Some Review

Angle in degreesAngle in rad.sin qcos qtan q0030p/645p/460p/390p/2

DECIBEL SCALELogarithmic scales are useful when plotting functions that vary over many orders of magnitude. for example, the signal received by your cell phone is often more than 12 orders of magnitude lower in power than the signaltransmitted from the base station! 10 log 2 = 20 log 210 log 10 =20 log 1010 log 100 = 20 log 100=20 log10 ...dst

DECIBEL SCALE The DECIBEL value is a logarithmic measurement of the ratio of one variable to another of the same type. Decibel value has no dimension. It is used for voltage, current and power gains.

Magnitude HDecibel Value HdB0.001-600.01-400.1-200.5-61/2-31023261020202610040

SEMILOG SCALE

BODE PLOTS Bode plots are APPROXIMATE semilog plots of the magnitude (in Decibels) and phase (in degrees) of a transfer function versus frequency. They are much easier to plot.High pass filter circuit magitude response.Bode plots are APPROXIMATE plots of the magnitude and phase responses.

BODE PLOTS, The Decade A DECADE is an interval between 2 frequencies with a ratio of 10 (between 10 Hz and 100 Hz or between 500 Hz and 5000 Hz). 20 dB/decade means that magnitude changes 20 dB whenever the frequency changes tenfold or one decade. The DC value ( 0) does not appear on Bode plots ( Log0 = - ). Slopes are expressed in dB/decade.

One Decade20 dBa decade is defined as any 10-to-1 frequency rangean octave is any 2-to-1 frequency range20 dB/decade = 6 dB/octave

Bode Plots: Case 120 log|K|0 degreesdBrad/srad/s00

BODE PLOTS To plot the Bode plots of a given transfer function. Change s with (j) 1.) Put the transfer function in STANDARD FORM. 2.) Write the Magnitude and phase equations from the STANDARD FORM. 3.) Plot the magnitude of each term separately. 4.) Add all magnitude terms to obtain the magnitude transfer function. 5.) Repeat 2-4 for the phase response. 6.) The total magnitude response in Decibel units is the summation and subtraction of the responses of different terms. 7.) The total phase response in degrees is the summation and subtraction of the phase responses of different terms.0,4 (1+jw/10)(1/jw) (1+jw/5)-2

Bode Plots: Case 2-90 degrees-20 dB/decade1100.1020-20dBrad/sPhaseangle01/s= 1/j.w = (1/jw).(j/j) = -(1/w).j misal w=1,maka = -j sehingga

Bode Plots: Case 4-20 dB/decade

Bode Plots: Case 4-90-451/(s+1) = 1/(jw+1) = (1/jw+1).(1-jw/1-jw) =1-jw/(1+w2) (1-jw)/(1+w2) --> misal w=0, arctg (0/1)=0 misal w=1, arctg (-1/2) arctg (-1) -45 misal w=10, arctg (-10/2) arctg (-10) -90

Bode Plots: Case 5Can we simplify?What does really mean?Can we let equal some value to help simplify the equation? = 1

Bode Plots: Case 5The equation from the last slide may be written as:-180-90-40 dB/decadeAll we need to do is double both of the plots from Case 4

SIMPLE ZERO Approximate the magnitude response of a simple zero by two linear curves before and after =z1 Approximate the phase response of a simple zero by three linear curves before =0.1z1 after =10z1 and between =0.1z1 and =10z1 CORNER FREQUENCYBREAK FREQUENCY3 dB FREQUENCY

BODE PLOT OF QUADRATIC ZERO The EXACT responses can be approximated by BODE plots in terms of the corner frequency n

BODE PLOT OF QUADRATIC POLE

Frequency Response Plots

Bode Plots Real Poles(break frequency or corner frequency)(break frequency or corner frequency)-3dB

Frequency Response Plots

Bode Plots Real Poles(break frequency or corner frequency)

Express transfer function in Standard form.

Express the magnitude and phase responses.

Two corner frequencies at =2, 10 and a zero at the origin =0. Sketch each term and add to find the total response.EXAMPLE 14.3 Construct Bode plots for

EXAMPLE 14.3 Construct Bode plots for 26 dBXXXX

Calculate 20log10 |H(j)| at =50 rad/s and =1000 rad/s

Thus, the approximate amplitude plot consists of two straight lines. For n, the straight line has a slope of -40 dB/decade. Thes two straight lines intersect at u=1 or =n.

Lihat pole & zero (ambil yg positifnya)