Sample *ASITIC* Sessions

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The following sample sessions are run with the following sample technology file named

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

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 ver 03.19.00.01.29.01 INPUT/OUTPUT LOG File # Generated on Thu May 24 15:23:51 2001 ####################################################

You can also invoke the command without any options wherebyASITIC> sq name=a len=175 w=10 s=.5 n=5 xorg=200 yorg=200 metal=m3 exit=m2

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

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.ASITIC> ind a Inductance of A = 4.13121 (nH). ASITIC> res a Resistance of A = 4.246441 (Ohms).

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:

TheASITIC> 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 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:

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> 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

Now we see an even more dramatic decrease in substrate resistance. The halo substrate contact is created using theASITIC> 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

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.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 analysis indicates that the SRF is around 7 GHz. Let's examine the equivalent circuit at this frequency:

This result took 40 seconds to generate. Note too thatASITIC> 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

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

You should now see both spirals in the layout.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

By making the spirals *friends* we can move them both
simultaneously. Let look at the magnetic coupling between these
devices

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.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

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?

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> 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.

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> 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

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. TheASITIC> wire name=c len=200 w=10 metal=m2 xorg=120 yorg=380

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

TheASITIC> showdir ASITIC> flip b ASITIC> flipphase b ASITIC> join a c b ASITIC> ind a Inductance of A = 8.80189 (nH).

The high frequency performance of this pair is disappointing

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).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

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.

The above discussion applies to non-square structures. For instance, theASITIC> 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 Wirehas 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

*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:

This structure resides on metal m3 and m2 in shunt and the exit occurs through layer m1. To see this, typeASITIC> sqsh name=a2 len=150 w=8 s=1 n=3.75 metal=m3 exit=m2 xorg=200 yorg=200 cbegincend exit90

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> psegs a2 . . . Segment 14: ( 119.0, 31.0, 45.0)-( 69.0, 31.0, 45.0) onShunt: ( 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

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> 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

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> 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

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.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

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

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> 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 low frequency results are close to our expectation. How about the high frequency resistance?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

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-resonanceASITIC> 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

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 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

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> 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

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

You'll notice thatASITIC> 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 can find the inductance matrix of the device at high frequency
with the `k2` command.

TheASITIC> 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

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, theASITIC> 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

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:

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.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

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:

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 toASITIC> 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).

Coming soon...