Pole-zero analysis¶
SLiCAP can accurately determine poles and zeros of transfer functions. To this end, SLiCAP writes the MNA equations of the electrical circuit in the differential form as a function of the Laplace variable and uses fast division-free algorithms for evaluation of the determinant.
SLiCAP has three data types for evaluation of poles and zeros:
The result object returns values of poles and zeros in [rad/s]. The results of a pole-zero analysis can be displayed on an HTML page: pz2html(<instructionresult>), or in the python console: listPZ(<instructionresult>). These display methods are sensitive to the setting of ini.Hz. If True the results are displayed in [Hz], else in [rad/s]
Data type ‘poles’¶
With instruction.dataType=’poles’ SLiCAP returns the solutions of the determinant of the network. Hence, it returns the solutions of the denominator of the transfer function set by intruction.gainType. These solutions are all poles of the network, including the non-observable or non-controllable poles. Both numeric and symbolic analysis methods are supported, however, symbolic calculation with may fail or take a long time.
>>> from SLiCAP import *
>>> prj = initProject('My first RC network') # Initialize a SLiCAP project
>>> instr = instruction() # Create an instance of an instruction object
>>> instr.setCircuit('myFirstRCnetwork.cir') # Create a circuit from 'myFirstRCnetwork.cir'
No errors found for circuit: 'My first RC network' from file: 'myFirstRCnetwork.cir'.
>>> instr.setSimType('symbolic') # Define the simulation type
>>> instr.setSource('V1') # Define the signal source
>>> instr.setDetector('V_out') # Nodal voltage 'V_out' is detector voltage
>>> instr.setGainType('gain') # Define the gain type
>>> instr.setDataType('poles') # Define the data type
>>> result = instr.execute() # Execute the instruction and assign the results to 'result'
>>> print result.poles # Print the poles of the gain
[-1/(C*R)]
>>> instr.setSimType('numeric') # Switch to numeric analysis
>>> result = instr.execute() # Execute the instruction and assign the results to 'result'
>>> print result.poles # Print the poles of the gain
[-6283.185307179608]
Note
The execution results of a pole-zero analysis are always in [rad/s].
Data type ‘zeros’¶
With instruction.dataType=’zeros’ SLiCAP returns the solutions of the determinant of the network after application of Cramer’s rule. Hence, it returns the solution of the numerator of the transfer function set by intruction.gainType. Both numeric and symbolic analysis methods are supported, however, symbolic calculation with may fail or take a long time.
>>> from SLiCAP import *
>>> prj = initProject('My first RC network') # Initialize a SLiCAP project
>>> instr = instruction() # Create an instance of an instruction object
>>> instr.setCircuit('myFirstRCnetwork.cir') # Create a circuit from 'myFirstRCnetwork.cir'
No errors found for circuit: 'My first RC network' from file: 'myFirstRCnetwork.cir'.
>>> instr.setSimType('symbolic') # Define the simulation type
>>> instr.setSource('V1') # Define the signal source
>>> instr.setDetector('V_out') # Nodal voltage 'V_out' is detector voltage
>>> instr.setGainType('gain') # Define the gain type
>>> instr.setDataType('zeros') # Define the data type
>>> result = instr.execute() # Execute the instruction and assign the results to 'result'
>>> print(result.zeros) # Print the poles of the gain
[]
Data type ‘pz’¶
With instruction.dataType=’pz’ SLiCAP returns the zero-frequency value of the transfer and a reduced set of poles and zeros. Poles and zeros that coincide within the numerical display resolution (set by ini.disp) are left out. These poles are called non-observable or non-controllable. Both numeric and symbolic analysis methods are supported, however, symbolic calculation with may fail or take a long time.
>>> from SLiCAP import *
>>> prj = initProject('My first RC network') # Initialize a SLiCAP project
>>> instr = instruction() # Create an instance of an instruction object
>>> instr.setCircuit('myFirstRCnetwork.cir') # Create a circuit from 'myFirstRCnetwork.cir'
No errors found for circuit: 'My first RC network' from file: 'myFirstRCnetwork.cir'.
>>> instr.setSimType('symbolic') # Define the simulation type
>>> instr.setSource('V1') # Define the signal source
>>> instr.setDetector('V_out') # Nodal voltage 'V_out' is detector voltage
>>> instr.setGainType('gain') # Define the gain type
>>> instr.setDataType('pz') # Define the data type
>>> result = instr.execute() # Execute the instruction and assign the results to 'result'
>>> print(result.poles) # Print the poles of the gain
[-1/(C*R)]
>>> print(result.zeros) # Print the zeros of the gain
[]
>>> print(result.DCvalue) # Print the zero-frequency value of the transfer
1.0
The function listPZ(<instructionresult>) can only print numeric pole-zero anlysis results. With ini.Hz==True the functions pz2html(<instructionresult>) and listPZ(<instructionresult>) display the values of poles and zeros in [Hz], else in [rad/s].
>>> print(ini.Hz) # Print diplay units for listPZ and pz2html
True
>>> instr.setSimType('numeric') # Switch to numeric analysis
>>> result = instr.execute() # Execute the instruction and assign the results to 'result'
>>> listPZ(result)
DC value of gain: 1.00e+0
Poles of gain:
n Real part [Hz] Imag part [Hz] Frequency [Hz] Q [-]
-- -------------- -------------- -------------- --------
0 -1.00e+03 0.00e+00 1.00e+03
Found no zeros.