def solve(self, freqs, complexfreq=False, refnode=gnd):
toolkit = self.toolkit
circuit_noloop = copy(self.cir)
circuit_noloop[self.device] = LoopBreaker(circuit_noloop[self.device],
self.inp,
self.inn,
self.outp,
self.outn,
parent=circuit_noloop,
instance_name=self.device)
x = self.toolkit.zeros(
self.cir.n) ## FIXME, this should come from the DC analysis
epar = self.epar
G = self.cir.G(x, epar)
G_noloop = circuit_noloop.G(x, epar)
C = self.cir.C(x, epar)
C_noloop = circuit_noloop.C(x, epar)
## Refer the voltages to the reference node by removing
## the rows and columns that corresponds to this node
irefnode = self.cir.get_node_index(refnode)
G, G_noloop, C, C_noloop = remove_row_col((G, G_noloop, C, C_noloop),
irefnode, self.toolkit)
if complexfreq:
slist = freqs
else:
slist = 2j * self.toolkit.pi * freqs
## Calculate return difference
def Ffunc(s):
Y = toolkit.toMatrix(G + s * C)
Y_noloop = toolkit.toMatrix(G_noloop + s * C_noloop)
return toolkit.det(Y) / toolkit.det(Y_noloop)
if isiterable(slist):
F = Waveform(self.toolkit.array(slist),
self.toolkit.array([Ffunc(s) for s in slist]),
xlabels=('frequency', ),
xunits=('Hz', ),
ylabel='F')
else:
F = Ffunc(slist)
## Calculate loop-gain
T = F - 1
result = InternalResultDict()
result['F'] = F
result['T'] = T
result['loopgain'] = -T
return result
def solve(self, freqs, complexfreq = False, refnode = gnd):
toolkit = self.toolkit
circuit_noloop = copy(self.cir)
circuit_noloop[self.device] = LoopBreaker(circuit_noloop[self.device],
self.inp,self.inn,
self.outp,self.outn,
parent = circuit_noloop,
instance_name = self.device)
x = self.toolkit.zeros(self.cir.n) ## FIXME, this should come from the DC analysis
epar = self.epar
G = self.cir.G(x, epar)
G_noloop = circuit_noloop.G(x, epar)
C = self.cir.C(x, epar)
C_noloop = circuit_noloop.C(x, epar)
## Refer the voltages to the reference node by removing
## the rows and columns that corresponds to this node
irefnode = self.cir.get_node_index(refnode)
G,G_noloop,C,C_noloop = remove_row_col((G,G_noloop,C,C_noloop),
irefnode, self.toolkit)
if complexfreq:
slist = freqs
else:
slist = 2j * self.toolkit.pi * freqs
## Calculate return difference
def Ffunc(s):
Y = toolkit.toMatrix(G + s*C)
Y_noloop = toolkit.toMatrix(G_noloop + s*C_noloop)
return toolkit.det(Y) / toolkit.det(Y_noloop)
if isiterable(slist):
F = Waveform(self.toolkit.array(slist),
self.toolkit.array([Ffunc(s) for s in slist]),
xlabels = ('frequency',),
xunits = ('Hz',),
ylabel = 'F')
else:
F = Ffunc(slist)
## Calculate loop-gain
T = F - 1
result = InternalResultDict()
result['F'] = F
result['T'] = T
result['loopgain'] = -T
return result
def ss_map_function(self, func, ss, refnode):
"""Apply a function over a list of frequencies or a single frequency"""
irefnode = self.cir.nodes.index(refnode)
def myfunc(s):
x = func(s)
# Insert reference node voltage
return self.toolkit.concatenate((x[:irefnode], self.toolkit.array([0.0]), x[irefnode:]))
if isiterable(ss):
return self.toolkit.array([myfunc(s) for s in ss]).swapaxes(0,1)
else:
return myfunc(ss)
def noise_map_function(self, func, ss, refnode):
"""Apply a function over a list of frequencies or a single frequency"""
irefnode = self.cir.nodes.index(refnode)
def myfunc(s):
x, g = func(s)
return x,g
if isiterable(ss):
xlist = []
glist = []
for s in ss:
x,g = myfunc(s)
xlist = xlist + [x]
glist = glist + [g]
return self.toolkit.array(xlist),self.toolkit.array(glist)
else:
return myfunc(ss)
def identify_sweep(x, maxerr=1e-6):
"""Identifies sweep from sweep values and return sweep instance"""
if isinstance(x, (LinSweep, LogSweep)):
return x
if not isiterable(x):
return LinSweep(x, x, 1)
values = np.array(list(x))
if len(values) == 1:
return LinSweep(values[0], values[0], 1)
linstep = np.diff(values)
if np.linalg.norm(linstep - linstep[0]) <= maxerr:
return LinSweep(values[0], values[-1], len(values))
else:
return Sweep(values)
def identify_sweep(x, maxerr=1e-6):
"""Identifies sweep from sweep values and return sweep instance"""
if isinstance(x, (LinSweep, LogSweep)):
return x
if not isiterable(x):
return LinSweep(x, x, 1)
values = np.array(list(x))
if len(values) == 1:
return LinSweep(values[0], values[0], 1)
linstep = np.diff(values)
if np.linalg.norm(linstep - linstep[0]) <= maxerr:
return LinSweep(values[0], values[-1], len(values))
else:
return Sweep(values)
def solve_s(self, freqs, complexfreq = False):
"""Calculate scattering (s) parameters of circuit
>>> c = SubCircuit()
>>> n1 = c.add_node('net1')
>>> n2 = c.add_node('net2')
>>> c['R1'] = R(n1, n2, r=9e3)
>>> c['R2'] = R(n2, gnd, r=1e3)
>>> an = TwoPortAnalysis(c, n1, gnd, n2, gnd)
>>> twoport = an.solve_s(freqs = 0)
>>> mu = 1/twoport.A[0,0]
>>> print mu
(0.1+0j)
"""
## The s-parameters of an n-port are defined as
## B = S * A
## where A and B are column-vectors of size n of
## the ingoing and outgoing waves respectively
## S is an NxN matrix containing the s-parameters
## The elements of the A and B vectors are defined as:
##
## a_n = (v_n + Z0 * i_n) / 2 * 1 / sqrt(|Re Z0|)
## b_n = (v_n - Z0 * i_n) / 2 * 1 / sqrt(|Re Z0|)
##
## where v is the port-voltage and i the current flowing
## into the device, Z0 is an arbitrary chosen impedance
##
## The straight-forward method to calculate the S matrix
## that is used here is to run n AC-analyses and in each
## analysis connect a voltage source of voltage 2V
## in series with a resistor with resistance R0 ohm
## (The chosen Z0 value is real). The other ports
## are terminated with resistance R0.
## The s-parameters S_k_n can now be calculated as:
## S_k_n = b_k / a_n
## where
## a_n = ((2-R0*i_n) + R0 * i+n) / 2 / sqrt(R0) = 1 / sqrt(R0)
## b_k = (v_k + v_k) / 2 / sqrt(R0) = v_k / sqrt(R0) | k != n
## b_n = ((2-R0*i_n) - R0*i_n) / 2 / sqrt(R0) = {i_n = (v_n - 2)/R0} =
## (2-2*R0*(v_n-2)/R0)/2/sqrt(R0) = (1 - v_n - 2) / sqrt(R0) =
## = (v_n - 1) / sqrt(R0)
## => S_k_n = b_k / a_n = v_k | k != n
## S_n_n = b_n / a_n = v_n - 1
##
##
toolkit = self.toolkit
# Reference impedance
g0 = 1
N = len(self.ports)
portnumbers = range(N)
S = np.zeros((N,N), dtype=object)
circuit = copy(self.cir)
refnode = self.ports[0][1]
## Place power sources at the ports
for n, sourceport in enumerate(self.ports):
circuit['_is%d'%n] = ISInternal(sourceport[1], sourceport[0], i=0,iac = 0, toolkit=toolkit)
circuit['_rl%d'%n] = G(sourceport[1], sourceport[0], g = g0, noisy=False, toolkit=toolkit)
if toolkit.symbolic:
## For now just one frequency is allowed
assert not isiterable(freqs)
Gmat, C, CY, u, x, ss = dc_steady_state(circuit, freqs,
refnode,
toolkit,
complexfreq = complexfreq,
epar = self.epar)
## Refer the voltages to the reference node by removing
## the rows and columns that corresponds to this node
irefnode = self.cir.get_node_index(refnode)
Gmat,C,CY,u = remove_row_col((Gmat,C,CY,u), irefnode, toolkit)
Y = C * ss + Gmat
detY = toolkit.det(Y)
for n, sourceport in enumerate(self.ports):
## Add stimulus to the port
circuit['_is%d'%n].ipar.iac = 2 * g0
## If symbolic the s-parameters are calculated using co-factors
if toolkit.symbolic:
u_wrefnode = circuit.u(x, analysis='internalac', epar=self.epar)
(u,) = circuit.remove_refnode((u_wrefnode,), refnode)
## Calculate s-parameters using cofactors
for k, port in enumerate(self.ports):
resname = "v(%s,%s)"%(port[0], port[1])
res = linearsolver_partial(Y, u, refnode, [resname],
circuit, toolkit, detY=detY)
if k == n:
S[k,n] = res[resname] - 1
else:
S[k,n] = res[resname]
else:
## Run AC-analysis
acana = AC(circuit, toolkit=toolkit, analysis='internalac')
res = acana.solve(freqs, refnode=refnode,
complexfreq = complexfreq)
## Obtain s-parameters
for k, port in enumerate(self.ports):
if k == n:
S[k,n] = res.v(port[0], port[1]) - 1
else:
S[k,n] = res.v(port[0], port[1])
## Clear stimulus to the port
circuit['_is%d'%n].ipar.iac = 0
## Find noise wave correlation matrix
## The method works as follows:
## 1. terminate all ports with z0
## 2. calculate transimpedances from a current source in each node
## to the port voltages by using the adjoint Y-matrix.
## As seen above the outgoing wave b is b=V(port_k) / sqrt(z0)
## for a terminated port.
## 3. Form a transform matrix T where the columns are the transimpedance
## vectors divided by sqrt(z0)
## 4. Calculate the correlation matrix as:
## CS = T * CY * T+
## Calculate transimpedances
branchlist = [Branch(*port) for port in self.ports]
transimpana = TransimpedanceAnalysis(circuit, toolkit=toolkit)
zmlist = transimpana.solve(freqs, branchlist, refnode=refnode,
complexfreq=complexfreq)
T = np.matrix(zmlist) * g0**0.5
## Complex frequency variable
if complexfreq:
s = freqs
else:
s = 2j*np.pi*freqs
## Calculate CY of circuit
x = np.zeros(circuit.n)
CY = circuit.CY(x, np.imag(s), epar = self.epar)
irefnode = circuit.get_node_index(refnode)
CY, = remove_row_col((CY,), irefnode, self.toolkit)
## Calculate noise wave correlation matrix
CS = np.array(T * CY * T.H)
return NPortS(S, CS, z0=1/toolkit.integer(g0))
def solve_s(self, freqs, complexfreq=False):
"""Calculate scattering (s) parameters of circuit
>>> c = SubCircuit()
>>> n1 = c.add_node('net1')
>>> n2 = c.add_node('net2')
>>> c['R1'] = R(n1, n2, r=9e3)
>>> c['R2'] = R(n2, gnd, r=1e3)
>>> an = TwoPortAnalysis(c, n1, gnd, n2, gnd)
>>> twoport = an.solve_s(freqs = 0)
>>> mu = 1/twoport.A[0,0]
>>> print mu
(0.1+0j)
"""
## The s-parameters of an n-port are defined as
## B = S * A
## where A and B are column-vectors of size n of
## the ingoing and outgoing waves respectively
## S is an NxN matrix containing the s-parameters
## The elements of the A and B vectors are defined as:
##
## a_n = (v_n + Z0 * i_n) / 2 * 1 / sqrt(|Re Z0|)
## b_n = (v_n - Z0 * i_n) / 2 * 1 / sqrt(|Re Z0|)
##
## where v is the port-voltage and i the current flowing
## into the device, Z0 is an arbitrary chosen impedance
##
## The straight-forward method to calculate the S matrix
## that is used here is to run n AC-analyses and in each
## analysis connect a voltage source of voltage 2V
## in series with a resistor with resistance R0 ohm
## (The chosen Z0 value is real). The other ports
## are terminated with resistance R0.
## The s-parameters S_k_n can now be calculated as:
## S_k_n = b_k / a_n
## where
## a_n = ((2-R0*i_n) + R0 * i+n) / 2 / sqrt(R0) = 1 / sqrt(R0)
## b_k = (v_k + v_k) / 2 / sqrt(R0) = v_k / sqrt(R0) | k != n
## b_n = ((2-R0*i_n) - R0*i_n) / 2 / sqrt(R0) = {i_n = (v_n - 2)/R0} =
## (2-2*R0*(v_n-2)/R0)/2/sqrt(R0) = (1 - v_n - 2) / sqrt(R0) =
## = (v_n - 1) / sqrt(R0)
## => S_k_n = b_k / a_n = v_k | k != n
## S_n_n = b_n / a_n = v_n - 1
##
##
toolkit = self.toolkit
# Reference impedance
g0 = 1
N = len(self.ports)
portnumbers = range(N)
S = np.zeros((N, N), dtype=object)
circuit = copy(self.cir)
refnode = self.ports[0][1]
## Place power sources at the ports
for n, sourceport in enumerate(self.ports):
circuit["_is%d" % n] = ISInternal(sourceport[1], sourceport[0], i=0, iac=0, toolkit=toolkit)
circuit["_rl%d" % n] = G(sourceport[1], sourceport[0], g=g0, noisy=False, toolkit=toolkit)
if toolkit.symbolic:
## For now just one frequency is allowed
assert not isiterable(freqs)
Gmat, C, CY, u, x, ss = dc_steady_state(
circuit, freqs, refnode, toolkit, complexfreq=complexfreq, epar=self.epar
)
## Refer the voltages to the reference node by removing
## the rows and columns that corresponds to this node
irefnode = self.cir.get_node_index(refnode)
Gmat, C, CY, u = remove_row_col((Gmat, C, CY, u), irefnode, toolkit)
Y = C * ss + Gmat
detY = toolkit.det(Y)
for n, sourceport in enumerate(self.ports):
## Add stimulus to the port
circuit["_is%d" % n].ipar.iac = 2 * g0
## If symbolic the s-parameters are calculated using co-factors
if toolkit.symbolic:
u_wrefnode = circuit.u(x, analysis="internalac", epar=self.epar)
(u,) = circuit.remove_refnode((u_wrefnode,), refnode)
## Calculate s-parameters using cofactors
for k, port in enumerate(self.ports):
resname = "v(%s,%s)" % (port[0], port[1])
res = linearsolver_partial(Y, u, refnode, [resname], circuit, toolkit, detY=detY)
if k == n:
S[k, n] = res[resname] - 1
else:
S[k, n] = res[resname]
else:
## Run AC-analysis
acana = AC(circuit, toolkit=toolkit, analysis="internalac")
res = acana.solve(freqs, refnode=refnode, complexfreq=complexfreq)
## Obtain s-parameters
for k, port in enumerate(self.ports):
if k == n:
S[k, n] = res.v(port[0], port[1]) - 1
else:
S[k, n] = res.v(port[0], port[1])
## Clear stimulus to the port
circuit["_is%d" % n].ipar.iac = 0
## Find noise wave correlation matrix
## The method works as follows:
## 1. terminate all ports with z0
## 2. calculate transimpedances from a current source in each node
## to the port voltages by using the adjoint Y-matrix.
## As seen above the outgoing wave b is b=V(port_k) / sqrt(z0)
## for a terminated port.
## 3. Form a transform matrix T where the columns are the transimpedance
## vectors divided by sqrt(z0)
## 4. Calculate the correlation matrix as:
## CS = T * CY * T+
## Calculate transimpedances
branchlist = [Branch(*port) for port in self.ports]
transimpana = TransimpedanceAnalysis(circuit, toolkit=toolkit)
zmlist = transimpana.solve(freqs, branchlist, refnode=refnode, complexfreq=complexfreq)
T = np.matrix(zmlist) * g0 ** 0.5
## Complex frequency variable
if complexfreq:
s = freqs
else:
s = 2j * np.pi * freqs
## Calculate CY of circuit
x = np.zeros(circuit.n)
CY = circuit.CY(x, np.imag(s), epar=self.epar)
irefnode = circuit.get_node_index(refnode)
CY, = remove_row_col((CY,), irefnode, self.toolkit)
## Calculate noise wave correlation matrix
CS = np.array(T * CY * T.H)
return NPortS(S, CS, z0=1 / toolkit.integer(g0))
