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发表于 2017-5-31 03:02:09
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回复 1# 曹明喜
spectre -h tline
*****************
Transmission Line
*****************
Lossy or lossless transmission line.
|-----------------|
t1 -o----------| |-----------o- t2
+ I1 -> | | <- I2 +
V1 | tline | V2
- I1 <- | | -> I2 -
b1 -o----------| |-----------o- b2
|-----------------|
The lossy transmission line model includes dielectric and conductor loss
effects. The conductor loss includes skin effect assuming finite or infinite
conductor thickness.
Only the odd mode is modeled, so only the voltage difference across each port
is important. (The absolute voltage of each terminal is not significant.)
Also, the current into one node of a port exactly equals the current leaving
the other node of the port.
Sample Instance Statement:
t1 (1 0 2 0) lmodel z0=100
Sample Model Statement:
model lmodel tline f=10M z0=50 alphac=8501 fc=10M dcr=88
This device is supported within altergroups.
Synopsis:
Name ( t1 b1 t2 b2 ) ModelName <parameter=value> ...
Name ( t1 b1 t2 b2 ) tline <parameter=value> ...
Model Synopsis:
model ModelName tline <parameter=value> ...
===================
Instance Parameters
===================
1 z0=50 Ohm Characteristic impedance of lossless line.
2 td (s) Time delay of a lossless line in seconds, a measure
of the electrical length.
3 f (Hz) Reference frequency (used in conjunction to the
normalized length to specify electrical length of
line).
4 nl=0.25 Normalized electrical length in wavelengths at `f' of
a lossless line.
5 vel=1 Propagation velocity of the line given as a multiple
of `c', the speed of light in free space. (vel <=
1).
6 len=0 m Physical length (used with `vel' to specify
electrical length of line).
7 m=1 Multiplicity factor.
Conductor loss parameters:
8 corner=0 Hz Corner frequency for skin effect, frequency where
skin depth equals the conductor's wall thickness.
9 dcr=0 Ohm/m DC series resistance per unit length.
10 fc (Hz) Conductor loss measurement frequency (use with `r',
`qc', or `alphac').
11 r=0 Ohm/m Conductor (series) resistance per unit length at
`fc'.
12 alphac=0 dB/m Conductor loss at `fc' (low loss approximation).
13 qc=infinity Conductor loss quality factor at `fc' (low loss
approximation).
Dielectric loss parameters:
14 fd (Hz) Dielectric loss measurement frequency (use with
`qd').
15 g=0 S/m Dielectric (shunt) conductance per unit length.
16 alphad=0 dB/m Dielectric loss (low loss approximation).
17 qd=infinity Dielectric loss quality factor at `fd' (low loss
approximation).
================
Model Parameters
================
1 z0=50 Ohm Characteristic impedance of lossless line.
2 f (Hz) Reference frequency (used in conjunction to the
normalized length to specify electrical length of
line).
3 vel=1 Propagation velocity of the line given as a multiple
of `c', the speed of light in free space. (vel <=
1).
Conductor loss parameters:
4 corner=0 Hz Corner frequency for skin effect, frequency where
skin depth equals the conductor's wall thickness.
5 dcr=0 Ohm/m DC series resistance per unit length.
6 fc (Hz) Conductor loss measurement frequency (use with `r',
`qc', or `alphac').
7 r=0 Ohm/m Conductor (series) resistance per unit length at
`fc'.
8 alphac=0 dB/m Conductor loss at `fc' (low loss approximation).
9 qc=infinity Conductor loss quality factor at `fc' (low loss
approximation).
Dielectric loss parameters:
10 fd (Hz) Dielectric loss measurement frequency (use with
`qd').
11 g=0 S/m Dielectric (shunt) conductance per unit length.
12 alphad=0 dB/m Dielectric loss (low loss approximation).
13 qd=infinity Dielectric loss quality factor at `fd' (low loss
approximation).
-------------
Lossless Case
-------------
The lossless transmission line is specified with parameters `z0' and `td'. The
device behavior is then:
V1(t) - z0*I1(t) = V2(t-td) + z0*I2(t-td)
and
V2(t) - zO*I2(t) = V1(t-td) + z0*I1(t-td).
where t is time and `td' is the delay. Note, if the device is terminated by a
matched impedance of `z0'( across t2 and b2), then it becomes an ideal delay.
i.e V2(t) = V1(t-td).
--------------------------------
To model both even and odd modes
--------------------------------
Use two lines as shown below.
tline_inner
|---------------|
i1------------| z0_inner |--------------i2
| td_inner |
----|---------------|-------
| |
o1--------| tline_outer |-------o2
| |---------------| |
----| z0_outer |-------
| td_outer |
----------|---------------|--------------
| |
gnd gnd
This model is suitable for a coax where tline_inner models the inner/outer
conductor line (or the odd mode) while tline_outer models the outer/ground line
(or the even mode). Note that this model is non-symmetric.
----------
Lossy Case
----------
In the frequency-domain the device is modeled by
V1(jw) - Z(jw)*I1(jw) = S12(jw)* [V2(jw) + Z(jw)I2(jw)]
and
V2(jw) - Z(jw)*I2(jw) = S21(jw)* [V1(jw) + Z(jw)I1(jw)]
where j=sqrt(-1) and w is the angular frequency in radians/s. The loss
coefficient is computed from
S21(jw) = S12(jw) = exp(-Gamma(jw)*len)
where
Gamma(jw) = sqrt( Zc(jw) * Yd(jw) )
where Zc represents the per-unit-length series impedance and Yd represents the
per-unit-length shunt admittance loss (as described below). The characteristic
impedance (Z) is computed from
Z(jw) = sqrt( Zc(jw) / Yd(jw) ).
The time-domain behavior of the lossy transmission line is computed through a
recursive convolution algorithm.
The dielectric loss (Yd) is computed from
Yd(jw) = G + j* w/(z0*c*vel)
where G is the per-unit-length shunt conductance and can be specified in three
ways.
1) G = g { when `g' is given }
2) G = 2/z0 * alphad { when `alphad' is given }
3) G = 2/z0 * fd/(2*qd*c*vel) { when `fd' and `qd' are given }
where `c' is the speed of light.
The series impedance (Zc) is computed from
Zc(jw) = Zi + j*w*z0/(c*vel).
where Zi represents the internal loss. When skin effect is not present then
Zi = dcr
where `dcr' is the DC series per-unit-length resistance.
Skin effect assuming finite thickness.
-------------------------------------
In this case the internal impedance (Zi) is computed from
Zi = Ri + j*w*Li
where Ri and Li exhibit the following behavior
Ri Li
| ** |
| **** L0|********
| ***** | **
| ****** | *
dcr|********* | **
| | **********
----------|------------------ ----------|-------------****
W_corner (freq) W_corner (freq)
The expressions for Ri and Li are
when w << W_corner: Ri ~ dcr and Li ~ dcr/(1.5*W_corner)
when w >> W_corner: Ri ~ dcr*sqrt(w/W_corner)
and
Li ~ dcr/(sqrt(w*W_corner))
Otherwise: Ri = dcr * nt * (sinh(2*nt)+sin(2*nt))/(cosh(2*nt)-cos(2*nt))
and
Li = dcr * nt * (sinh(2*nt)-sin(2*nt))/(cosh(2*nt)-cos(2*nt)) / w
where nt=sqrt(w/W_corner) is the normalized thickness
The equations can be found in:
Ramo, Whinnery, Van Duzer. Fields and waves in communication electronics. 1965.
See Section on "Impedance of thin-walled conductors". Pg 301.
The corner frequency (W_corner) results from skin effect on conductors of
finite thickness. As frequency decreases, skin depth increases resulting in
more conductor to pass the current, which results in lower loss. However, at
the corner frequency, the skin depth equals the radius of the conductor.
Decreasing the frequency below that point does not further reduce the loss.
The corner frequency (W_corner) can be specified in two ways.
1) When `dcr' and `corner' are given, then
W_corner= 2*pi*corner.
2) When `dcr', `r', and `fc' are given, then
W_corner = 2*pi*fc* (dcr/r)^2
In addition, there are two alternative ways to specify `r'.
1) r = 2*z0*alphac { when 'alphac' is given }
2) r = 2*z0*fc/(2*qc*c*vel) { when `qc' is given }
where 'c' is the speed of light are defined below.
Skin effect assuming infinite thickness
----------------------------------------
In this case there is no corner frequency (and no `dcr'), and the internal loss
(Zi) is computed from
Zi= Ri + j*w*Li
where Ri = r*sqrt(w/(2*pi*fc)) and Li = r/sqrt(w*2*pi*fc).
Again, `r' can be specified directly, or using `alphac' or `qc' as described
above in the case of finite thickness.
---------------------------------------------
Three ways to specify `vel', `td', and `len'
---------------------------------------------
1) When `vel' and `len' are given
td = len/(vel*c)
2) When `td' and `vel' are given
len = td*vel*c
3) When `f', `nl' and `vel' are given
td = nl/f
len = (nl/f)*vel*c
The parameter `len' is the physical length, `c' is the speed of light and `vel'
is the propagation velocity as a multiple of `c' (Recall that velocity =
c/sqrt(relative dielectric constant)). The parameter `f' is a reference
frequency and `nl' is the normalized electrical length in wavelengths at `f'.
===============
Parameter Index
===============
alphac .... I-12 f .......... I-3 len ........ I-6 r .......... M-7
alphac ..... M-8 f .......... M-2 m .......... I-7 td ......... I-2
alphad .... I-16 fc ........ I-10 nl ......... I-4 vel ........ I-5
alphad .... M-12 fc ......... M-6 qc ........ I-13 vel ........ M-3
corner ..... I-8 fd ........ I-14 qc ......... M-9 z0 ......... I-1
corner ..... M-4 fd ........ M-10 qd ........ I-17 z0 ......... M-1
dcr ........ I-9 g ......... I-15 qd ........ M-13
dcr ........ M-5 g ......... M-11 r ......... I-11 |
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