Problem 14.5

a)

We will make a table of each function, it's AR plateau, its break frequency (wb), and slope.

where N.A. means that there is no break frequency. In general,

f for 10 = tan-1(0/10) = 0o

f for 10s+1 = tan-1(10w/1) = tan-1(10w)

f for s+1 = tan-1(w/1) = tan-1(w)

f total = 0 - tan-1(10w) - tan-1(w)

We must calculate ARtotal and ftotal, which is shown in the table below:

The asymptotic plot is shown below (note that we were only asked to plot AR and not f):

b)

We will make a table of each function, it's AR plateau, its break frequency (wb), and slope.

where N.A. means that there is no break frequency. In general,

f for 10 = tan-1(0/10) = 0o

f for 10s+1 = tan-1(10w/1) = tan-1(10w)

f for (s+1)2 = 2tan-1(w/1) = 2tan-1(w)

f total = 0 - tan-1(10w) - 2tan-1(w)

We must calculate ARtotal and ftotal, which is shown in the table below:

The asymptotic plot is shown below (note that we were only asked to plot AR and not f):

c)

We will make a table of each function, it's AR plateau, its break frequency (wb), and slope.

where N.A. means that there is no break frequency. In general,

f for 10 = tan-1(0/10) = 0o

f for s+1 = tan-1(w/1) = tan-1(w)

f for 10s+1 = tan-1(10w/1) = tan-1(10w)

f for (0.1s+1) = tan-1(0.1w/1) = tan-1(0.1w)

f total = 0 + tan-1(w) - tan-1(10w) - tan-1(0.1w)

We must calculate ARtotal and ftotal, which is shown in the table below:

The asymptotic plot is shown below (note that we were only asked to plot AR and not f):

d)

We will make a table of each function, it's AR plateau, its break frequency (wb), and slope.

where N.A. means that there is no break frequency. In general,

f for 10 = tan-1(0/10) = 0o

f for -s+1 = tan-1(-w/1) = tan-1(-w)

f for 10s+1 = tan-1(10w/1) = tan-1(10w)

f for (0.1s+1) = tan-1(0.1w/1) = tan-1(0.1w)

f total = 0 - tan-1(w) - tan-1(10w) - tan-1(0.1w)

We must calculate ARtotal and ftotal, which is shown in the table below:

The asymptotic plot is shown below (note that we were only asked to plot AR and not f):

e)

f for 10 = tan-1(0/10) = 0o

f for s = tan-1(w/0) = tan-1(infinity) = 90o

f for 10s+1 = tan-1(10w/1) = tan-1(10w)

f total = 90o - tan-1(10w)

We must calculate ARtotal and ftotal, which is shown in the table below:

The asymptotic plot is shown below (note that we were only asked to plot AR and not f):

f)

f for 10 = tan-1(0/10) = 0o

f for s+1 = tan-1(w/1) = tan-1(w)

f for s = tan-1(w/0) = tan-1(infinity) = 90o

f for 10s+1 = tan-1(10w/1) = tan-1(10w)

f for (0.1s+1) = tan-1(0.1w/1) = tan-1(0.1w)

f total = tan-1(w) - 90o - tan-1(10w) - tan-1(0.1w)

The asymptotic plot is shown below (note that we were only asked to plot AR and not f):