In this paper we address the minimum-energy broadcast problem in multi-hop wireless networks, so that all broadcast requests initiated by different source nodes take place on the same broadcast tree. Our approach differs from the most commonly used one where the determination of the broadcast tree depends on the source node, thus resulting in different tree construction processes for different source nodes. Using a single broadcast tree simplifies considerably the tree maintenance problem and allows scaling to larger networks. We first show that, using the same broadcast tree, the total power consumed for broadcasting from a given source node is at most twice the total power consumed for broadcasting from any other source node. We next develop a polynomial-time approximation algorithm for the construction of a single broadcast tree. The performance analysis of the algorithm indicates that the total power consumed for broadcasting from any source node is within 2H(n-1) from the optimal,...