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move some functions

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spar
Jan Petykiewicz 1 month ago
parent 9ef62b92d5
commit 35b5a8c5b9
2 changed files with 193 additions and 11 deletions
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4
nom-eme.py
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@ -364,7 +364,7 @@ def generalize_S(
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])
U = numpy.eye(S.shape[-1]).reshape((S.ndim - 2) * (1,) + (S.shape[-2], S.shape[-1]))
S_gen = pinv(D.conj()) @ (S - G.conj()) @ pinv(U - G @ S) @ D
return S_gen
@ -375,7 +375,7 @@ def change_R0(
r2: float,
) -> NDArray[numpy.complex128]:
g = (r2 - r1) / (r2 + r1)
U = numpy.eye(S.shape[0])
U = numpy.eye(S.shape[-1]).reshape((S.ndim - 2) * (1,) + (S.shape[-2], S.shape[-1]))
G = U * g
S_r2 = (S - G) @ pinv(U - G @ S)
return S_r2

200
spconv.py
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@ -1,6 +1,8 @@
import scipy
import numpy
from numpy import sqrt, real, abs
from numpy.typing import ArrayLike, NDArray
from numpy.linalg import pinv
from numpy import sqrt, real, abs, pi
def diag(twod):
@ -29,7 +31,9 @@ def change_of_zref(
# A = inv(G0') @ G0 @ inv(I - rho*) (diagonal)
# rho = (Z0' - Z0) @ inv(Z0' + Z0) (diagonal)
I = numpy.eye(SL.shape[-1])[None, :, :]
I = numpy.zeros_like(SL)
numpy.einsum('...jj->...j', I)[...] = 1
zref_old = numpy.array(zref_old, copy=False)
zref_new = numpy.array(zref_new, copy=False)
@ -51,10 +55,14 @@ def embedding(
SL, # (nf, ni, ni)
):
# Reveyrand, doi:10.1109/INMMIC.2018.8430023
I = numpy.eye(SL.shape[-1])[None, :, :]
I = numpy.zeros_like(SL)
numpy.einsum('...jj->...j', I)[...] = 1
S_tot = See + Sei @ pinv(I - SL @ Sii) @ SL @ Sie
return S_tot
def deembedding(
Sei, # (nf, ne, ni)
Sie, # (nf, ni, ne)
@ -73,14 +81,188 @@ def thru_with_Zref_change(
zref0, # (nf,)
zref1, # (nf,)
):
nf = zref0.shape[0]
s = numpy.empty((nf, 2, 2), dtype=complex)
s[:, 0, 0] = zref1 - zref0
s[:, 0, 1] = 2 * sqrt(zref0 * zref1)
s[:, 1, 0] = s[:, 0, 1]
s[:, 1, 1] = -s[:, 0, 0]
s = numpy.empty(tuple(zref0.shape) + (2, 2), dtype=complex)
s[..., 0, 0] = zref1 - zref0
s[..., 0, 1] = 2 * sqrt(zref0 * zref1)
s[..., 1, 0] = s[..., 0, 1]
s[..., 1, 1] = -s[..., 0, 0]
s /= zref0 + zref1
return s
def propagation_matrix(mode_neffs: ArrayLike, wavelength: float, distance: float):
eigenv = numpy.array(mode_neffs, copy=False) * 2 * 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])
ll = slice(l, l + 1)
kk = slice(k, k + 1)
denom = 1 - A[..., kk, kk] * B[..., ll, ll]
Anew = A + A[..., kk, :] * B[..., ll, ll] * A[..., :, kk] / denom
Bnew = A[..., kk, :] * B[..., :, ll] / denom
Anew = numpy.delete(Anew, (k,), 1)
Anew = numpy.delete(Anew, (k,), 2)
Bnew = numpy.delete(Bnew, (l,), 1)
Bnew = numpy.delete(Bnew, (l,), 2)
dtype = (A[0, 0] * B[0, 0]).dtype
C = numpy.zeros(tuple(A.shape[:-2]) + (nC, nC), 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 = numpy.delete(C, (k, l), 1)
C = numpy.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[-1]).reshape((S.ndim - 2) * (1,) + (S.shape[-2], S.shape[-1]))
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[-1]).reshape((S.ndim - 2) * (1,) + (S.shape[-2], S.shape[-1]))
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)

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