solution

π
ω p = 10 , a straight line (reference to log10 ω ) achieves the − phase change, as
2
shown (dashed line).
jω
π
Similarly, for part , for low frequencies ( ω ω p 10 ) and 0 for high
jω
+ 10 2
π
frequencies ( ω 10ω p ), a straight line at ω p /10 < ω < 10ωp
gives the − phase
2
change, as shown (dotted line).
At last, applying composition rules to get the final phase asymptote, as shown (solid
line).
phase factor
phase factor
Code:
2
1
0
-1
-2
10 -1
2
1
0
-1
-2
10 -1
10 0
10 0
omg = 0.1:0.1:1000;
omg_p = 10;
omg1 = 0.1:0.1:omg_p;
omg2 = omg_p+0.1:0.1:1000;
ym = zeros(size(omg));
ym_1 = ones(size(omg1)); % get the magnitude asymptote for low frequency
ym_2 = omg_p./omg2; % get the magnitude asymptote for high frequency
ym(1:length(omg1)) = ym_1;
ym(length(omg1)+1:end)= ym_2;
10 1
ω
10 1
ω
10 2
10 2
10 3
10 3