SummaryA power divider is ideally a lossless reciprocal device performing vector summation of two or more input signals, which is an extremely important circuit component in wireless communication systems or radar systems. In this paper, a general concept of lumped‐element power divider is discussed. Then, a semi‐analytical synthesis technique is presented. General odd‐mode and even‐mode analysis method is proposed for multi‐port symmetrical network and applied in the analysis of N‐way lumped‐element power dividers. The transmission networks and the matching networks can be synthesized step by step, which greatly simplify their analysis. The transmission networks can be synthesized by those well‐known synthesis techniques for two‐port networks, and thus the transmission property of power dividers can be accurately controlled. The matching networks are determined by optimization to ensure certain isolation between the output ports. The design procedure is simple and accurate. Apart from the capability of power division, power dividers are also able to play the role of impedance transform and signal processing. Some examples of power dividers with filtering capability are presented for demonstration. In this paper, a general concept of lumped‐element power divider is discussed. Then, a semi‐analytical synthesis technique is presented. General odd‐mode and even‐mode analysis method is proposed for multi‐port symmetrical network and applied in the analysis of N‐way lumped‐element power dividers. Transmission networks and matching networks can be synthesized step by step, which greatly simplify their analysis. Apart from the capability of power division, power dividers are also able to play the role of impedance transform and signal processing.