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87 lines
2.4 KiB
Python
87 lines
2.4 KiB
Python
import numpy
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from numpy import sqrt, real, abs
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from numpy.linalg import pinv
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def diag(twod):
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# numpy.diag() but makes a stack of diagonal matrices
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return numpy.einsum('ij,jk->ijk', twod, numpy.eye(twod.shape[-1], dtype=twod.dtype))
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def s2z(s, zref):
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# G0_inv @ inv(I - S) @ (S Z0 + Z0*) @ G0
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# Where Z0 is diag(zref) and G0 = diag(1/sqrt(abs(real(zref))))
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nf = s.shape[-1]
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I = numpy.eye(nf)[None, :, :]
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zref = numpy.array(zref, copy=False)
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gref = 1 / sqrt(abs(zref.real))
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z = diag(1 / gref) @ pinv(I - s) @ ( S @ diag(zref) + diag(zref).conj()) @ diag(gref)
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return z
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def change_of_zref(
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s, # (nf, np, np)
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zref_old, # (nf, np)
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zref_new, # (nf, np)
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):
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# Change-of-Z0 to Z0'
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# S' = inv(A) @ (S - rho*) @ inv(I - rho @ S) @ A*
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# A = inv(G0') @ G0 @ inv(I - rho*) (diagonal)
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# rho = (Z0' - Z0) @ inv(Z0' + Z0) (diagonal)
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I = numpy.eye(SL.shape[-1])[None, :, :]
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zref_old = numpy.array(zref_old, copy=False)
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zref_new = numpy.array(zref_new, copy=False)
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g_old = 1 / sqrt(abs(zref_old.real))
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r_new = sqrt(abs(zref_new.real))
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rhov = (zref_new - zref_old) / (zref_new + zref_old)
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av = r_new * g_old / (1 - rhov.conj())
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s_new = diag(1 / av) @ (s - diag(rhov.conj())) @ pinv(I[None, :] - diag(rhov) @ S) @ diag(av.conj())
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return s_new
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def embedding(
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See, # (nf, ne, ne)
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Sei, # (nf, ne, ni)
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Sie, # (nf, ni, ne)
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Sii, # (nf, ni, ni)
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SL, # (nf, ni, ni)
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):
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# Reveyrand, doi:10.1109/INMMIC.2018.8430023
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I = numpy.eye(SL.shape[-1])[None, :, :]
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S_tot = See + Sei @ pinv(I - SL @ Sii) @ SL @ Sie
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return S_tot
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def deembedding(
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Sei, # (nf, ne, ni)
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Sie, # (nf, ni, ne)
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Sext, # (nf, ne, ne)
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See, # (nf, ne, ne)
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Si, # (nf, ni, ni)
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):
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# Reveyrand, doi:10.1109/INMMIC.2018.8430023
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# Requires balanced number of ports, similar to VNA calibration
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Sei_inv = pinv(Sei)
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Sdif = Sext - See
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return Sei_inv @ Sdif @ pinv(Sie + Sii @ Sei_inv @ Sdif)
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def thru_with_Zref_change(
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zref0, # (nf,)
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zref1, # (nf,)
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):
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nf = zref0.shape[0]
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s = numpy.empty((nf, 2, 2), dtype=complex)
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s[:, 0, 0] = zref1 - zref0
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s[:, 0, 1] = 2 * sqrt(zref0 * zref1)
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s[:, 1, 0] = s[:, 0, 1]
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s[:, 1, 1] = -s[:, 0, 0]
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s /= zref0 + zref1
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return s
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