Summary: This paper presents a method for synthesizing a coherent 1-input 3-output optical delay-line circuit with N stages that is composed of 2(N + 1) directional couplers, N optical delay-lines, 2(N + 1) phase shifters and one external phase shifter with phase value φc . The path difference is equal to the delay time difference Δτ. Synthesis algorithm is based on the division of the transfer matrix into basic component transfer matrices and factorization is completed by repeated size-reduction. A set of recursion equations are also defined to obtain the unknown circuit parameters. In the developed method, it is shown that (13) optical delay-line circuit has the same transmission characteristics as finite impulse response (FIR) digital filters with complex expansion coefficients. Band-pass flat group delay type filter is considered as an example in this paper. It is also confirmed that developed (13) optical delay-line circuit can realize 100% power transmittance.