Lecture 201 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

Lecture 202 Sinusoidal Frequency Analysis The transfer function is composed of both magnitude and phase information as a function of frequency where |H(jω)| is the magnitude and φ(ω) is the phase angle Plots of the magnitude and phase characteristics are used to fully describe the frequency response

Lecture 203 Bode Plots A Bode plot is a semilog plot of transfer function's magnitude and phase as a function frequency The gain magnitude is many times expressed in terms of decibels (dB) dB = 20 log 10 A where A is the amplitude or gain –a decade is defined as any 10-to-1 frequency range –an octave is any 2-to-1 frequency range 20 dB/decade = 6 dB/octave

Lecture 204 Bode Plots Straight-line approximations of the Bode plot may be drawn quickly from knowing the poles and zeros –response approaches a minimum near the zeros –response approaches a maximum near the poles The overall effect of constant, zero and pole terms

Lecture 205 Bode Plots Express the transfer function in standard form There are four different factors: 1.Constant gain term, K 2.Poles or zeros at the origin, (j  ) ±N 3.Poles or zeros of the form (1+ j  ) 4.Quadratic poles or zeros of the form 1+2  (j  )+(j  ) 2

Lecture 206 Bode Plots We can combine the constant gain term and the poles/zeros at the origin such that the magnitude crosses 0dB at Define the break frequency to be at ω=1/τ with magnitude at ±3dB and phase at ±45°

Lecture 207 Bode Plots where N is the number of roots of value τ

Lecture 208 Class Examples Extension Exercise E12.3 Extension Exercise E12.4 Extension Exercise E12.5

Lecture 209 MATLAB Exercise Here we will use MATLAB to create Bode plots for Extension Exercise E12.3 Start MATLAB and open the file BodePlt.m from the class webpage