def solve(self, freqs, refnode = gnd, complexfreq = False):
toolkit = self.toolkit
x = self.toolkit.zeros(self.cir.n) ## FIXME, this should be replaced by DC-analysis
self.loopprobe['vinj'].ipar.vac = 1
self.loopprobe['iinj'].ipar.iac = 0
ac_vinj = AC(self.cir, toolkit=toolkit)
res_vinj = ac_vinj.solve(freqs, refnode = refnode,
complexfreq=complexfreq,
u = self.cir.u(x, analysis='feedback'))
self.loopprobe['vinj'].ipar.vac = 0
self.loopprobe['iinj'].ipar.iac = 1
ac_iinj = AC(self.cir, toolkit=toolkit)
res_iinj = ac_iinj.solve(freqs, refnode = refnode,
complexfreq=complexfreq,
u = self.cir.u(x, analysis='feedback'))
B = res_vinj.i(self.loopprobe_name + '.vinj.plus')
D = res_vinj.v(self.loopprobe_name + '.inp', self.loopprobe_name + '.inn')
A = res_iinj.i(self.loopprobe_name + '.vinj.plus')
C = res_iinj.v(self.loopprobe_name + '.inp', self.loopprobe_name + '.inn')
T = (2*(A*D - B*C) - A + D) / (2*(B*C - A*D) + A - D + 1)
result = InternalResultDict()
result['F'] = 1 + T
result['T'] = T
result['loopgain'] = -T
return result
def solve_abcd(self, freqs, refnode=gnd, complexfreq=False):
(inp, inn), (outp, outn) = self.ports
toolkit = self.toolkit
## Add voltage source at input port and create
## copies with output open and shorted respectively
circuit_vs_open = copy(self.cir)
circuit_vs_open["VS_TwoPort"] = VS(inp, inn, vac=1)
circuit_vs_shorted = copy(circuit_vs_open)
circuit_vs_shorted["VL_TwoPort"] = VS(outp, outn, vac=0)
## Run AC-analysis on the two circuits
ac_open = AC(circuit_vs_open, toolkit=toolkit)
ac_shorted = AC(circuit_vs_shorted, toolkit=toolkit)
res_open = ac_open.solve(freqs, refnode=refnode, complexfreq=complexfreq)
res_shorted = ac_shorted.solve(freqs, refnode=refnode, complexfreq=complexfreq)
A = res_open.v(inp, inn) / res_open.v(outp, outn)
B = res_shorted.v(inp, inn) / res_shorted.i("VL_TwoPort.plus")
C = res_open.i("VS_TwoPort.minus") / res_open.v(outp, outn)
D = res_shorted.i("VS_TwoPort.minus") / res_shorted.i("VL_TwoPort.plus")
return np.array([[A, B], [C, D]], dtype=object)
def solve_abcd(self, freqs, refnode = gnd, complexfreq = False):
(inp, inn), (outp, outn) = self.ports
toolkit = self.toolkit
## Add voltage source at input port and create
## copies with output open and shorted respectively
circuit_vs_open = copy(self.cir)
circuit_vs_open['VS_TwoPort'] = VS(inp, inn, vac=1)
circuit_vs_shorted = copy(circuit_vs_open)
circuit_vs_shorted['VL_TwoPort'] = VS(outp, outn, vac=0)
## Run AC-analysis on the two circuits
ac_open = AC(circuit_vs_open, toolkit=toolkit)
ac_shorted = AC(circuit_vs_shorted, toolkit=toolkit)
res_open = ac_open.solve(freqs, refnode = refnode,
complexfreq=complexfreq)
res_shorted = ac_shorted.solve(freqs, refnode = refnode,
complexfreq=complexfreq)
A = res_open.v(inp, inn) / res_open.v(outp, outn)
B = res_shorted.v(inp, inn) / res_shorted.i('VL_TwoPort.plus')
C = res_open.i('VS_TwoPort.minus') / res_open.v(outp, outn)
D = res_shorted.i('VS_TwoPort.minus') / res_shorted.i('VL_TwoPort.plus')
return np.array([[A,B],[C,D]], dtype=object)
def solve(self, freqs, refnode=gnd, complexfreq=False):
toolkit = self.toolkit
x = self.toolkit.zeros(
self.cir.n) ## FIXME, this should be replaced by DC-analysis
self.loopprobe['vinj'].ipar.vac = 1
self.loopprobe['iinj'].ipar.iac = 0
ac_vinj = AC(self.cir, toolkit=toolkit)
res_vinj = ac_vinj.solve(freqs,
refnode=refnode,
complexfreq=complexfreq,
u=self.cir.u(x, analysis='feedback'))
self.loopprobe['vinj'].ipar.vac = 0
self.loopprobe['iinj'].ipar.iac = 1
ac_iinj = AC(self.cir, toolkit=toolkit)
res_iinj = ac_iinj.solve(freqs,
refnode=refnode,
complexfreq=complexfreq,
u=self.cir.u(x, analysis='feedback'))
B = res_vinj.i(self.loopprobe_name + '.vinj.plus')
D = res_vinj.v(self.loopprobe_name + '.inp',
self.loopprobe_name + '.inn')
A = res_iinj.i(self.loopprobe_name + '.vinj.plus')
C = res_iinj.v(self.loopprobe_name + '.inp',
self.loopprobe_name + '.inn')
T = (2 * (A * D - B * C) - A + D) / (2 * (B * C - A * D) + A - D + 1)
result = InternalResultDict()
result['F'] = 1 + T
result['T'] = T
result['loopgain'] = -T
return result
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))
