Bode plot is method of Presenting Frequency-Response Characteristics in Graphical Forms.
Bode diagram consists of two graphs:
One is a plot of the logarithm of the magnitude of a sinusoidal transfer function; the
other is a plot of the phase angle; both are plotted against the frequency on a logarithmic
scale.The standard representation of the logarithmic magnitude of G(jw) is 20 l o g l ~ ( j w ) ) ,
where the base of the logarithm is 10.
The unit used in this representation of the magnitude is the decibel, usually abbreviated dB.The main
advantage of using the Bode diagram is that multiplication of magnitudes can be converted into
addition.it is not possible to plot the curves right down to zero frequency because of the
logarithmic frequency (log0 = -m),.
As stated earlier, the main advantage in using the
logarithmic plot is the relative ease of plotting frequency-response curves. The basic
factors that very frequently occur in an arbitrary transfer function G ( j w ) H ( j w )are
1. Gain K
2. Integral and derivative factors ( j w)
3. First-order factors ( 1 + j w T)
4. Quadratic factors [I + 2 ζ [(jw /wn ) + ( j w / wn ) 2]
The Gain K.
The log-magnitude curve for a constant gain K is a horizontal straight line at the magnitude of 20 log K
decibels. The phase angle of the gain K is zero. The effect of varying the gain K in the transfer function
is that it raises or lowers the log-magnitude curve of the transfer function by the corresponding constant
amount, but it has no effect on the phase curve
example
As a number increases by a factor of 10, the corresponding decibel value increases by a factor of 20
20log(K x 10) = 20 log K + 20
Similarly,
20 log(K x 10^n) = 20 log K+20n
when expressed in decibels, the reciprocal of a number differs from its value only in sign; that is, for
the number K
20logK =-20log1/K
Integral and Derivative Factors ( jW)
logarithmic magnitude of l / j w in The decibels is
20 log[1/jw]=-20 log w Db
The phase angle of l / j w is constant and equal to -90 degree.In Bode diagrams, frequency
ratios are expressed in terms of octaves or decades. An octave is a frequency band from w1
2w1,where w1 is any frequency value. A decade is frequency band from w, to low,, where again
w, is any frequency.For example, the horizontal distance from w = 1 to w = 10 is equal to
that from w = 3 to w = 30.).If the log magnitude -20 log w dB is plotted against w on a
logarithmic scale, it is a straight line.The phase angle of jw is constant and equal to 90°.The
log-magnitude curve is a straight line with a slope of 20 dB/decade
EXAMPLE
