An active infinite-impulse response (IIR) filter using coupled fiber ring is presented in this paper. The theoretical model is built by using Z-transform technique. Optimal coupling coefficients are sorted for simulating narrow band-pass filters. Those narrow band-pass filters are centered at 160 GHz for next generation high-speed optical communication systems. The pass band can be designed as narrow as 18.75 MHz. The gain of the active IIR filter can be designed up to 67 dB.the Z-transform technique. Due to energy conservation, the coupling ratios of the couplers should satisfy K,, K2, K7, K3 + ~ and K5 + ~«; being any value between 0 and 1, respectively.Simplifying (4), we can find