"""
S-parameter utilities for PyChOpMarg.
Original author: David Banas <capn.freako@gmail.com>
Original date: March 3, 2024
Copyright (c) 2024 David Banas; all rights reserved World wide.
"""
from pathlib import Path
import numpy as np # type: ignore
import skrf as rf
from numpy import array
from pychopmarg.common import Rvec, PI, TWOPI
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def sdd_21(ntwk: rf.Network, norm: float = 0.5, renumber: bool = False) -> rf.Network:
"""
Given a 4-port single-ended network, return its differential throughput
as a 2-port network.
Args:
ntwk: 4-port single ended network.
Keyword Args:
norm: Normalization factor. (Default = 0.5)
renumber: Automatically detect and correct through path when True.
Default: False
Returns:
Sdd (2-port).
Notes:
1. A "1->2/3->4" port ordering convention is assumed when `renumber` is False.
2. Automatic renumbering should not be used unless a solid d.c. thru path exists.
"""
mm = se2mm(ntwk, norm=norm, renumber=renumber)
return rf.Network(frequency=ntwk.f, s=mm.s[:, 0:2, 0:2], z0=mm.z0[:, 0:2])
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def se2mm(ntwk: rf.Network, norm: float = 0.5, renumber: bool = False) -> rf.Network:
"""
Given a 4-port single-ended network,
return its mixed mode equivalent in the following format:
.. math::
\\begin{bmatrix}
Sdd11 & Sdd12 & Sdc11 & Sdc12 \\\\
Sdd21 & Sdd22 & Sdc21 & Sdc22 \\\\
Scd11 & Scd12 & Scc11 & Scc12 \\\\
Scd21 & Scd22 & Scc21 & Scc22
\\end{bmatrix}
Args:
ntwk: 4-port single ended network.
Keyword Args:
norm: Normalization factor. (Default = 0.5)
renumber: Automatically detect and correct through path when True.
Default: False
Returns:
Mixed mode equivalent network.
Notes:
1. A "1->2/3->4" port ordering convention is assumed when `renumber` is False.
2. Automatic renumbering should not be used unless a solid d.c. thru path exists.
"""
# Confirm correct network dimmensions.
(_, rs, cs) = ntwk.s.shape
assert rs == cs, "Non-square Touchstone file S-matrix!"
assert rs == 4, "Touchstone file must have 4 ports!"
# Detect/correct "1 => 3" port numbering if requested.
if renumber:
ix = 1
if abs(ntwk.s21.s[ix, 0, 0]) < abs(ntwk.s31.s[ix, 0, 0]): # 1 ==> 3 port numbering?
ntwk.renumber((1, 2), (2, 1))
# Convert S-parameter data.
s = np.zeros(ntwk.s.shape, dtype=complex)
s[:, 0, 0] = norm * (ntwk.s11 - ntwk.s13 - ntwk.s31 + ntwk.s33).s.flatten()
s[:, 0, 1] = norm * (ntwk.s12 - ntwk.s14 - ntwk.s32 + ntwk.s34).s.flatten()
s[:, 0, 2] = norm * (ntwk.s11 + ntwk.s13 - ntwk.s31 - ntwk.s33).s.flatten()
s[:, 0, 3] = norm * (ntwk.s12 + ntwk.s14 - ntwk.s32 - ntwk.s34).s.flatten()
s[:, 1, 0] = norm * (ntwk.s21 - ntwk.s23 - ntwk.s41 + ntwk.s43).s.flatten()
s[:, 1, 1] = norm * (ntwk.s22 - ntwk.s24 - ntwk.s42 + ntwk.s44).s.flatten()
s[:, 1, 2] = norm * (ntwk.s21 + ntwk.s23 - ntwk.s41 - ntwk.s43).s.flatten()
s[:, 1, 3] = norm * (ntwk.s22 + ntwk.s24 - ntwk.s42 - ntwk.s44).s.flatten()
s[:, 2, 0] = norm * (ntwk.s11 - ntwk.s13 + ntwk.s31 - ntwk.s33).s.flatten()
s[:, 2, 1] = norm * (ntwk.s12 - ntwk.s14 + ntwk.s32 - ntwk.s34).s.flatten()
s[:, 2, 2] = norm * (ntwk.s11 + ntwk.s13 + ntwk.s31 + ntwk.s33).s.flatten()
s[:, 2, 3] = norm * (ntwk.s12 + ntwk.s14 + ntwk.s32 + ntwk.s34).s.flatten()
s[:, 3, 0] = norm * (ntwk.s21 - ntwk.s23 + ntwk.s41 - ntwk.s43).s.flatten()
s[:, 3, 1] = norm * (ntwk.s22 - ntwk.s24 + ntwk.s42 - ntwk.s44).s.flatten()
s[:, 3, 2] = norm * (ntwk.s21 + ntwk.s23 + ntwk.s41 + ntwk.s43).s.flatten()
s[:, 3, 3] = norm * (ntwk.s22 + ntwk.s24 + ntwk.s42 + ntwk.s44).s.flatten()
# Convert port impedances.
f = ntwk.f
z = np.zeros((len(f), 4), dtype=complex)
z[:, 0] = ntwk.z0[:, 0] + ntwk.z0[:, 2]
z[:, 1] = ntwk.z0[:, 1] + ntwk.z0[:, 3]
z[:, 2] = (ntwk.z0[:, 0] + ntwk.z0[:, 2]) / 2
z[:, 3] = (ntwk.z0[:, 1] + ntwk.z0[:, 3]) / 2
return rf.Network(frequency=f, s=s, z0=z)
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def import_s32p( # pylint: disable=too-many-locals
filename: Path, vic_chnl: int = 1
) -> list[tuple[rf.Network, str]]:
"""Read in a 32-port Touchstone file, and return an equivalent list
of 8 2-port differential networks: a single victim through channel and
7 crosstalk aggressors, according to the VITA 68.2 convention.
Args:
filename: Name of Touchstone file to read in.
Keyword Args:
vic_chnl: Victim channel number (from 1).
Default = 1
Returns:
List of 8 pairs, each consisting of:
- a 2-port network representing a *differential* channel, and
- the type of that channel, one of: 'THRU', 'NEXT', or 'FEXT.
(First element is the victim and the only one of type 'THRU'.)
Raises:
ValueError: If Touchstone file is not 32-port.
Notes:
1. Input Touchstone file is assumed single-ended.
2. The differential through and xtalk channels are returned.
3. Port 2 of all returned channels correspond to the same physical circuit node,
typically, the Rx input node.
"""
# Import and sanity check the Touchstone file.
ntwk = rf.Network(filename)
(_, rs, cs) = ntwk.s.shape
assert rs == cs, "Non-square Touchstone file S-matrix!"
assert rs == 32, f"Touchstone file must have 32 ports!\n\t{ntwk}"
# Extract the victim and aggressors.
def ports_from_chnls(left, right):
"""
Return list of 4 ports (from 0) corresponding to a particular
left and right channel ID (from 1), assuming "1=>2/3=>4" convention.
Args:
left(int): Left side channel number (from 1).
right(int): Right side channel number (from 1).
Returns:
List of ports (from 0) for desired channel.
"""
left0 = left - 1 # 0-based
right0 = right - 1
return [left0 * 4, right0 * 4 + 1, left0 * 4 + 2, right0 * 4 + 3]
vic_ports = ports_from_chnls(vic_chnl, vic_chnl)
vic = sdd_21(rf.subnetwork(ntwk, vic_ports))
vic = (vic, 'THRU')
if vic_chnl % 2: # odd?
vic_rx_ports = [vic_ports[n] for n in [0, 2]]
else:
vic_rx_ports = [vic_ports[n] for n in [1, 3]]
agg_chnls = list(np.array(range(8)) + 1)
agg_chnls.remove(vic_chnl)
aggs = []
for agg_chnl in agg_chnls:
agg_ports = ports_from_chnls(agg_chnl, agg_chnl)
if agg_chnl % 2: # odd?
agg_tx_ports = [agg_ports[n] for n in [1, 3]]
else:
agg_tx_ports = [agg_ports[n] for n in [0, 2]]
sub_ports = np.concatenate(list(zip(agg_tx_ports, vic_rx_ports)))
subntwk = sdd_21(ntwk.subnetwork(sub_ports))
if (vic_chnl + agg_chnl) % 2:
subntwk = (subntwk, 'NEXT')
else:
subntwk = (subntwk, 'FEXT')
aggs.append(subntwk)
return [vic] + aggs
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def sCshunt(freqs: Rvec, c: float, r0: float = 50.0) -> rf.Network:
"""
Calculate the 2-port network for a shunt capacitance.
Args:
freqs: The frequencies at which to calculate network data (Hz).
c: The capacitance (F).
Keyword Args:
r0: The reference impedance for the network (Ohms).
Default: 50 Ohms.
Returns:
The network corresponding to a shunt capacitance, ``c``,
calculated at the given frequencies, ``freqs``.
"""
w = TWOPI * np.array(freqs)
s = 1j * w
jwRC = s * r0 * c
s11 = -jwRC / (2 + jwRC)
s21 = 2 / (2 + jwRC)
return rf.Network(s=np.array(list(zip(zip(s11, s21), zip(s21, s11)))), f=freqs, z0=r0)
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def sLseries(freqs: Rvec, inductance: float, r0: float = 50.0) -> rf.Network:
"""
Calculate the 2-port network for a series inductance.
Args:
freqs: The frequencies at which to calculate network data (Hz).
inductance: The inductance (H).
Keyword Args:
r0: The reference impedance for the network (Ohms).
Default: 50 Ohms.
Returns:
The network corresponding to a series inductance, ``inductance``,
calculated at the given frequencies, ``freqs``.
"""
w = TWOPI * np.array(freqs)
s = 1j * w
w2L2 = w**2 * inductance**2
jwRL = s * r0 * inductance
R2x2 = 2 * r0**2
den = 2 * R2x2 + w2L2
s11 = (w2L2 + 2 * jwRL) / den
s21 = 2 * (R2x2 - jwRL) / den
return rf.Network(s=np.array(list(zip(zip(s11, s21), zip(s21, s11)))), f=freqs, z0=r0)
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def sDieLadderSegment(freqs: Rvec, trip: tuple[float, float, float]) -> rf.Network:
"""
Calculate one segment of the on-die parasitic ladder network.
Args:
f: List of frequencies to use for network creation (Hz).
trip: Triple containing:
- R0: Reference impedance for network (Ohms).
- Cd: Shunt capacitance (F).
- Ls: Series inductance (H).
Returns:
Two port network for segment.
"""
R0, Cd, Ls = trip
return sCshunt(freqs, Cd, r0=R0) ** sLseries(freqs, Ls, r0=R0)
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def sPkgTline( # pylint: disable=too-many-arguments,too-many-positional-arguments
f: Rvec, r0: float, a1: float, a2: float, tau: float,
gamma0: float, z_pairs: list[tuple[float, float]]
) -> rf.Network:
"""
Return the 2-port network corresponding to a package transmission line,
according to (93A-9:14).
Args:
f: Frequencies at which to calculate S-parameters (Hz).
r0: System reference impedance (Ohms).
a1: First polynomial coefficient (sqrt_ns/mm).
a2: Second polynomial coefficient (ns/mm).
tau: Propagation delay (ns/mm).
gamma0: Propagation loss constant (1/mm).
z_pairs: List of pairs defining the T-line segments, each containing:
- zc: Characteristic impedance of segment (Ohms).
- zp: Length of segment (mm).
Returns:
2-port network equivalent to package transmission line.
"""
f_GHz = f / 1e9 # noqa E221
gamma1 = a1 * (1 + 1j)
def gamma2(f: float) -> complex:
"f in GHz!"
return a2 * (1 - 1j * (2 / PI) * np.log(f)) + 1j * TWOPI * tau
def gamma(f: float) -> complex:
"Return complex propagation coefficient at frequency f (GHz)."
if f == 0:
return gamma0
return gamma0 + gamma1 * np.sqrt(f) + gamma2(f) * f
g = array(list(map(gamma, f_GHz)))
def mk_s2p(z_pair: tuple[float, float]) -> rf.Network:
"""
Make two port network for a leg of T-line.
Args:
z_pair: Pair consisting of:
- zc: Characteristic impedance of leg (Ohms).
- zp: Length of leg (mm).
Returns:
s2p: Two port network for the leg.
"""
zc, zp = z_pair
rho = (zc - 2 * r0) / (zc + 2 * r0) # noqa E221
s11 = rho * (1 - np.exp(-g * 2 * zp)) / (1 - rho**2 * np.exp(-g * 2 * zp))
s21 = (1 - rho**2) * np.exp(-g * zp) / (1 - rho**2 * np.exp(-g * 2 * zp))
return rf.Network(s=array(list(zip(zip(s11, s21), zip(s21, s11)))), f=f, z0=r0)
return rf.network.cascade_list(list(map(mk_s2p, z_pairs)))