Aicos (wit) A。cos(@it+6) H() Figure 1: Input Output behavior of a linear circuit in steady state. The output amplitude, A., and the output phase, o, depend on H() as follows: A₁ = A¡ |H[1]] and $=ZH(1) To determine H(@) from experimental measurements of a circuit, find the steady-state sinusoidal response to a wide range of input frequencies. From each sinusoidal response, measure A. and . Fill in a table such as the one below for each input frequency. @₁ | 0=H(@1)||H(@1)|=A。/A₁| 20log | H(1)| Consider, for example, the response, y(t), of a system with input x(t)=sin(3лt) shown below. For this input, ₁=3л, and A₁ = 1. For the signal in steady-state, measure A. and AT, the time lag. The phase lag in degrees is calculated from == 360° AT T if the output is shifted to the right and $ = 360° where T is the period of the signal. AT T if the output is shifted to the left 1.5- 0.5 1 0 -0.5- -1F -x(t) - y(t) M -1.55 1.5 1 0.5 Time (sec) 2.5 The period T = 2π/0₁ = 0.67. From the plot, AT = 0.12s and A. = 1.17. So | H(1)| = A。/A = 1.17 and =-0.12(360)/T-64.7°. @₁ | 0=ZH(@1) | |H(@₁)|=A./Ai | 20log |H(@1)|| 3元 -64.7° 1.17 1.36dB Select a wide range of values of input frequencies that fully characterize the frequency response. Once the data is collected, plot all the points on semilog paper to obtain the Bode plot of the system.