def loop_analysis(g, ctrl_src, tree, types={}):
"""Loop analysis respect to the tree of the network graph g"""
eqs = []
vars = []
# loop equations of the cobranch voltages
cobranches = g.branches() - tree.branches()
for cobranch in cobranches:
if btype(cobranch, types) not in 'IFG':
lpos, lneg = g.loop(cobranch, tree, include_cobranch=True)
lhs_pos = [Calculus(f_u(b, ctrl_src, types)) for b in lpos]
lhs_neg = [Calculus(f_u(b, ctrl_src, types)) for b in lneg]
lhs = Add(*lhs_pos) - Add(*lhs_neg)
eqs.append(lhs)
if btype(cobranch, types) not in 'U':
vars.append(Calculus('I_' + cobranch))
if btype(cobranch, types) in 'N':
vars.append(Calculus('V_' + cobranch))
# cut equations of the tree currents (for substitution or additional)
tcur = {}
for tb in tree.branches():
bpos, bneg = g.cut(tb, tree, include_tree_branch=False)
# moving (bpos, bneg) from lhs to rhs by negation
rhs_pos = [Calculus(branch_current(b, ctrl_src, types)) for b in bneg]
rhs_neg = [Calculus(branch_current(b, ctrl_src, types)) for b in bpos]
rhs = Add(*rhs_pos) - Add(*rhs_neg)
if btype(tb, types) not in 'IFGU':
tcur[Calculus('I_' + tb)] = rhs.expand()
if btype(tb, types) in 'N':
vars.append(Calculus('V_' + tb))
else:
eqs.append(Calculus(f_i(tb, ctrl_src, types)) - rhs)
if btype(tb, types) not in 'U':
vars.append(Calculus('V_' + tb))
# finally add variables and equations of controlled sources
for src, ctrl in ctrl_src.items():
if btype(src, types) in 'EG' and btype(ctrl, types) != 'V':
v_ctrl = Calculus('V_' + ctrl)
if v_ctrl not in vars: # ctrl is no 'IFG' in tree
# control voltage is unknown
vars.append(v_ctrl)
# try if control voltage can be substituted
# then control branch is a (controlled) voltage source
lhs = v_ctrl - f_u(ctrl, ctrl_src, types)
if lhs == 0:
# ctrl is a current source
if ctrl in cobranches:
# add missing loop equation for v_ctrl which
# was omitted due to: btype(cobranch, types) not in 'IFG'
lpos, lneg = g.loop(ctrl, tree, include_cobranch=False)
lhs_pos = [
Calculus(f_u(b, ctrl_src, types)) for b in lpos
]
lhs_neg = [
Calculus(f_u(b, ctrl_src, types)) for b in lneg
]
lhs = v_ctrl + Add(*lhs_pos) - Add(*lhs_neg)
# if v_ctrl is in tree then var and cut equation are
# already added because ctrl is a current source
eqs.append(lhs)
elif btype(src, types) in 'F' and src in cobranches:
if ctrl in tree.branches() and btype(ctrl, types) not in 'IFG':
i_ctrl = Calculus('I_' + ctrl)
# just a test avoiding duplication
if i_ctrl not in vars:
# control current is unknown
vars.append(i_ctrl)
# remove cut equation for ctrl from tcur and add it to eqs
eqs.append(i_ctrl - tcur.pop(i_ctrl))
# substitute tree currents by cobranch currents
eqs = [e.subs(tcur).expand() for e in eqs]
return eqs, vars
def cut_analysis(g, ctrl_src, tree, types={}):
"""Cut analysis respect to the tree of the network graph g"""
eqs = []
vars = []
# cut equations of the tree currents
for tb in tree.branches():
if btype(tb, types) not in 'VEH':
bpos, bneg = g.cut(tb, tree)
lhs_pos = [Calculus(f_i(b, ctrl_src, types)) for b in bpos]
lhs_neg = [Calculus(f_i(b, ctrl_src, types)) for b in bneg]
lhs = Add(*lhs_pos) - Add(*lhs_neg)
eqs.append(lhs)
if btype(tb, types) not in 'U':
vars.append(Calculus(branch_voltage(tb, ctrl_src, types)))
if btype(tb, types) in 'N':
vars.append(Calculus(branch_current(tb, ctrl_src, types)))
# loop equations of the cobranch voltages
cobranches = g.branches() - tree.branches()
covolts = {}
for cobranch in cobranches:
lpos, lneg = g.loop(cobranch, tree)
# moving (bpos, bneg) from lhs to rhs by negation
rhs_pos = [Calculus(branch_voltage(b, ctrl_src, types)) for b in lneg]
rhs_neg = [Calculus(branch_voltage(b, ctrl_src, types)) for b in lpos]
rhs = Add(*rhs_pos) - Add(*rhs_neg)
rhs = rhs.expand()
if btype(cobranch, types) not in 'VEHU':
covolts[Calculus(branch_voltage(cobranch, ctrl_src, types))] = rhs
if btype(cobranch, types) in 'N':
vars.append(Calculus('I_' + cobranch))
else:
eqs.append(Calculus(f_u(cobranch, ctrl_src, types)) - rhs)
if btype(cobranch, types) not in 'U':
vars.append(Calculus('I_' + cobranch))
# finally add variables and equations of controlled sources
for src, ctrl in ctrl_src.items():
if btype(src, types) in 'FH' and btype(ctrl, types) != 'I':
i_ctrl = Calculus('I_' + ctrl)
if i_ctrl not in vars: # ctrl is no 'VEH' in cotree
# control current is unknown
vars.append(i_ctrl)
# try if control current can be substituted
# then control branch is a (controlled) current source
lhs = i_ctrl - Calculus(f_i(ctrl, ctrl_src, types))
if lhs == 0:
# ctrl is a voltage source
if ctrl in tree.branches():
# add missing cut equation for i_ctrl which
# was omitted due to: btype(tb, types) not in 'VEH'
bpos, bneg = g.cut(ctrl,
tree,
include_tree_branch=False)
lhs_pos = [
Calculus(f_i(b, ctrl_src, types)) for b in bpos
]
lhs_neg = [
Calculus(f_i(b, ctrl_src, types)) for b in bneg
]
lhs = i_ctrl + Add(*lhs_pos) - Add(*lhs_neg)
# if i_ctrl is in cotree then var and loop equation are
# already added because ctrl is a voltage source
eqs.append(lhs)
elif btype(src, types) in 'E' and src in tree.branches():
if ctrl in cobranches and btype(ctrl, types) not in 'VEH':
v_ctrl = Calculus('V_' + ctrl)
# just a test avoiding duplication
if v_ctrl not in vars:
# control voltage is unknown
vars.append(v_ctrl)
# remove loop equation for ctrl from covolts and add to eqs
eqs.append(v_ctrl - covolts.pop(v_ctrl))
# substitute cobranch voltages by tree voltages
eqs = [e.subs(covolts).expand() for e in eqs]
return eqs, vars