You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
389 lines
13 KiB
Python
389 lines
13 KiB
Python
import scipy
|
|
import numpy
|
|
from numpy.typing import ArrayLike, NDarray
|
|
|
|
|
|
#from simphony.elements import Model
|
|
#from simphony.netlist import Subcircuit
|
|
#from simphony.simulation import SweepSimulation
|
|
#
|
|
#from matplotlib import pyplot as plt
|
|
#
|
|
#
|
|
#class PeriodicLayer(Model):
|
|
# def __init__(self, left_modes, right_modes, s_params):
|
|
# self.left_modes = left_modes
|
|
# self.right_modes = right_modes
|
|
# self.left_ports = len(self.left_modes)
|
|
# self.right_ports = len(self.right_modes)
|
|
# self.normalize_fields()
|
|
# self.s_params = s_params
|
|
#
|
|
# def normalize_fields(self):
|
|
# for mode in range(len(self.left_modes)):
|
|
# self.left_modes[mode].normalize()
|
|
# for mode in range(len(self.right_modes)):
|
|
# self.right_modes[mode].normalize()
|
|
#
|
|
#
|
|
#class PeriodicEME:
|
|
# def __init__(self, layers=[], num_periods=1):
|
|
# self.layers = layers
|
|
# self.num_periods = num_periods
|
|
# self.wavelength = wavelength
|
|
#
|
|
# def propagate(self):
|
|
# wl = self.wavelength
|
|
# if not len(self.layers):
|
|
# raise Exception("Must place layers before propagating")
|
|
#
|
|
# num_modes = max([l.num_modes for l in self.layers])
|
|
# iface = InterfaceSingleMode if num_modes == 1 else InterfaceMultiMode
|
|
#
|
|
# eme = EME(layers=self.layers)
|
|
# left, right = eme.propagate()
|
|
# self.single_period = eme.s_matrix
|
|
#
|
|
# period_layer = PeriodicLayer(left.modes, right.modes, self.single_period)
|
|
# current_layer = PeriodicLayer(left.modes, right.modes, self.single_period)
|
|
# interface = iface(right, left)
|
|
#
|
|
# for _ in range(self.num_periods - 1):
|
|
# current_layer.s_params = cascade(current_layer, interface, wl)
|
|
# current_layer.s_params = cascade(current_layer, period_layer, wl)
|
|
#
|
|
# self.s_params = current_layer.s_params
|
|
#
|
|
#
|
|
#class EME:
|
|
# def __init__(self, layers=[]):
|
|
# self.layers = layers
|
|
# self.wavelength = None
|
|
#
|
|
# def propagate(self):
|
|
# layers = self.layers
|
|
# wl = layers[0].wavelength if self.wavelength is None else self.wavelength
|
|
# if not len(layers):
|
|
# raise Exception("Must place layers before propagating")
|
|
#
|
|
# num_modes = max([l.num_modes for l in layers])
|
|
# iface = InterfaceSingleMode if num_modes == 1 else InterfaceMultiMode
|
|
#
|
|
# first_layer = layers[0]
|
|
# current = Current(wl, first_layer)
|
|
# interface = iface(first_layer, layers[1])
|
|
#
|
|
# current.s = cascade(current, interface, wl)
|
|
# current.right_pins = interface.right_pins
|
|
#
|
|
# for index in range(1, len(layers) - 1):
|
|
# layer1 = layers[index]
|
|
# layer2 = layers[index + 1]
|
|
# interface = iface(layer1, layer2)
|
|
#
|
|
# current.s = cascade(current, layer1, wl)
|
|
# current.right_pins = layer1.right_pins
|
|
#
|
|
# current.s = cascade(current, interface, wl)
|
|
# current.right_pins = interface.right_pins
|
|
#
|
|
# last_layer = layers[-1]
|
|
# current.s = cascade(current, last_layer, wl)
|
|
# current.right_pins = last_layer.right_pins
|
|
#
|
|
# self.s_matrix = current.s
|
|
# return first_layer, last_layer
|
|
#
|
|
#
|
|
#def stack(sa, sb):
|
|
# qab = numpy.eye() - sa.r11 @ sb.r11
|
|
# qba = numpy.eye() - sa.r11 @ sb.r11
|
|
# #s.t12 = sa.t12 @ numpy.pinv(qab) @ sb.t12
|
|
# #s.r21 = sa.t12 @ numpy.pinv(qab) @ sb.r22 @ sa.t21 + sa.r22
|
|
# #s.r12 = sb.t21 @ numpy.pinv(qba) @ sa.r11 @ sb.t12 + sb.r11
|
|
# #s.t21 = sb.t21 @ numpy.pinv(qba) @ sa.t21
|
|
# s.t12 = sa.t12 @ numpy.linalg.solve(qab, sb.t12)
|
|
# s.r21 = sa.t12 @ numpy.linalg.solve(qab, sb.r22 @ sa.t21) + sa.r22
|
|
# s.r12 = sb.t21 @ numpy.linalg.solve(qba, sa.r11 @ sb.t12) + sb.r11
|
|
# s.t21 = sb.t21 @ numpy.linalg.solve(qba, sa.t21)
|
|
# return s
|
|
#
|
|
#
|
|
#def cascade(first, second, wavelength):
|
|
# circuit = Subcircuit("Device")
|
|
#
|
|
# circuit.add([(first, "first"), (second, "second")])
|
|
# for port in range(first.right_ports):
|
|
# circuit.connect("first", "right" + str(port), "second", "left" + str(port))
|
|
#
|
|
# simulation = SweepSimulation(circuit, wavelength, wavelength, num=1)
|
|
# result = simulation.simulate()
|
|
# return result.s
|
|
#
|
|
#
|
|
#class InterfaceSingleMode(Model):
|
|
# def __init__(self, layer1, layer2, num_modes=1):
|
|
# self.num_modes = num_modes
|
|
# self.num_ports = 2 * num_modes
|
|
# self.s = self.solve(layer1, layer2, num_modes)
|
|
#
|
|
# def solve(self, layer1, layer2, num_modes):
|
|
# nm = num_modes
|
|
# s = numpy.zeros((2 * nm, 2 * nm), dtype=complex)
|
|
#
|
|
# for ii, left_mode in enumerate(layer1.modes):
|
|
# for oo, right_mode in enumerate(layer2.modes):
|
|
# r, t = get_rt(left_mode, right_mode)
|
|
# s[ oo, ii] = r
|
|
# s[nm + oo, ii] = t
|
|
#
|
|
# for ii, right_mode in enumerate(layer2.modes):
|
|
# for oo, left_mode in enumerate(layer1.modes):
|
|
# r, t = get_rt(right_mode, left_mode)
|
|
# s[ oo, nm + ii] = t
|
|
# s[nm + oo, nm + ii] = r
|
|
# return s
|
|
#
|
|
#
|
|
#class InterfaceMultiMode(Model):
|
|
# def __init__(self, layer1, layer2):
|
|
# self.s = self.solve(layer1, layer2)
|
|
#
|
|
# def solve(self, layer1, layer2):
|
|
# n1p = layer1.num_modes
|
|
# n2p = layer2.num_modes
|
|
# num_ports = n1p + n2p
|
|
# s = numpy.zeros((num_ports, num_ports), dtype=complex)
|
|
#
|
|
# for l1p in range(n1p):
|
|
# ts = get_t(l1p, layer1, layer2)
|
|
# rs = get_r(l1p, layer1, layer2, ts)
|
|
# s[n1p:, l1p] = ts
|
|
# s[:n1p, l1p] = rs
|
|
#
|
|
# for l2p in range(n2p):
|
|
# ts = get_t(l2p, layer2, layer1)
|
|
# rs = get_r(l2p, layer2, layer1, ts)
|
|
# s[:n1p, n1p + l2p] = ts
|
|
# s[n1p:, n1p + l2p] = rs
|
|
#
|
|
# return s
|
|
|
|
|
|
def get_t(p, left, right):
|
|
A = numpy.empty(left.num_modes, right.num_modes, dtype=complex)
|
|
for i in range(left.num_modes):
|
|
for k in range(right.num_modes):
|
|
# TODO optimize loop
|
|
A[i, k] = inner_product(right[k], left[i]) + inner_product(left[i], right[k])
|
|
|
|
b = numpy.zeros(left.num_modes)
|
|
b[p] = 2 * inner_product(left[p], left[p])
|
|
|
|
x = numpy.linalg.solve(A, b)
|
|
# NOTE: `A` does not depend on `p`, so it might make sense to partially precompute
|
|
# the solution (pinv(A), or LU decomposition?)
|
|
# Actually solve() can take multiple vectors, so just pass it something with the full diagonal?
|
|
|
|
xx = numpy.matmul(numpy.linalg.pinv(A), b) #TODO verify
|
|
assert numpy.allclose(xx, x)
|
|
return x
|
|
|
|
|
|
def get_r(p, left, right, t):
|
|
r = numpy.empty(left.num_modes, dtype=complex)
|
|
for ii in range(left.num_modes):
|
|
r[ii] = sum((inner_product(right[kk], left[ii]) - inner_product(left[ii], right[kk])) * t[kk]
|
|
for kk in range(right.num_modes)
|
|
) / (2 * inner_product(left[ii], left[ii]))
|
|
return r
|
|
|
|
|
|
def get_rt(left, right):
|
|
a = 0.5 * (inner_product(left, right) + inner_product(right, left))
|
|
b = 0.5 * (inner_product(left, right) - inner_product(right, left))
|
|
t = (a ** 2 - b ** 2) / a
|
|
r = 1 - t / (a + b)
|
|
return -r, t
|
|
|
|
|
|
def inner_product(left_E, right_H, dxes):
|
|
# ExHy' - EyHx'
|
|
cross_z = left_E[0] * right_H[1].conj() - left_E[1] * right_H[0].conj()
|
|
# cross_z = numpy.cross(left_E, numpy.conj(right_H), axisa=0, axisb=0, axisc=0)[2]
|
|
return numpy.trapz(numpy.trapz(cross_z, dxes[0][0]), dxes[0][1]) / 2 # TODO might need cumsum on dxes
|
|
|
|
|
|
def propagation_matrix(mode_neffs: ArrayLike, wavelength: float, distance: float):
|
|
eigenv = numpy.array(mode_neffs, copy=False) * 2 * numpy.pi / wavelength
|
|
prop_diag = numpy.diag(numpy.exp(distance * 1j * numpy.hstack((eigenv, eigenv))))
|
|
prop_matrix = numpy.roll(prop_diag, len(eigenv), axis=0)
|
|
return prop_matrix
|
|
|
|
|
|
def connect_s(
|
|
A: NDArray[numpy.complex128],
|
|
k: int,
|
|
B: NDArray[numpy.complex128],
|
|
l: int,
|
|
) -> NDArray[numpy.complex128]:
|
|
"""
|
|
TODO
|
|
freq x ... x n x n
|
|
|
|
Based on skrf implementation
|
|
|
|
Connect two n-port networks' s-matrices together.
|
|
|
|
Specifically, connect port `k` on network `A` to port `l` on network
|
|
`B`. The resultant network has nports = (A.rank + B.rank-2); first
|
|
(A.rank - 1) ports are from `A`, remainder are from B.
|
|
|
|
Assumes same reference impedance for both `k` and `l`; may need to
|
|
connect an "impedance mismatch" thru element first!
|
|
|
|
Args:
|
|
A: S-parameter matrix of `A`, shape is fxnxn
|
|
k: port index on `A` (port indices start from 0)
|
|
B: S-parameter matrix of `B`, shape is fxnxn
|
|
l: port index on `B`
|
|
|
|
Returns:
|
|
new S-parameter matrix
|
|
"""
|
|
if k > A.shape[-1] - 1 or l > B.shape[-1] - 1:
|
|
raise ValueError("port indices are out of range")
|
|
|
|
#C = scipy.sparse.block_diag((A, B), dtype=complex)
|
|
#return innerconnect_s(C, k, A.shape[0] + l)
|
|
|
|
nA = A.shape[-1]
|
|
nB = B.shape[-1]
|
|
nC = nA + nB - 2
|
|
assert numpy.array_equal(A.shape[:-2], B.shape[:-2])
|
|
|
|
denom = 1 - A[..., k, k] * B[..., l, l]
|
|
Anew = A + A[..., k, :] * B[..., l, l] * A[..., :, k] / denom
|
|
Bnew = A[..., k, :] * B[..., :, l] / denom
|
|
Anew = npy.delete(Anew, (k,), 1)
|
|
Anew = npy.delete(Anew, (k,), 2)
|
|
Bnew = npy.delete(Bnew, (l,), 1)
|
|
Bnew = npy.delete(Bnew, (l,), 2)
|
|
|
|
dtype = (A[0, 0] * B[0, 0]).dtype
|
|
C = numpy.zeros(tuple(A.shape[:-2]) + (nn, nn), dtype=dtype)
|
|
C[..., :nA - 1, :nA - 1] = Anew
|
|
C[..., nA - 1:, nA - 1:] = Bnew
|
|
return C
|
|
|
|
|
|
def innerconnect_s(
|
|
S: NDArray[numpy.complex128],
|
|
k: int,
|
|
l: int,
|
|
) -> NDArray[numpy.complex128]:
|
|
"""
|
|
TODO
|
|
freq x ... x n x n
|
|
|
|
Based on skrf implementation
|
|
|
|
|
|
Connect two ports of a single n-port network's s-matrix.
|
|
Specifically, connect port `k` to port `l` on `S`. This results in
|
|
a (n-2)-port network.
|
|
|
|
Assumes same reference impedance for both `k` and `l`; may need to
|
|
connect an "impedance mismatch" thru element first!
|
|
|
|
Args:
|
|
S: S-parameter matrix of `S`, shape is fxnxn
|
|
k: port index on `S` (port indices start from 0)
|
|
l: port index on `S`
|
|
|
|
Returns:
|
|
new S-parameter matrix
|
|
|
|
Notes:
|
|
- Compton, R.C., "Perspectives in microwave circuit analysis",
|
|
doi:10.1109/MWSCAS.1989.101955
|
|
- Filipsson, G., "A New General Computer Algorithm for S-Matrix Calculation
|
|
of Interconnected Multiports",
|
|
doi:10.1109/EUMA.1981.332972
|
|
"""
|
|
if k > S.shape[-1] - 1 or l > S.shape[-1] - 1:
|
|
raise ValueError("port indices are out of range")
|
|
|
|
ll = slice(l, l + 1)
|
|
kk = slice(k, k + 1)
|
|
|
|
mkl = 1 - S[..., kk, ll]
|
|
mlk = 1 - S[..., ll, kk]
|
|
C = S + (
|
|
S[..., kk, :] * S[..., :, l] * mlk
|
|
+ S[..., ll, :] * S[..., :, k] * mkl
|
|
+ S[..., kk, :] * S[..., l, l] * S[..., :, kk]
|
|
+ S[..., ll, :] * S[..., k, k] * S[..., :, ll]
|
|
) / (
|
|
mlk * mkl - S[..., kk, kk] * S[..., ll, ll]
|
|
)
|
|
|
|
# remove connected ports
|
|
C = npy.delete(C, (k, l), 1)
|
|
C = npy.delete(C, (k, l), 2)
|
|
|
|
return C
|
|
|
|
|
|
def s2abcd(
|
|
S: NDArray[numpy.complex128],
|
|
z0: NDArray[numpy.complex128],
|
|
) -> NDArray[numpy.complex128]:
|
|
assert numpy.array_equal(S.shape[:2] == (2, 2))
|
|
Z1, Z2 = z0
|
|
cross = S[0, 1] * S[1, 0]
|
|
|
|
T = numpy.empty_like(S, dtype=complex)
|
|
T[0, 0, :] = (Z1.conj() + S[0, 0] * Z1) * (1 - S[1, 1]) + cross * Z1 # A numerator
|
|
T[0, 1, :] = (Z1.conj() + S[0, 0] * Z1) * (Z1.conj() + S[1, 1] * Z2) - cross * Z1 * Z2 # B numerator
|
|
T[1, 0, :] = (1 - S[0, 0]) * (1 - S[1, 1]) - cross # C numerator
|
|
T[1, 1, :] = (1 - S[0, 0]) * (Z2.conj() + S[1, 1] * Z2) + cross * Z2 # D numerator
|
|
det = 2 * S[1, 0] * numpy.sqrt(Z1.real * Z2.real)
|
|
T /= det
|
|
return T
|
|
|
|
|
|
def generalize_S(
|
|
S: NDArray[numpy.complex128],
|
|
r0: float,
|
|
z0: NDArray[numpy.complex128],
|
|
) -> NDArray[numpy.complex128]:
|
|
g = (z0 - r0) / (z0 + r0)
|
|
D = numpy.diag((1 - g) / numpy.abs(1 - g.conj()) * numpy.sqrt(1 - numpy.abs(g * g.conj())))
|
|
G = numpy.diag(g)
|
|
U = numpy.eye(S.shape[0])
|
|
S_gen = pinv(D.conj()) @ (S - G.conj()) @ pinv(U - G @ S) @ D
|
|
return S_gen
|
|
|
|
|
|
def change_R0(
|
|
S: NDArray[numpy.complex128],
|
|
r1: float,
|
|
r2: float,
|
|
) -> NDArray[numpy.complex128]:
|
|
g = (r2 - r1) / (r2 + r1)
|
|
U = numpy.eye(S.shape[0])
|
|
G = U * g
|
|
S_r2 = (S - G) @ pinv(U - G @ S)
|
|
return S_r2
|
|
|
|
# Zc = numpy.sqrt(B / C)
|
|
# gamma = numpy.arccosh(A) / L_TL
|
|
# n_eff = -1j * gamma * c_light / (2 * pi * f)
|
|
# n_eff_grp = n_eff + f * diff(n_eff) / diff(f)
|
|
# attenuation = (1 - S[0, 0] * S[0, 0].conj()) / (S[1, 0] * S[1, 0].conj())
|
|
# R = numpy.real(gamma * Zc)
|
|
# C = numpy.real(gamma / Zc)
|
|
# L = numpy.imag(gamma * Zc) / (-1j * 2 * pi * f)
|
|
# G = numpy.imag(gamma / Zc) / (-1j * 2 * pi * f)
|