
Why Agentic Theorem Prover Works: A Statistical Provability Theory of Mathematical Reasoning Models
Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathema…
Mathematical ReasoningLarge Language Models' Understanding of Math: Source Criticism and Extrapolation
It has been suggested that large language models such as GPT-4 have acquired some form of understanding beyond the correlations among the words in text including some understanding of mathematics as well. Here, we perfor…
Automated Theorem ProvingMathMathematical ProofsSentenceProofOptimizer: Training Language Models to Simplify Proofs without Human Demonstrations
Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal sys…
Reinforcement Learning