1.5 200 600 800 1000 Radian Frequency o 180 1000 Figure 11.2 Linear frequency response curves of HGjo 11.3 Bode Diagrams A Bode diagram consists of plots of the gain and phase of a transfer function, each with respect to logarithmically scaled frequency axes. In addition, the gain of the transfer function is scaled in decibels according to the hlds haB 20 logo(jo) This definition relates to transfer functions which are ratios of voltages and/or currents. The decibel gain between two powers has a multiplying factor of 10 rather than 20. This method of plotting frequency response information was popularized by H w. Bode in the 1930s. There are two main advantages of the Bode approach The first is that, with it, the gain and phase curves can be easily and accurately drawn. Second, once drawn, features of the curves can be identified both qualitatively and quantitatively with relative ease, even when those features occur over a wide dynamic range. Digital computers have rendered the first advantage obsolete. Ease of interpretation, however, remains a powerful advantage, and the Bode diagram is today the most common method chosen for the display of frequency response data A Bode diagram is drawn by applying a set of simple rules or procedures to a transfer fund on. The rules relate directly to the set of poles and zeros and/or time constants of the function. Before constructing a Bode diagram, the transfer function is normalized so that each pole or zero term(except those at s= 0)has a dc H(s)=Ks+o1-=02so2+1 sτ.+1 s(s+op)0ps(s/02+1) s(sτn+1) e 2000 by CRC Press LLC© 2000 by CRC Press LLC 11.3 Bode Diagrams A Bode diagram consists of plots of the gain and phase of a transfer function, each with respect to logarithmically scaled frequency axes. In addition, the gain of the transfer function is scaled in decibels according to the definition This definition relates to transfer functions which are ratios of voltages and/or currents. The decibel gain between two powers has a multiplying factor of 10 rather than 20. This method of plotting frequency response information was popularized by H.W. Bode in the 1930s. There are two main advantages of the Bode approach. The first is that, with it, the gain and phase curves can be easily and accurately drawn. Second, once drawn, features of the curves can be identified both qualitatively and quantitatively with relative ease, even when those features occur over a wide dynamic range. Digital computers have rendered the first advantage obsolete. Ease of interpretation, however, remains a powerful advantage, and the Bode diagram is today the most common method chosen for the display of frequency response data. A Bode diagram is drawn by applying a set of simple rules or procedures to a transfer function. The rules relate directly to the set of poles and zeros and/or time constants of the function. Before constructing a Bode diagram, the transfer function is normalized so that each pole or zero term (except those at s = 0) has a dc gain of one. For instance: Figure 11.2 Linear frequency response curves of H(jw). * * H H *H j * dB = dB = 20 10 log ( w) H s K s s s K s s s K s s s z p z p z p z p ( ) ( ) / ( / ) ( ) = + + = + + = ¢ + + w w w w w w t t 1 1 1 1