coupler which adds the signals coming from both lines the delay lines have a fixed time delay difference u03c4 one of the optical couplers has a tunable coupling ratio i e the optical power ratio in the two delay lines can be tuned according to what is claimed in patent pt 104237 the proposed mzdi consists of an optical filter with tunable response which approximately corresponds to a weighted average of the delay lines responses the tuning is carried out through the adjustment of the optical power ratio between the two delay lines as a result a desired todl with a tuning ranging from 0 to u03c4 is obtained in terms of a mathematic expression the frequency response of the mzdi is given by where 0 u2266 u03b1 u2266 1 is the coupling ratio and f is the frequency the amplitude response u2225 h u0192 u2225 2 and the group delay u03c4 u0192 can be derived from 1 both derived equations show that the todl has a periodic frequency response with a period 1 u03c4 the amplitude response and the group delay are depicted in fig1 for different values of u03b1 as predicted by 2 1 and 2 2 both the amplitude response and the group delay are affected by u03b1 as a result the optical signal must be properly centered with the mzdi 39 s frequency response the absolute value of the amplitude response can be adjusted by means of variable optical attenuators voa 39 s located at the input or output of the todl.