Let c(t)=A_ccos(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 v_o(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 3f_m, to produce an amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then a/b is