Let c(t) = A_c cos (2πf_ct) and m(t) = cos (2πf_mt). It is given that f_c ≫ 5f_m. The signal c(t) + m(t) is applied to the input of a non-linear device, whose output v_o(t) is related to the input v_i(t) as v₀(t) = av_i(t) + bv_i²(t) where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency f_c and bandwidth 3 f_m, to produce an amplitude modulated (AM) wave. If it is desired to have the side band power of the AM wave to be half of the carrier power, then a/b is