Using MathCad to obtain Bode Plots and Nyquist
Plots of Transfer Functions:
Step 1: Define the range of frequencies as powers of 10, i.e. in anticipation of logarithmic scale,
Number_of_terms
k
200
0 .. Number_of_terms
Min_exponent
Max_exponent
Exponent( k )
(this will make the lower bound of ω as 10-1)
1
(this will make the upper bound of ω as 101)
k
. ( Max_exponent Min_exponent )
Min_exponent
Number_of_terms
1
(this is just a simple linear interpolation formula)
Exponent( k )
ωk
10
( Note that "[" was used for subscript here. )
Step 2. Set the parameters and define G(s).
K 1.0
τ n 1.0
ζ
( Note that "." was used for subscript here.)
0.1
G( s )
K
2 2
τ n .s
2. τ n. ζ. s
1
Step 3. Next calculate the log modulus and phase shift.
Log_Modulusk
20. log
G i . ωk
( Note that the function log in MathCAD is already
in base 10. Also, key in "1i" for the imaginary
number, key in "2i" for 2 times the imaginary
number, etc.)
Phase_Shiftk
180
arg G i . ωk .
π
ω
π
20
(dB)
0
Log_Modulus
k
20
40
0.1
1
10
ωk
Frequency (rad/s)
(degrees)
0
Phase_Shift
k
100
200
0.1
1
10
ωk
Step 4. For the Nyquist plots,
Real_Gk
Re G i . ωk
Imag_Gk
Im G i . ωk
0
2
Imag_G
k
4
6
3
2
1
0
Real_G
1
k
2
3