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22 1. A Short Introduction
In[24]:= p1 = poles1 /. designpoint
Out[24]= s 19.1299
We now verify the above result by computing the exact pole locations, employing the function
PolesByQZ (Section 3.8.4) on the original equation system.
In[25]:= poles = PolesByQZ[mnaAC741]
Out[25]=
4.19822 10 10 , 3.02054 10 10 , 3.97873 10 7 7.96404 10 7 ,
3.97873 10 7 7.96404 10 7 , 6.47642 10 6 ,
8.33125 10 7 1.17 10 8 , 8.33125 10 7 1.17 10 8 ,
2.53983 10 8 , 2.04133 10 8 , 2.02066 10 8 , 3.85479 10 8 ,
6.26147 10 8 , 8.75148 10 8 , 19.507726973459277,
9.68714 10 8 , 1.2364 10 9 , 2.15863 10 9 6.82302 10 8 ,
2.15863 10 9 6.82302 10 8 , 2.63327 10 9 , 7.93728 10 9 ,
9.89724 10 9 , 1.58287 10 10 , 1.46898 10 10
Now we sort the poles in ascending order of their absolute values.
In[26]:= Sort[poles, Abs[#1] < Abs[#2] &]
Out[26]=
19.507726973459277, 6.47642 10 6 ,
3.97873 10 7 7.96404 10 7 , 3.97873 10 7 7.96404 10 7 ,
8.33125 10 7 1.17 10 8 , 8.33125 10 7 1.17 10 8 ,
2.02066 10 8 , 2.04133 10 8 , 2.53983 10 8 , 3.85479 10 8 ,
6.26147 10 8 , 8.75148 10 8 , 9.68714 10 8 , 1.2364 10 9 ,
2.15863 10 9 6.82302 10 8 , 2.15863 10 9 6.82302 10 8 ,
2.63327 10 9 , 7.93728 10 9 , 9.89724 10 9 , 1.46898 10 10 ,
1.58287 10 10 , 3.02054 10 10 , 4.19822 10 10
This yields a list, whose first entry represents the equivalent to the numerical solution which was
found before with the help of the approximated transfer function. Since both values match well, this
is another indication that the extracted formula for the pole indeed describes the dominant pole of
the operational amplifier.
For further insights, there are various graphics functions available to visualize the extracted
information, such as the functions RootLocusPlot (Section 3.9.5) or NyquistPlot (Section 3.9.4).
For details please refer to the respective sections.
Conclusion
This example showed the application of Analog Insydes on the analysis of the ΜA741 operational
amplifier for extracting a formula for the corner frequency of the small-signal transfer function. In a
first step we imported the netlist and simulation data files from PSpice, set up the equations in Analog
Insydes and verified the numerical solution. A complexity estimation showed that calculating the
transfer function for the original equation system is not possible, thus we applied an approximation
routine to achieve a simplified equation system. Using this system it was possible to symbolically
calculate its transfer function. Finally, we achieved a symbolic formula describing the pole of the
simplified transfer function and the dominant pole of the original transfer function. An additional