Sample ASITIC Sessions
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Invoke ASITIC with the sample.tek file as follows:
tcsh> asitic -t sample.tek
The prompt should change notifying you that you are now in the ASITIC environment. A corresponding entry will be made in your log file similar to the following
####################################################
# ASITIC ver 03.19.00.01.29.01 INPUT/OUTPUT LOG File
# Generated on Thu May 24 15:23:51 2001
####################################################
The entire session will be recorded in the asitic.LOG file for future
reference. Now to create a square spiral inductor, type the following
commands
ASITIC> sq name=a len=175 w=10 s=.5 n=5 xorg=200 yorg=200 metal=m3 exit=m2
You can also invoke the command without any options whereby
ASITIC will prompt you for the above parameters. Two useful
options for the sq command for further layout customization
are CBEGIN, CEND, and EXIT90. These
options allow you to begin and end the winding in the center of the
structure and furthermore modify the direction of the last segment
(the underpass). You should now see a layout of the device generated
by ASITIC similar to the following:
Notice the the structure is approximately centered on the chip area. A grid is also drawn in the chip area. You can change the grid size with the grid command. With a numerical argument, the zoom value command will zoom in (value > 1) or out (value < 1). To fit the entire layout in the window use the bb command. This will limit the viewing area to the bounding box containing the structure. You can zoom back to the entire chip with the zoom chip command.
With the focus on the layout window, the "z" and "Z" keys zoom out and in by a factor of two. The arrow keys pan the layout, while the "f" key serves the same purpose as the bb command ("f" is for "fit"). The zoom function is also assigned to the right mouse key. Simply drag a rectangle to the desired viewing area.
The layout can be manipulated. For instance, the rotate, vflip, hflip commands do the obvious transformations. The command move displaces the structure. You can stretch segments in the spiral with the str command. This is useful for customizing the layout of the device. Type help edit for a full listing of editing commands. The following commands calculate the DC resistance and inductance of the device
ASITIC> ind a
Inductance of A = 4.13121 (nH).
ASITIC> res a
Resistance of A = 4.246441 (Ohms).
Did you notice something funny? We found the inductance of an open
loop! In reality, this is the partial inductance of the structure and
the actual inductance depends on how currents returns to the input
port. In a real circuit, this path might be through a resonanting
capacitor, through a bypass cap, or even off-chip through bonding
wires.
The DC commands are very fast but they are only valid at DC. They are based on the Greenhouse/Grover formulation. Let's calculate the high frequency behavior. First, though, let's turn on the timing feature of ASITIC to time a typical run:
ASITIC> timing
Turning ON Timer Mode.
ASITIC> pix a 2
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (105x105)...
Generating inductance matrix (126x126)..
Inverting matrix......
Ind Timing: tot = 1045, setup = 08, fill = 762
invert = 266, reduce = 05, eddy = 00
Calc Times (ms): total = 1378, cap = 309, ind = 1063, node = 05
Pi Model at f=2.00 GHz: Q = 7.02, 7.16, 8.20
L = 4.06 nH R = 5.29
Cs1= 104 fF Rs1= 638
Cs2= 97 fF Rs2= 710 f_res = 7.74GHz
The pix command extracts a pi model for the device at
the requested frequency. Observe that the AC inductance is slightly
lower than the DC value. The resistance, though, is much higher. By
default the back of the substrate is assumed to be a perfect ground.
ASITIC reports the capacitance to ground from the input and
output port of the device at around 100 fF. These are lossy
capacitors with series resistance of 638 and 710 ohms since the
substrate currents must travel through two lossy substrate layers
before reaching the back plane.
The commands still execute quickly. On my laptop the total analysis time was just over one second. The compuation has three separate phases, the capacitance matrix calculation (309 msec), the inductance matrix calculation (1063 msec), and the nodal analysis (5 msec).
Let's provide a shorter path to ground by employing a substrate tap near the structure. To do this we create a rectangle on metal layer MSUB which is placed inside the substrate:
ASITIC> wire name=gnd len=200 wid=20 xorg=180 yorg=180 metal=msub
ASITIC> pix a 2 gnd
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (115x115)...
Generating inductance matrix (126x126)..
Inverting matrix......
Pi Model at f=2.00 GHz: Q = 7.47, 7.51, 8.20
L = 3.99 nH R = 5.58
Cs1= 115 fF Rs1= 127
Cs2= 106 fF Rs2= 153 f_res = 10.18GHz
Note that the substrate tap decreased the substrate resistance value
substantially. This impacted the quality factor of the
device. You can create more elaborate grounding structures such as a
ring:
ASITIC> del gnd
ASITIC> sq name=halo len=200 wid=200 w=20 n=1 xorg=180 yorg=180 s=10 metal=msub
ASITIC> mv halo 5 5
ASITIC> pix a 2 halo
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (141x141)...
Generating inductance matrix (126x126)..
Inverting matrix......
Pi Model at f=2.00 GHz: Q = 7.85, 7.81, 8.20
L = 3.98 nH R = 5.83
Cs1= 117 fF Rs1= 13.2
Cs2= 108 fF Rs2= 29.5 f_res = 7.39GHz
Now we see an even more dramatic decrease in substrate resistance.
The halo substrate contact is created using the sq command by
only specifying one turn to be wound. Also, the spacing controls the
gap in the ring. The "gnd" option in pix is only included in
the capacitance matrix calculation. Thus, the inductance is not
affected directly. To see this, put a solid conductor under the
device and re-calculate the pi model:
ASITIC> del halo
ASITIC> wire name=solid len=200 wid=200 metal=msub xorg=185 yorg=185
ASITIC> pix a 2 solid
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (205x205)...
Generating inductance matrix (126x126)..
Inverting matrix......
Pi Model at f=2.00 GHz: Q = 7.88, 7.95, 8.22
L = 3.98 nH R = 5.86
Cs1= 117 fF Rs1= 1.74
Cs2= 108 fF Rs2=-0.793 f_res = 7.37GHz
The inductance is still high, indicating that the eddy currents that
flow in the solid shield are not taken into account. There is an
advantage to this in that you can model the effect of a patterned
shield without actually patterning the shield. A well designed
patterned shield should give similar performance to the above
result.
The analysis indicates that the SRF is around 7 GHz. Let's examine the equivalent circuit at this frequency:
ASITIC> pix a 7
lambda = 10714.29, delta = 1.04
maxL = 535.71, maxT = 0.83, maxW = 0.83
Performing Analysis at 7.00 GHz
Generating capacitance matrix (105x105).
Warning: Could not open data file at frequency = 7.00.
Tried using . as path.
Generating data at 7.00 GHz...
Writing data.....
Generating inductance matrix (504x504)..
Inverting matrix......
Ind Timing: tot = 25431, setup = 26, fill = 5662
invert = 19626, reduce = 114, eddy = 00
Calc Times (ms): total = 39612, cap = 14157, ind = 25449, node = 05
Pi Model at f=7.00 GHz: Q = 3.88, 4.29, 9.86
L = 4.59 nH R = -3.69
Cs1= 52.1 fF Rs1= 525
Cs2= 52 fF Rs2= 629 f_res = 10.30GHz
This result took 40 seconds to generate. Note too that ASTIIC
had to take an extra step in generating the FFT data file at 7 GHz.
This computation only needs to be done once and any new analysis at 7
GHz will not require this step. A second run took only 20 seconds.
Notice that the device is not self-resonanting just yet. The SRF
reported by ASITIC is just a guess. As you see, the pi
parameters vary as a function of frequency. At high frequency the
displacement current in the substrate is significant and we see a
decrease in the capacitance to ground since the substrate capacitance
appears in series with the oxide capacitance. Why is the resistance
negative? There is an explanation of this in the FAQ but rest assured
that Re[Z] > 0 for this device for both ports in question. You can
verify this with the
ASITIC> del solid
ASITIC> cp a b
ASITIC> mv a -100 0
ASITIC> mv b 100 0
ASITIC> friend a b
ASITIC> mv a -25 0
You should now see both spirals in the layout.
By making the spirals friends we can move them both simultaneously. Let look at the magnetic coupling between these devices
ASITIC> k a b
Coupling coefficient of A and B: k = -0.02748 and M = -0.11355
(nH).
ASITIC> k2 2 a b
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Generating inductance matrix (252x252)..
Inverting matrix......
Ind Timing: tot = 4673, setup = 20, fill = 2117
invert = 2526, reduce = 33, eddy = 00
L(A,A) = 4.03648 nH R(A,A) = 6.120
L(A,B) = -0.11181 nH R(A,B) = -0.074
L(B,B) = 4.03624 nH R(B,B) = 6.127
The first command is strictly the DC coupling factor. When we compute
the coupling at 2 GHz, we get similar results from the partial indutance
matrix for these two devices. Each winding has a certain self
inductance and resistance. The resistance is much higher than the DC
resistance due to skin and proximity effects, in other words due to
eddy currents in the metallization. The coupling term Z(A,B) is of
course equal to Z(B,A) since the devices are passive. The imaginary
part of the coupling is of course the mutual inductance but the real
part is due to the change in the distributed current flow when one
device is placed next to the other. In fact, if we were to connect
these devices in series, then this term would lead to a reduction in
the total series R by a small amount.
How well are these devices isolated from one another? In other words, if we ground one device and compute the impedance to ground from the other device, what do we get?
ASITIC> cap a 2 b
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (233x233)..
At 2.000 GHz:
Total Capacitance = 281.395 (fF)
Total Resistance = 240.863.
Again this capacitance is lossy due to the substrate losses. Let's
treat these two inductors as two windings of a transformer. What's the
equivalent circuit?
ASITIC> calctrans a b 2
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (233x233)...
Generating inductance matrix (315x315)..
Inverting matrix......
Ind Timing: tot = 8065, setup = -10, fill = 3714
invert = 4357, reduce = 28, eddy = 00
Narrowband Model at f=2.00 GHz:
L1= 4.12 R1= 6.46 L2= 4.09 R2= 6.25 M=-0.117 (k=-0.0286) Re(Z12) = -0.0852
This result is very similar to what we would expect since the coupling
is small. The magnetic coupling term is one order of magnitude larger
than the substrate coupling term (the real part).
Let's now join these two devices in series. First, create a wire to
physically connect them:
ASITIC> wire name=c len=200 w=10 metal=m2 xorg=120 yorg=380
In practice you can move the wire to the proper location by selecting
it with the mouse and moving it by dragging the structure to the
appropriate location. The snap command controls the snap to
grid size. Observe that the grid size and snap size are independent
parameters. The coordinates of the mouse should be continuously
displayed in the upper left corner of the window.
Since we are now about to create a user defined structure (as opposed to an internally synthesized structure), we have to exercise caution. Inside ASTIIC each device is a series interconnection of super segments. Each super segment consists of an arbitrary number of segments connected in shunt. To see this, use the psegs command (print segments). Now, in order to join spirals A and B in series, we have to make sure that the segments are in correct order with current flowing in the correct direction. We first must thus flip spiral B and change the phase since current now enters the inner port and exits from the outer port. The follwoing commands show this
ASITIC> showdir
ASITIC> flip b
ASITIC> flipphase b
ASITIC> join a c b
ASITIC> ind a
Inductance of A = 8.80189 (nH).
The showdir command shows the phase of each segment. The
total DC inductance is as we expect 2*(L+M). Here is the final layout:
The high frequency performance of this pair is disappointing
ASITIC> pix a 2
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (215x215)...
Generating inductance matrix (258x258)..
Inverting matrix......
Ind Timing: tot = 3048, setup = 24, fill = 1294
invert = 1720, reduce = 06, eddy = 00
Calc Times (ms): total = 5684, cap = 2595, ind = 3059, node = 29
Pi Model at f=2.00 GHz: Q = 4.58, 4.42, 6.82
L = 8.93 nH R = 8.66
Cs1= 195 fF Rs1= 653
Cs2= 203 fF Rs2= 616 f_res = 3.82GHz
The capacitance is now doubled as expected. But notice that the Q of
the device is reduced substantially due to increased substrate
parasitics. In absence of substrate parasitics Q should be the same
since we doubled both the series inductance and resistance. On the
other hand, if we drive the structure differentially, then the Q
degradation is tolerable (the third Q number of 6.82 is the
differential Q).
Notice that we could also join the spirals by simply joining the inner ports directly. To make this modification we'll have to split the devices up, delete the extra segments, and rejoin the spirals:
ASITIC> split a 0 b
ASITIC> split b 2 c
ASITIC> split b 0 d
ASITIC> del d
ASITIC> split a -1 e
ASITIC> del e
ASITIC> mv b 0 -65
ASITIC> who
List of Spirals:
C
B
A
ASITIC> join a b c
ASITIC> ind a
Inductance of A = 8.57191 (nH).
The split command with a "0" argument splits a device down the middle creating a new device. With a non-zero argument i > 0, the device is cut after the i'th segment. With i < 0, the couting starts from the end. Hence the split a -1 e command removes the last segment from the spiral.
As expected, the partial inductance is reduced since we have reduced the electrical path from input to output, or equivalently the mangetic flux of the device.
The following commands calculate the equivalent pi circuit of the new device with and without a shield.
ASITIC> pix a 2
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (205x205)...
Generating inductance matrix (246x246)..
Inverting matrix......
Ind Timing: tot = 3964, setup = 02, fill = 1994
invert = 1963, reduce = 04, eddy = 00
Calc Times (ms): total = 6084, cap = 2099, ind = 3983, node = 02
Pi Model at f=2.00 GHz: Q = 4.90, 4.77, 7.36
L = 8.64 nH R = 7.67
Cs1= 187 fF Rs1= 648
Cs2= 193 fF Rs2= 624 f_res = 3.96GHz
ASITIC> wire name=sh len=450 wid=200 metal=msub
ASITIC> mv sh 37 -13
ASITIC> geom sh
Wire
The above discussion applies to non-square structures. For instance,
the spiral command creates a polygon structure while the
symsq command creates symmetric inductors. See the
creation reference sections for more details.
ASITIC has several built in commands that generate inductors on
multiple metal layers. The command sqsh creates a spiral
inductor identical in layout to the sq command with the
exception that multiple metal layers are put in parallel to lower the
resistance of the device. Let's first try a two layer structure:
ASITIC> sqsh name=a2 len=150 w=8 s=1 n=3.75 metal=m3 exit=m2 xorg=200 yorg=200 cbegincend exit90
This structure resides on metal m3 and m2 in shunt and the exit occurs
through layer m1. To see this, type psegs to see a list of
segments:
ASITIC> psegs a2
.
.
.
Segment 14: ( 119.0, 31.0, 45.0)-( 69.0, 31.0, 45.0) on
Notice that ASITIC reports that each segment before the last two are
"super" segments as they consist of two metal layers strapped
together. Even though you can't see this (there are no vias), rest
assured that this is the case. Let's compare the low-frequency impedance of
this structure to an identical single layer structure:
ASITIC> hide a2
ASITIC> sq name=a1 len=150 w=8 s=1 n=3.75 metal=m3 exit=m2 xorg=200 yorg=200 cbegin cend exit90
ASITIC> indmat a1 .1
lambda = 750000.00, delta = 10.07
maxL = 37500.00, maxT = 8.05, maxW = 8.05
Generating inductance matrix (16x16)..
Inverting matrix......
L = 2.4777073e-09 R = 8.50000000
ASITIC> indmat a2 .1
lambda = 750000.00, delta = 10.07
maxL = 37500.00, maxT = 8.05, maxW = 8.05
Generating inductance matrix (31x31)..
Inverting matrix......
L = 2.3760413e-09 R = 4.35750000
As expected, the low frequency resistance dropped by about a factor of
2 and the inductance dropped slightly since the two stacked windings
are strongly coupled. Let's compare the high frequency behavior:
ASITIC> pix a1 3
lambda = 25000.00, delta = 1.84
maxL = 1250.00, maxT = 1.47, maxW = 1.47
Performing Analysis at 3.00 GHz
Generating capacitance matrix (64x64)...
Generating inductance matrix (80x80)..
Inverting matrix......
Pi Model at f=3.00 GHz: Q = 4.62, 4.66, 4.95
L = 2.47 nH R = 8.77
Cs1= 50.6 fF Rs1= 633
Cs2= 47 fF Rs2= 704 f_res = 14.25GHz
ASITIC> pix a2 3
lambda = 25000.00, delta = 1.84
maxL = 1250.00, maxT = 1.47, maxW = 1.47
Performing Analysis at 3.00 GHz
Generating capacitance matrix (124x124)...
Generating inductance matrix (155x155)..
Inverting matrix......
Pi Model at f=3.00 GHz: Q = 7.02, 7.10, 7.89
L = 2.31 nH R = 4.9
Cs1= 63.2 fF Rs1= 639
Cs2= 59.9 fF Rs2= 702 f_res = 13.16GHz
Also as expected, the stacked structure has higher capacitance as it
lies closer to the substrate. Also at 3 GHz the quality factor of the two
layer structure is better due to the lower winding loss. How about a
three layer structure?
ASITIC> timing
ASITIC> hide a1
ASITIC> sqsh name=a3 len=150 w=8 s=1 n=3.75 metal=m3 exit=m1 xorg=200 yorg=200 cbegin cend exit90
ASITIC> pix a3 3
lambda = 25000.00, delta = 1.84
maxL = 1250.00, maxT = 1.47, maxW = 1.47
Performing Analysis at 3.00 GHz
Generating capacitance matrix (184x184)...
Generating inductance matrix (230x230)..
Inverting matrix......
Ind Timing: tot = 3006, setup = 32, fill = 2444
invert = 495, reduce = 32, eddy = 00
Calc Times (ms): total = 5508, cap = 2502, ind = 3000, node = 05
Pi Model at f=3.00 GHz: Q = 7.33, 7.34, 8.59
L = 2.21 nH R = 4.04
Cs1= 89.2 fF Rs1= 665
Cs2= 89.7 fF Rs2= 683 f_res = 11.34GHz
We're getting close to a point of of diminishing returns. While the
series lesses drop, the increased substrate losses due to the close
proximity of the substrate begin to limit the improvement in Q.
The following figure shows the three devices side-by-side for a
comparison.
While the sqsh structures tend to reduce loss at
approximately constant inductance, the sqmm series connected
devices increase inductance almost quadratically with the number of
turns with only a linear increase in resistance. Let's see this
ASITIC> del a1 a2 a3
ASITIC> sq name=s1 len=200 w=10 s=1 n=4 metal=m3 exit=m2 xorg=200 yorg=200 exit90
ASITIC> sqmm name=s2 len=200 w=10 s=1 n=4 metal=m3 exit=m2 xorg=200 yorg=200 exit90
The figure below shows how the multi-layer series device is wound.
Observe that the successive winding on layers below run parrallel to
the top windings in order to reinforce the magnetic field. Simply
stacking two windings in series would result in a reduction of
inductance.
ASITIC> indmat s1 .1
lambda = 750000.00, delta = 10.07
maxL = 37500.00, maxT = 8.05, maxW = 8.05
Generating inductance matrix (17x17)..
Inverting matrix......
Ind Timing: tot = 24, setup = 00, fill = 19
invert = 02, reduce = 01, eddy = 00
L = 4.0726003e-09 R = 10.25600000
ASITIC> indmat s2 .1
lambda = 750000.00, delta = 10.07
maxL = 37500.00, maxT = 8.05, maxW = 8.05
Generating inductance matrix (32x32)..
Inverting matrix......
Ind Timing: tot = 92, setup = 00, fill = 76
invert = 10, reduce = 03, eddy = 00
L = 1.4433833e-08 R = 20.08800000
The low frequency results are close to our expectation. How about the
high frequency resistance?
ASITIC> indmat s1 3
lambda = 25000.00, delta = 1.84
maxL = 1250.00, maxT = 1.47, maxW = 1.47
Generating inductance matrix (119x119)..
Inverting matrix......
Ind Timing: tot = 1314, setup = 02, fill = 1160
invert = 126, reduce = 22, eddy = 00
L = 4.0283518e-09 R = 11.61582699
ASITIC> indmat s2 3
lambda = 25000.00, delta = 1.84
maxL = 1250.00, maxT = 1.47, maxW = 1.47
Generating inductance matrix (224x224)..
Inverting matrix......
Ind Timing: tot = 3285, setup = 31, fill = 2039
invert = 1207, reduce = 03, eddy = 00
L = 1.517041e-08 R = 29.20356681
Notice that the AC resistance of the stacked device is much higher
(45% increase) whereas the single layer stucture shows a less
pronounced increase in loss (13%). Another issue with a multi-layer
structure is the large inter-winding capacitance which lowers the
frequency of self-resonance
ASITIC> pix s1 3
lambda = 25000.00, delta = 1.84
maxL = 1250.00, maxT = 1.47, maxW = 1.47
Performing Analysis at 3.00 GHz
Generating capacitance matrix (85x85)...
Generating inductance matrix (119x119)..
Inverting matrix......
Ind Timing: tot = 1477, setup = 11, fill = 1167
invert = 269, reduce = 26, eddy = 00
Calc Times (ms): total = 2032, cap = 539, ind = 1487, node = 06
Pi Model at f=3.00 GHz: Q = 5.04, 5.16, 6.24
L = 4.11 nH R = 9.8
Cs1= 80.2 fF Rs1= 614
Cs2= 75.5 fF Rs2= 677 f_res = 8.77GHz
ASITIC> pix s2 3
lambda = 25000.00, delta = 1.84
maxL = 1250.00, maxT = 1.47, maxW = 1.47
Performing Analysis at 3.00 GHz
Generating capacitance matrix (160x160)...
Generating inductance matrix (224x224)..
Inverting matrix......
Ind Timing: tot = 5379, setup = 10, fill = 3759
invert = 1522, reduce = 85, eddy = 00
Calc Times (ms): total = 8759, cap = 3338, ind = 5391, node = 28
Pi Model at f=3.00 GHz: Q = 3.06, 1.66, 3.52
C = 75.3 fF R = 75.1
Cs1= 47 fF Rs1=1.23e+03
Cs2= 148 fF Rs2= 441
Even at 3 GHz, the device has experienced self-resonance and looks
like a capacitor. Whereas the single layer device is still a healthy
inductor. Let's check at a lower frequency (1 GHz)
ASITIC> pix s1 1
lambda = 75000.00, delta = 3.18
maxL = 3750.00, maxT = 2.55, maxW = 2.55
Performing Analysis at 1.00 GHz
Generating capacitance matrix (68x68)...
Generating inductance matrix (68x68)..
Inverting matrix......
Ind Timing: tot = 101, setup = 01, fill = 78
invert = 14, reduce = 07, eddy = 00
Calc Times (ms): total = 282, cap = 174, ind = 102, node = 05
Pi Model at f=1.00 GHz: Q = 2.40, 2.40, 2.44
L = 4.06 nH R = 10.3
Cs1= 94.8 fF Rs1= 642
Cs2= 88.2 fF Rs2= 690 f_res = 8.11GHz
ASITIC> pix s2 1
lambda = 75000.00, delta = 3.18
maxL = 3750.00, maxT = 2.55, maxW = 2.55
Performing Analysis at 1.00 GHz
Generating capacitance matrix (128x128)...
Generating inductance matrix (128x128)..
Inverting matrix......
Ind Timing: tot = 807, setup = 12, fill = 703
invert = 83, reduce = 06, eddy = 00
Calc Times (ms): total = 2488, cap = 1663, ind = 803, node = 21
Pi Model at f=1.00 GHz: Q = 3.64, 3.04, 3.75
L = 17.5 nH R = 26.9
Cs1= 65.7 fF Rs1=1.19e+03
Cs2= 173 fF Rs2= 465 f_res = 4.69GHz
Now things look better at 1 GHz. Note that the multi-layer structure
has a self-shiedling property. In other words, the bottom coil acts
as a substrate shield and thus the substrate losses of the top shield
are reduced.
ASITIC> trans name=t len=250 w=10 s=2 n=3.75
ASITIC> mv t-p 120 120
ASITIC concatenates a "-P" and "-S" to the name you specify in
order to designate the primary and secondary windings. In the above
case we wound the primary and secondary similarly (with equal turns
and width). Let's create an asymmetric transformer as follows
ASITIC> hide t-p t-s
ASITIC> mv x-p 120 120
ASITIC> trans name=x len=250 w=10 s=2 np=4.5 ns=2
You'll notice that ASITIC made the primary and secondary
windings "friends". Thus when you move one, the other moves as well.
Otherwise the windings are two distict independent spiral.
You can find the inductance matrix of the device at high frequency with the k2 command.
ASITIC> k2 1.2 t-s t-p
lambda = 62500.00, delta = 2.52
maxL = 3125.00, maxT = 2.01, maxW = 2.01
Generating inductance matrix (160x160)..
Inverting matrix......
L(T-S,T-S) = 3.34111 nH R(T-S,T-S) = 5.135
L(T-S,T-P) = 2.66867 nH R(T-S,T-P) = 0.300
L(T-P,T-P) = 3.34187 nH R(T-P,T-P) = 5.404
ASITIC> k2 1.2 x-s x-p
lambda = 62500.00, delta = 2.52
maxL = 3125.00, maxT = 2.01, maxW = 2.01
Generating inductance matrix (140x140)..
Inverting matrix......
L(X-S,X-S) = 1.83162 nH R(X-S,X-S) = 3.480
L(X-S,X-P) = 1.83813 nH R(X-S,X-P) = 0.152
L(X-P,X-P) = 3.67132 nH R(X-P,X-P) = 5.598
The calctrans command computes the high-frequency inductance
and capacitive behavior of the device at a particular frequency:
ASITIC> calctrans t-s t-p 2
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (160x160)...
Generating inductance matrix (192x192)..
Inverting matrix......
Narrowband Model at f=2.00 GHz:
L1= 3.4 R1= 5.16 L2= 3.4 R2= 5.44 M= 2.73 (k= 0.805) Re(Z12) = 0.818
It's important to realize that this is not a circuit model for the
transformer but simply a translation of the 2-port z-parameters into a
particular circuit representation. In other words, R1 + i*w*L1 = z11,
and M = imag(z12)/(2*pi*freq), and so on. To actually design a
broadband model for the spiral, the transs command should be
used to generate s-parameters over a wide frequency range. See
the section broading modeling for more details.
If a large turns ratio transformer is desired for a particular application more exotic structures can be synthesized by hand. For instance, multi-layer spirals are very easy to generate and analyze:
ASITIC> del t-p t-s x-p x-s
ASITIC> sq name=pri len=200 w=8 s=8 n=5 metal=m3 exit=m1
ASITIC> sq name=sec len=200 w=4 s=4 n=10 metal=m2 exit=m1
ASITIC> rot sec 90
ASITIC> k2 2 pri sec
lambda = 37500.00, delta = 1.95
maxL = 1875.00, maxT = 1.56, maxW = 1.56
Generating inductance matrix (228x228)..
Inverting matrix......
L(PRI,PRI) = 3.69316 nH R(PRI,PRI) = 6.410
L(PRI,SEC) = 6.18359 nH R(PRI,SEC) = 1.071
L(SEC,SEC) = 13.55803 nH R(SEC,SEC) = 103.351
Notice that a large secondary to primary inductance ratio is
obtained. Even larger ratios can be obtained by mixing a multi-layer
spiral with a single layer spiral. For instance the primary can have
two metal layers in series and the secondary can have two metal layers
in shunt. You get the idea.
To realize a balun, we can tap the center of the secondary and create a three-port device with respect to a common ground. The "inductive" center, though, does not naturally coincide with the geometric center and this implies asymmetric capacitance and resistance on the secondary windings. For fully-differential circutis this is undesirable. The balun command solves this problem by creating a symmetric structure:
ASITIC> balun name=b len=200 w1=10 s=1 n=5 metal=m3 metal2=m2 xorg=200 yorg=200
ASITIC> mv b-s -50 -50
ASITIC> ind b-s
Inductance of B-S = 0.96325 (nH).
ASITIC> ind b-p
Inductance of B-P = 1.76683 (nH).
ASITIC> split b-p 0 b-p2
ASITIC> ind b-p
Inductance of B-P = 0.646206 (nH).
ASITIC> ind b-p2
Inductance of B-P2 = 0.646206 (nH).
ASITIC> res b-p
Resistance of B-P = 1.576453 (Ohms).
ASITIC> res b-p2
Resistance of B-P2 = 1.576453 (Ohms).
ASITIC> k b-s b-p
Coupling coefficient of B-S and B-P: k = 0.67907 and M = 0.53576 (nH).
ASITIC> k b-s b-p2
Coupling coefficient of B-S and B-P2: k = 0.67925 and M = 0.53590 (nH).
The above DC commands show that the balun has the desired properties.
How do we analyze the structure at high frequency? There are two
approaches. First, ignore the center tap and simply analyze the balun
as a two-port transformer. A more accurate approach is to
split the transformer as we did above and to use the
3port command.
Coming soon...