def get_variables(circ):
"""Get a sympy matrix containing the circuit variables to be solved for.
**Parameters:**
circ : circuit instance
The circuit
**Returns:**
vars : sympy matrix, shape (n, 1)
The variables in a column vector.
"""
# numero di soluzioni di tensione (al netto del ref)
nv_1 = circ.get_nodes_number() - 1
# descrizioni dei componenti non definibili in tensione
idescr = [elem.part_id.upper()
for elem in circ if circuit.is_elem_voltage_defined(elem)]
mna_size = nv_1 + len(idescr)
x = smzeros(mna_size, 1)
for i in range(mna_size):
if i < nv_1:
x[i, 0] = _symbol_factory("V" + str(circ.nodes_dict[i + 1]))
else:
x[i, 0] = _symbol_factory("I[" + idescr[i - nv_1] + "]")
return x
def _expand_matrix(mat, add_a_row=False, add_a_col=False):
if add_a_row:
row = smzeros(1, mat.shape[1])
mat = mat.row_insert(mat.shape[0], row)
if add_a_col:
col = sympy.zeros(mat.shape[0], 1)
mat = mat.col_insert(mat.shape[1], col)
return mat
def get_variables(circ):
"""Returns a sympy matrix with the circuit variables to be solved for.
"""
nv_1 = len(circ.nodes_dict) - 1 # numero di soluzioni di tensione (al netto del ref)
# descrizioni dei componenti non definibili in tensione
idescr = [ (elem.letter_id.upper() + elem.descr) \
for elem in circ.elements if circuit.is_elem_voltage_defined(elem) ]
mna_size = nv_1 + len(idescr)
x = smzeros((mna_size, 1))
for i in range(mna_size):
if i < nv_1:
x[i, 0] = sympy.Symbol("V" + str(circ.nodes_dict[i + 1]))
else:
x[i, 0] = sympy.Symbol("I["+idescr[i - nv_1]+"]")
return x
def get_variables(circ):
"""Returns a sympy matrix with the circuit variables to be solved for.
"""
nv_1 = len(circ.nodes_dict) - 1 # numero di soluzioni di tensione (al netto del ref)
# descrizioni dei componenti non definibili in tensione
idescr = [ (elem.letter_id.upper() + elem.descr) \
for elem in circ.elements if circuit.is_elem_voltage_defined(elem) ]
mna_size = nv_1 + len(idescr)
x = smzeros((mna_size, 1))
for i in range(mna_size):
if i < nv_1:
x[i, 0] = sympy.Symbol("V" + str(circ.nodes_dict[i + 1]))
else:
x[i, 0] = sympy.Symbol("I["+idescr[i - nv_1]+"]")
return x
def generate_mna_and_N(circ, opts, ac=False, verbose=3):
"""Generates a symbolic Modified Nodal Analysis matrix and N vector.
"""
# print options
n_of_nodes = len(circ.nodes_dict)
mna = smzeros(n_of_nodes)
N = smzeros((n_of_nodes, 1))
s = sympy.Symbol('s', complex=True)
subs_g = {}
for elem in circ:
if isinstance(elem, devices.Resistor):
# we use conductances instead of 1/R because there is a significant
# overhead handling many 1/R terms in sympy.
if elem.is_symbolic:
R = sympy.Symbol(elem.part_id.upper(),
real=True,
positive=True)
G = sympy.Symbol('G' + elem.part_id[1:],
real=True,
positive=True)
# but we keep track of which is which and substitute back after
# solving.
subs_g.update({G: 1 / R})
else:
R = elem.value
G = 1.0 / R
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + G
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - G
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - G
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + G
elif isinstance(elem, devices.Capacitor):
if ac:
if elem.is_symbolic:
capa = sympy.Symbol(elem.part_id.upper(),
real=True,
positive=True)
else:
capa = elem.value
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + s * capa
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - s * capa
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + s * capa
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - s * capa
else:
pass
elif isinstance(elem, devices.Inductor):
pass
elif isinstance(elem, devices.GISource):
if elem.is_symbolic:
alpha = sympy.Symbol(elem.part_id.upper(), real=True)
else:
alpha = elem.value
mna[elem.n1, elem.sn1] = mna[elem.n1, elem.sn1] + alpha
mna[elem.n1, elem.sn2] = mna[elem.n1, elem.sn2] - alpha
mna[elem.n2, elem.sn1] = mna[elem.n2, elem.sn1] - alpha
mna[elem.n2, elem.sn2] = mna[elem.n2, elem.sn2] + alpha
elif isinstance(elem, devices.ISource):
if elem.is_symbolic:
IDC = sympy.Symbol(elem.part_id.upper(), real=True)
else:
IDC = elem.dc_value
N[elem.n1, 0] = N[elem.n1, 0] + IDC
N[elem.n2, 0] = N[elem.n2, 0] - IDC
elif isinstance(elem, mosq.mosq_device) or isinstance(
elem, ekv.ekv_device):
gm = sympy.Symbol('gm_' + elem.part_id, real=True, positive=True)
mna[elem.n1, elem.ng] = mna[elem.n1, elem.ng] + gm
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - gm
mna[elem.n2, elem.ng] = mna[elem.n2, elem.ng] - gm
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + gm
if opts['r0s']:
r0 = sympy.Symbol('r0_' + elem.part_id,
real=True,
positive=True)
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + 1 / r0
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - 1 / r0
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - 1 / r0
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + 1 / r0
elif isinstance(elem, diode.diode):
gd = sympy.Symbol("g" + elem.part_id, positive=True)
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + gd
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - gd
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - gd
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + gd
elif isinstance(elem, devices.InductorCoupling):
pass
# this is taken care of within the inductors
elif circuit.is_elem_voltage_defined(elem):
pass
# we'll add its lines afterwards
elif verbose:
printing.print_warning("Skipped elem %s: not implemented." %
(elem.part_id.upper(), ))
pre_vde = mna.shape[0]
for elem in circ:
if circuit.is_elem_voltage_defined(elem):
index = mna.shape[0] # get_matrix_size(mna)[0]
mna = expand_matrix(mna, add_a_row=True, add_a_col=True)
N = expand_matrix(N, add_a_row=True, add_a_col=False)
# KCL
mna[elem.n1, index] = +1
mna[elem.n2, index] = -1
# KVL
mna[index, elem.n1] = +1
mna[index, elem.n2] = -1
if isinstance(elem, devices.VSource):
if elem.is_symbolic:
VDC = sympy.Symbol(elem.part_id.upper(), real=True)
else:
VDC = elem.dc_value
N[index, 0] = -VDC
elif isinstance(elem, devices.EVSource):
if elem.is_symbolic:
alpha = sympy.Symbol(elem.part_id.upper(), real=True)
else:
alpha = elem.alpha
mna[index, elem.sn1] = -alpha
mna[index, elem.sn2] = +alpha
elif isinstance(elem, devices.Inductor):
if ac:
if elem.is_symbolic:
L = sympy.Symbol(elem.part_id.upper(),
real=True,
positive=True)
else:
L = elem.L
mna[index, index] = -s * L
else:
pass
# already so: commented out
# N[index,0] = 0
elif isinstance(elem, devices.HVSource):
printing.print_warning(
"symbolic.py: BUG - hvsources are not implemented yet.")
sys.exit(33)
for elem in circ:
if circuit.is_elem_voltage_defined(elem):
if isinstance(elem, devices.Inductor):
if ac:
# find its index to know which column corresponds to its
# current
this_index = circ.find_vde_index(elem.part_id, verbose=0)
for cd in elem.coupling_devices:
if cd.is_symbolic:
M = sympy.Symbol(cd.part_id,
real=True,
positive=True)
else:
M = cd.K
# get `part_id` of the other inductor (eg. "L32")
other_id_wdescr = cd.get_other_inductor(elem.part_id)
# find its index to know which column corresponds to
# its current
other_index = circ.find_vde_index(other_id_wdescr,
verbose=0)
# add the term.
mna[pre_vde + this_index,
pre_vde + other_index] += -s * M
else:
pass
# all done
return (mna, N, subs_g)
def generate_mna_and_N(circ, opts, ac=False, verbose=3):
"""Generates a symbolic Modified Nodal Analysis matrix and N vector.
"""
# print options
n_of_nodes = len(circ.nodes_dict)
mna = smzeros(n_of_nodes)
N = smzeros((n_of_nodes, 1))
subs_g = {}
for elem in circ:
if isinstance(elem, devices.Resistor):
# we use conductances instead of 1/R because there is a significant
# overhead handling many 1/R terms in sympy.
if elem.is_symbolic:
R = _symbol_factory(
elem.part_id.upper(), real=True, positive=True)
G = _symbol_factory('G' + elem.part_id[1:], real=True, positive=True)
# but we keep track of which is which and substitute back after
# solving.
subs_g.update({G: 1 / R})
else:
R = elem.value
G = 1.0 / R
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + G
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - G
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - G
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + G
elif isinstance(elem, devices.Capacitor):
if ac:
if elem.is_symbolic:
capa = _symbol_factory(
elem.part_id.upper(), real=True, positive=True)
else:
capa = elem.value
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + s * capa
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - s * capa
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + s * capa
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - s * capa
else:
pass
elif isinstance(elem, devices.Inductor):
pass
elif isinstance(elem, devices.GISource):
if elem.is_symbolic:
alpha = _symbol_factory(elem.part_id.upper(), real=True)
else:
alpha = elem.value
mna[elem.n1, elem.sn1] = mna[elem.n1, elem.sn1] + alpha
mna[elem.n1, elem.sn2] = mna[elem.n1, elem.sn2] - alpha
mna[elem.n2, elem.sn1] = mna[elem.n2, elem.sn1] - alpha
mna[elem.n2, elem.sn2] = mna[elem.n2, elem.sn2] + alpha
elif isinstance(elem, devices.ISource):
if elem.is_symbolic:
IDC = _symbol_factory(elem.part_id.upper())
else:
IDC = elem.dc_value
N[elem.n1, 0] = N[elem.n1, 0] + IDC
N[elem.n2, 0] = N[elem.n2, 0] - IDC
elif isinstance(elem, mosq.mosq_device) or isinstance(elem, ekv.ekv_device):
gm = _symbol_factory('gm_' + elem.part_id, real=True, positive=True)
mna[elem.n1, elem.ng] = mna[elem.n1, elem.ng] + gm
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - gm
mna[elem.n2, elem.ng] = mna[elem.n2, elem.ng] - gm
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + gm
if opts['r0s']:
r0 = _symbol_factory(
'r0_' + elem.part_id, real=True, positive=True)
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + 1 / r0
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - 1 / r0
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - 1 / r0
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + 1 / r0
elif isinstance(elem, diode.diode):
gd = _symbol_factory("g" + elem.part_id, positive=True)
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + gd
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - gd
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - gd
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + gd
elif isinstance(elem, devices.InductorCoupling):
pass
# this is taken care of within the inductors
elif circuit.is_elem_voltage_defined(elem):
pass
# we'll add its lines afterwards
elif verbose:
printing.print_warning(
"Skipped elem %s: not implemented." % (elem.part_id.upper(),))
pre_vde = mna.shape[0]
for elem in circ:
if circuit.is_elem_voltage_defined(elem):
index = mna.shape[0] # get_matrix_size(mna)[0]
mna = expand_matrix(mna, add_a_row=True, add_a_col=True)
N = expand_matrix(N, add_a_row=True, add_a_col=False)
# KCL
mna[elem.n1, index] = +1
mna[elem.n2, index] = -1
# KVL
mna[index, elem.n1] = +1
mna[index, elem.n2] = -1
if isinstance(elem, devices.VSource):
if elem.is_symbolic:
VDC = _symbol_factory(elem.part_id.upper())
else:
VDC = elem.dc_value
N[index, 0] = -VDC
elif isinstance(elem, devices.EVSource):
if elem.is_symbolic:
alpha = _symbol_factory(elem.part_id.upper(), real=True)
else:
alpha = elem.alpha
mna[index, elem.sn1] = -alpha
mna[index, elem.sn2] = +alpha
elif isinstance(elem, devices.Inductor):
if ac:
if elem.is_symbolic:
L = _symbol_factory(
elem.part_id.upper(), real=True, positive=True)
else:
L = elem.L
mna[index, index] = -s * L
else:
pass
# already so: commented out
# N[index,0] = 0
elif isinstance(elem, devices.HVSource):
printing.print_warning(
"symbolic.py: BUG - hvsources are not implemented yet.")
sys.exit(33)
for elem in circ:
if circuit.is_elem_voltage_defined(elem):
if isinstance(elem, devices.Inductor):
if ac:
# find its index to know which column corresponds to its
# current
this_index = circ.find_vde_index(elem.part_id, verbose=0)
for cd in elem.coupling_devices:
if cd.is_symbolic:
M = _symbol_factory(
cd.part_id, real=True, positive=True)
else:
M = cd.K
# get `part_id` of the other inductor (eg. "L32")
other_id_wdescr = cd.get_other_inductor(elem.part_id)
# find its index to know which column corresponds to
# its current
other_index = circ.find_vde_index(
other_id_wdescr, verbose=0)
# add the term.
mna[pre_vde + this_index,
pre_vde + other_index] += -s * M
else:
pass
# all done
return (mna, N, subs_g)
def generate_mna_and_N(circ, opts, ac=False, subs=None, verbose=3):
"""Generate a symbolic Modified Nodal Analysis matrix and N vector.
Only elements that have an ``is_symbolic`` attribute set to ``True``
(the default) are considered symbolically. Simply set the attribute to
``False`` to employ the numeric value. This allows to simplify and speed
up the work of the symbolic solver.
The formulation can be performed using conductances or resistances. The
choice is made setting the global ``options.symb_formulate_with_gs`` value
to ``True``. A formulation done in terms of resistors, may result in many
separate :math:`1/R` terms in the matrices. Historically, ``sympy`` choked
on those, because of a long-standing bug in polys. Now the issue seems to
have been solved and the two computations should be symbolically equivalent
albeit computationally different (as expected). The option value
``options.symb_formulate_with_gs`` is provided to restore the old
functionality in case you use an old version of ``sympy``.
**Parameters:**
circ : circuit instance
The circuit.
opts : dict
The options to be used for the generation of the matrices. As of now,
the only supported option is ``'r0s'`` which can be set to either
``True`` or ``False``, and selects whether the equivalent output
resistance of the transistors should be taken into account or not.
ac : bool, optional
Flag to trigger the inclusion of frequency-dependent elements. Defaults
to ``False`` currently (but may change).
subs : dict, optional
The substitution dictionary, composed by mappings of
``<symbol>``:``<sympy expression>``.
verbose : int, optional
Verbosity flag, from ``0`` (silent) to ``6`` (very logorrhoic). Defaults
to ``3``.
**Returns:**
mna, N : Sympy matrices
The MNA matrix and the contant term of symbolic type.
subs_gs : dict of symbols
In case the formulation of the MNA is performed in terms of
conducatances, this dictionary is to be used to substitute away the
conducatances for the resistor symbols, after the circuit is solved but
before the results are shown to the user. ``sympy``'s ``sub()`` can take
care of that for you. If not necessary, this dictionary is empty.
.. note::
Setting ``opts['r0s'] = True``, ie considering all the transistors output
resistances, can significantly slow down -- or even prevent by consuming
all available memory -- the solution of complex circuits with several
active elements.
We recommend a combination of the following:
* setting the above option in simple circuits only,
* inserting explicitely the :math:`r_0` you wish to consider at circuit
level,
* beefing up your machine with extra RAM and extra computing power,
* being patient.
"""
n_of_nodes = circ.get_nodes_number()
mna = smzeros(n_of_nodes)
N = smzeros(n_of_nodes, 1)
subs_g = {}
for elem in circ:
if isinstance(elem, devices.Resistor):
# we use conductances instead of 1/R because there is a significant
# overhead handling many 1/R terms in sympy.
if elem.is_symbolic:
R = _symbol_factory(elem.part_id.upper(), real=True,
positive=True)
if R in subs: # instant substitution
R = subs[R]
if options.symb_formulate_with_gs:
G = _symbol_factory('Gxxx' + str(R)[1:], real=True,
positive=True)
# but we keep track of which is which and substitute back after
# solving.
subs_g.update({G:1/R})
else:
G = 1.0/R
else:
G = 1.0/elem.value
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + G
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - G
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - G
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + G
elif isinstance(elem, devices.Capacitor):
if ac:
if elem.is_symbolic:
capa = _symbol_factory(
elem.part_id.upper(), real=True, positive=True)
if capa in subs: # instant substitution
capa = subs[capa]
else:
capa = elem.value
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + s * capa
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - s * capa
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + s * capa
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - s * capa
else:
pass
elif isinstance(elem, devices.Inductor):
pass
elif isinstance(elem, devices.GISource):
if elem.is_symbolic:
alpha = _symbol_factory(elem.part_id.upper(), real=True)
if alpha in subs: # instant substitution
alpha = subs[alpha]
else:
alpha = elem.value
mna[elem.n1, elem.sn1] = mna[elem.n1, elem.sn1] + alpha
mna[elem.n1, elem.sn2] = mna[elem.n1, elem.sn2] - alpha
mna[elem.n2, elem.sn1] = mna[elem.n2, elem.sn1] - alpha
mna[elem.n2, elem.sn2] = mna[elem.n2, elem.sn2] + alpha
elif isinstance(elem, devices.ISource):
if elem.is_symbolic:
IDC = _symbol_factory(elem.part_id.upper())
if IDC in subs: # instant substitution
IDC = subs[IDC]
else:
IDC = elem.dc_value
N[elem.n1, 0] = N[elem.n1, 0] + IDC
N[elem.n2, 0] = N[elem.n2, 0] - IDC
elif isinstance(elem, mosq.mosq_device) or isinstance(elem, ekv.ekv_device):
gm = _symbol_factory('gm_' + elem.part_id, real=True, positive=True)
if gm in subs: # instant substitution
gm = subs[gm]
mna[elem.n1, elem.ng] = mna[elem.n1, elem.ng] + gm
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - gm
mna[elem.n2, elem.ng] = mna[elem.n2, elem.ng] - gm
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + gm
if opts['r0s']:
r0 = _symbol_factory(
'r0_' + elem.part_id, real=True, positive=True)
if r0 in subs: # instant substitution
r0 = subs[r0]
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + 1 / r0
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - 1 / r0
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - 1 / r0
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + 1 / r0
elif isinstance(elem, diode.diode):
gd = _symbol_factory("g" + elem.part_id, positive=True)
if gd in subs: # instant substitution
gd = subs[gd]
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + gd
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - gd
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - gd
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + gd
elif isinstance(elem, devices.FISource):
# These are added after all VDEs have been accounted for
pass
elif isinstance(elem, devices.InductorCoupling):
pass
# this is taken care of within the inductors
elif circuit.is_elem_voltage_defined(elem):
pass
# we'll add its lines afterwards
elif verbose:
printing.print_warning("Skipped elem %s: not implemented." %
(elem.part_id.upper(),))
pre_vde = mna.shape[0]
for elem in circ:
if circuit.is_elem_voltage_defined(elem):
index = mna.shape[0] # get_matrix_size(mna)[0]
mna = _expand_matrix(mna, add_a_row=True, add_a_col=True)
N = _expand_matrix(N, add_a_row=True, add_a_col=False)
# KCL
mna[elem.n1, index] = +1
mna[elem.n2, index] = -1
# KVL
mna[index, elem.n1] = +1
mna[index, elem.n2] = -1
if isinstance(elem, devices.VSource):
if elem.is_symbolic:
VDC = _symbol_factory(elem.part_id.upper())
if VDC in subs: # instant substitution
VDC = subs[VDC]
else:
VDC = elem.dc_value
N[index, 0] = -VDC
elif isinstance(elem, devices.EVSource):
if elem.is_symbolic:
alpha = _symbol_factory(elem.part_id.upper(), real=True)
if alpha in subs: # instant substitution
alpha = subs[alpha]
else:
alpha = elem.alpha
mna[index, elem.sn1] = -alpha
mna[index, elem.sn2] = +alpha
elif isinstance(elem, devices.HVSource):
if elem.is_symbolic:
alpha = _symbol_factory(elem.part_id.upper(), real=True)
if alpha in subs: # instant substitution
alpha = subs[alpha]
else:
alpha = elem.alpha
source_index = circ.find_vde_index(elem.source_id)
mna[index, n_of_nodes + source_index] = +alpha
elif isinstance(elem, devices.Inductor):
if ac:
if elem.is_symbolic:
L = _symbol_factory(
elem.part_id.upper(), real=True, positive=True)
if L in subs: # instant substitution
L = subs[L]
else:
L = elem.L
mna[index, index] = -s * L
else:
pass
# already so: commented out
# N[index,0] = 0
else:
raise circuit.CircuitError('Element %s is not supported. ' +
'Please report this bug.' %
elem.__class__)
for elem in circ:
if ac and isinstance(elem, devices.Inductor):
# find its index to know which column corresponds to its
# current
this_index = circ.find_vde_index(elem.part_id, verbose=0)
for cd in elem.coupling_devices:
if cd.is_symbolic:
M = _symbol_factory(
cd.part_id, real=True, positive=True)
if M in subs: # instant substitution
M = subs[M]
else:
M = cd.K
# get `part_id` of the other inductor (eg. "L32")
other_id_wdescr = cd.get_other_inductor(elem.part_id)
# find its index to know which column corresponds to
# its current
other_index = circ.find_vde_index(
other_id_wdescr, verbose=0)
# add the term.
mna[pre_vde + this_index,
pre_vde + other_index] += -s * M
elif isinstance(elem, devices.FISource):
source_current_index = circ.find_vde_index(elem.source_id, verbose=0)
if elem.is_symbolic:
F = _symbol_factory(elem.part_id, real=True)
if F in subs: # instant substitution
F = subs[F]
else:
F = elem.alpha
mna[elem.n1, pre_vde + source_current_index] += +F
mna[elem.n2, pre_vde + source_current_index] += -F
else:
pass
# all done
return mna, N, subs_g
def generate_mna_and_N(circ, opts, ac=False):
"""Generates a symbolic Modified Nodal Analysis matrix and N vector.
"""
#print options
n_of_nodes = len(circ.nodes_dict)
mna = smzeros(n_of_nodes)
N = smzeros((n_of_nodes, 1))
s = sympy.Symbol("s", complex=True)
subs_g = {}
#process_elements()
for elem in circ.elements:
#if elem.is_nonlinear and not (isinstance(elem, mosq.mosq_device) or isinstance(elem, ekv.ekv_device)):
# print "Skipped elem "+elem.letter_id.upper()+elem.descr + ": not implemented."
# continue
if isinstance(elem, devices.resistor):
# we use conductances instead of 1/R because there is a significant
# overhead handling many 1/R terms in sympy.
if elem.is_symbolic:
R = sympy.Symbol(elem.letter_id.upper()+elem.descr, real=True)
G = sympy.Symbol("G"+elem.descr, real=True)
# but we keep track of which is which and substitute back after solving.
subs_g.update({G:1/R})
else:
R = elem.R
G = 1.0/R
#mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + 1/R
#mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - 1/R
#mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - 1/R
#mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + 1/R
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + G
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - G
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - G
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + G
elif isinstance(elem, devices.capacitor):
if ac:
if elem.is_symbolic:
capa = sympy.Symbol(elem.letter_id.upper()+elem.descr, real=True)
else:
capa = elem.C
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + s*capa
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - s*capa
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + s*capa
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - s*capa
else:
pass
elif isinstance(elem, devices.inductor):
pass
elif isinstance(elem, devices.gisource):
if elem.is_symbolic:
alpha = sympy.Symbol(elem.letter_id+elem.descr, real=True)
else:
alpha = elem.alpha
mna[elem.n1, elem.sn1] = mna[elem.n1, elem.sn1] + alpha
mna[elem.n1, elem.sn2] = mna[elem.n1, elem.sn2] - alpha
mna[elem.n2, elem.sn1] = mna[elem.n2, elem.sn1] - alpha
mna[elem.n2, elem.sn2] = mna[elem.n2, elem.sn2] + alpha
elif isinstance(elem, devices.isource):
if elem.is_symbolic:
IDC = sympy.Symbol(elem.letter_id.upper()+elem.descr, real=True)
else:
IDC = elem.idc
N[elem.n1, 0] = N[elem.n1, 0] + IDC
N[elem.n2, 0] = N[elem.n2, 0] - IDC
elif isinstance(elem, mosq.mosq_device) or isinstance(elem, ekv.ekv_device):
gm = sympy.Symbol('gm_'+elem.letter_id+elem.descr, real=True)
mna[elem.n1, elem.ng] = mna[elem.n1, elem.ng] + gm
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - gm
mna[elem.n2, elem.ng] = mna[elem.n2, elem.ng] - gm
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + gm
if opts['r0s']:
r0 = sympy.Symbol('r0_'+elem.letter_id+elem.descr, real=True)
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + 1/r0
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - 1/r0
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - 1/r0
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + 1/r0
elif isinstance(elem, diode.diode):
gd = sympy.Symbol("g"+elem.letter_id+elem.descr)
mna[elem.n1, elem.n1] = mna[elem.n1, elem.n1] + gd
mna[elem.n1, elem.n2] = mna[elem.n1, elem.n2] - gd
mna[elem.n2, elem.n1] = mna[elem.n2, elem.n1] - gd
mna[elem.n2, elem.n2] = mna[elem.n2, elem.n2] + gd
elif isinstance(elem, devices.inductor_coupling):
pass
# this is taken care of within the inductors
elif circuit.is_elem_voltage_defined(elem):
pass
#we'll add its lines afterwards
else:
printing.print_warning("Skipped elem %s: not implemented." % (elem.letter_id.upper()+elem.descr,))
pre_vde = mna.shape[0]
for elem in circ.elements:
if circuit.is_elem_voltage_defined(elem):
index = mna.shape[0] #get_matrix_size(mna)[0]
mna = expand_matrix(mna, add_a_row=True, add_a_col=True)
N = expand_matrix(N, add_a_row=True, add_a_col=False)
# KCL
mna[elem.n1, index] = +1
mna[elem.n2, index] = -1
# KVL
mna[index, elem.n1] = +1
mna[index, elem.n2] = -1
if isinstance(elem, devices.vsource):
if elem.is_symbolic:
VDC = sympy.Symbol(elem.letter_id.upper() + elem.descr, real=True)
else:
VDC = elem.vdc
N[index, 0] = -VDC
elif isinstance(elem, devices.evsource):
if elem.is_symbolic:
alpha = sympy.Symbol(elem.letter_id.upper() + elem.descr, real=True)
else:
alpha = elem.alpha
mna[index, elem.sn1] = -alpha
mna[index, elem.sn2] = +alpha
elif isinstance(elem, devices.inductor):
if ac:
if elem.is_symbolic:
L = sympy.Symbol(elem.letter_id.upper() + elem.descr, real=True)
else:
L = elem.L
mna[index, index] = -s*L
else:
pass
# already so: commented out
# N[index,0] = 0
elif isinstance(elem, devices.hvsource):
printing.print_warning("symbolic.py: BUG - hvsources are not implemented yet.")
sys.exit(33)
for elem in circ.elements:
if circuit.is_elem_voltage_defined(elem):
if isinstance(elem, devices.inductor):
if ac:
# find its index to know which column corresponds to its current
this_index = circ.find_vde_index("L"+elem.descr, verbose=0)
for cd in elem.coupling_devices:
if cd.is_symbolic:
M = sympy.Symbol("M" + cd.descr, real=True)
else:
M = cd.K
# get id+descr of the other inductor (eg. "L32")
other_id_wdescr = cd.get_other_inductor("L"+elem.descr)
# find its index to know which column corresponds to its current
other_index = circ.find_vde_index(other_id_wdescr, verbose=0)
# add the term.
#print "other_index: "+str(other_index)
#print "this_index: "+str(this_index)
mna[pre_vde+this_index,pre_vde+other_index] += -s*M
#print mna
else:
pass
# already so: commented out
# N[index,0] = 0
#all done
return (mna, N, subs_g)