Sample ASITIC Sessions

Introduction Command Reference Environmental Variables Installation Technology File Quickstart FAQ

The following sample sessions are run with the following sample technology file named sample1.tek. This file is included in the latest ASITIC distribution. You are encouraged to run the following commands locally to ensure your installation is working properly.

Analysis of a Square Inductor

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 2pzin command. The actual SRF can be determined by finding the frequency when L is zero.

Analysis of an Inductor Pair

So far we have only looked at a single device. Let's create a replica of this spiral and look at the interaction between two spirals.

 

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  has the following geometry:
L = 450.00, W = 200.00, Metal = MSUB
Total length =  450.00 (um), Total Area = 90000.00 (um^2)
Located at (37.00,187.00) with 1 segments.

ASITIC>  pix a 2 sh

lambda = 37500.00, delta =  1.95

maxL = 1875.00, maxT =  1.56, maxW =  1.56
Performing Analysis at 2.00 GHz
Generating capacitance matrix (435x435)...
Generating inductance matrix (246x246)..
Inverting matrix......
Ind Timing:  tot =  3156, setup =    21, fill =  1306
           invert =  1823, reduce =    03, eddy =    00
Calc Times (ms):  total = 16351, cap = 13176, ind =  3147, node =    26
Pi Model at f=2.00 GHz:  Q = 6.39, 6.35, 7.73
L  =  7.65 nH	R  =  10.6
Cs1=   232 fF	Rs1=  2.73
Cs2=   241 fF	Rs2=  1.61	f_res =  3.77GHz

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.

Multi-Layer Stacked Inductors

Note: For the purpose of this discussion, please locate the technology file sample2.tek. This technology file resembles a modern multi-layer IC process.

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 
        Shunt:  (  119.0,   31.0,   47.0)-(   69.0,   31.0,   47.0) on 
Segment  15:  (   65.8,   31.0,   47.0)-(   72.2,   31.0,   45.0) on 
Segment  16:  (   69.0,   31.0,   48.0)-(   69.0,   -8.0,   48.0) 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.


Transformers and Baluns

Planar transformers can be created with the trans command:

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...

Substrate Coupling

Broadband Modeling

Geometry Optimization