Section 7–3 / Polar Plots 431ImRev = 001v`Figure 7–30
Polar plot of
1 + 2 zaj forz>0.
v
vnb+ ajv
vnb2Next, consider the following sinusoidal transfer function:
The low-frequency portion of the curve is
and the high-frequency portion is
Since the imaginary part of G(jv)is positive for v>0and is monotonically increasing,
and the real part of G(jv)is monotonically decreasing from unity, the general shape of
the polar plot of G(jv)is as shown in Figure 7–30. The phase angle is between 0° and
180°.
EXAMPLE 7–8 Consider the following second-order transfer function:
Sketch a polar plot of this transfer function.
Since the sinusoidal transfer function can be writtenthe low-frequency portion of the polar plot becomesand the high-frequency portion becomesvlimSqG(jv)=^0 - j^0vlimS 0 G(jv)=-T-jqG(jv)=1
jv(1+jvT)=-
T
1 +v^2 T^2- j
1
vA 1 +v^2 T^2 BG(s)=1
s(Ts+1)vlimSqG(jv)=q^ /^180 °
vlimS 0 G(jv)=^1 /^0 °
=a 1 -
v^2
v^2 n
b+ja
2 zv
vn
bG(jv)= 1 + 2 zaj
v
vn
b +aj
v
vn
b2