Gain-Bandwidth-Product-Induced Technical Bound in Time Transfer System without Inline Amplifiers

TL;DR

This paper establishes a theoretical lower bound on signal stability for long-distance time transfer systems without inline amplifiers, highlighting the impact of gain-bandwidth limitations and guiding system optimization.

Contribution

It introduces a novel theoretical model that defines the fundamental stability limit based on gain-bandwidth products for non-amplified time transfer over long distances.

Findings

Stability is limited by receiver noise at short distances.

At 300 km, stability can reach below 10 ns without inline amplifiers.

The model guides optimizing receiver design for long-distance time transfer.

Abstract

Time transfer plays a dispensable role in many fields including navigation and positioning, geodesy, and fundamental tests. However, in certain scenarios where effective relay node deployment is often not feasible, such as harsh environments with extremely poor infrastructure and emergency conditions, effective time transfer without inline amplifiers becomes crucial. In this situation, the maximum transmission distance is limited by the receiver's measurement capability, particularly its ability to amplify the signal. Here we propose a theoretical model, giving a technical lower bound of the detected signal stability at different transmission distances, induced by limited gain-bandwidth products. The results under common gain-bandwidth products show that while for shorter transmission distances, stability is mainly limited by the background noise of the time interval counter, for longer distances reaching the scale of 300 kilometers, the technical lower bound is below the level of 10 nanoseconds without any inline amplification devices. Therefore, the given technical bound offers guidance on managing the balance between distance and stability, together with the optimization of the receiver in long-distance time transfer without inline amplification.