INDUSTRIA AGROALIMENTARIA

In older IE3D versions, we have to use the Process->PI-Network Equivalent command on MODUA to find the R, L and Q values of the spiral inductor. We did not have any utility to display them and we had to use Excel or other tools to display them on graph. On IE3D 14, the results are readily available on the Process->S-Parameters and Lumped Equivalent Circuit command. Just select the “2-Port PI with Series RL and Shunt RC” (see Figure 6.44). Then, you can select Add Graph to define some graphs displaying R, L and Q.

The L-values from different meshing schemes are compared in Figure 6.44 while the R and Q are compared in Figure 6.45. As you can see, the Fmax=200 GHz cases agree very well while the Fmax = 15 GHz case is a little bit off. The case with Fmax = 200 GHz and AEC = 0.05 have better edge cells. It is supposed to be more accurate.

Please note that there are different definitions for the equivalent circuit. For example, some people may define the R, L and Q as: R = - 1 / Re(Y12), L = - j / [  Im(Y12) ) and Q = Im(Y12) / Re( Y12 ). On

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IE3D, you have different options. You can define the R, L and Q based upon Figure 6.43 with Q =  L / R.

You can also convert the 2-port s-parameters into 1-port and define the R, L and Q based upon the 1-port (or 2-terminal) series R and L model.

On the s-parameters processing dialog (Figure 6.44), you can select s-parameters data in the list box and select Save Model to save the R, L and Q values into an ASCII file. Table 6.7 shows a sample of it.

Figure 6.44 The L value of the PI-network with different meshing schemes.

(a) R (b) Q

Figure 6.45 The comparisons on R and Q between different meshing schemes

6-33 Table 6.7 The PI-equivalent circuit of the spiral simulated in .\ie3d\practice\spiral1.geo.

Current S-Parameters (spiral1) Fmax=200,AEC=0.05

!The 1st line is the s-parameter file name if it is available.

!The 2nd line is the comment identifying the model.

!Any line starts with exclamation is a comment of the file and it will be discarded in parsing.

!

!IE3D Frequency-Dependent Lumped Model File

!IE3D File Type Number Version Model Type 6830 12.00 10

!Model Type is a unique number to denote the type of equivalent circuit.

!

!Model Type Name: 2-Port PI with Series RL and Shunt RC

!Port Number is the s-parameters port number. Final Port Number is the equiv ckt port number.

!Port Number Final Port Number Precise Model 2 2 1

!

!Warning: Please understand that an equivalent ckt is just a fitted model. It is based upon

! your selection of the model you want to fit the s-parameters into. The values of

1.0000000000e-001 7.3780896936e-001 4.3209333742e+000 3.6285341532e+000 -5.3360178889e-002 3.9412225663e+002 9.9215002933e-002 2.8234154099e+002 2.0000000000e-001 1.4276489037e+000 4.3265578100e+000 3.7004578143e+000 -1.3623883536e-002 3.9916701826e+002 6.1206256881e-002 2.7981183719e+002 3.0000000000e-001 2.0349909078e+000 4.3238568884e+000 3.8032906979e+000 2.8088889461e-003 4.0131505969e+002 4.4962796786e-002 2.7873728373e+002 4.0000000000e-001 2.5425982816e+000 4.3191327246e+000 3.9365441674e+000 1.0113578634e-002 4.0227487619e+002 3.7508618084e-002 2.7822843097e+002 5.0000000000e-001 2.9457406370e+000 4.3136378014e+000 4.0997722449e+000 1.3803949326e-002 4.0275504876e+002 3.3572471946e-002 2.7794180219e+002 6.0000000000e-001 3.2493656822e+000 4.3077828340e+000 4.2925681202e+000 1.5869818131e-002 4.0301861957e+002 3.1244749012e-002 2.7775559306e+002 7.0000000000e-001 3.4644408835e+000 4.3017379479e+000 4.5145598021e+000 1.7121309514e-002 4.0317465265e+002 2.9747694709e-002 2.7762096414e+002 8.0000000000e-001 3.6046597127e+000 4.2955830907e+000 4.7654053166e+000 1.7929237007e-002 4.0327323002e+002 2.8724055964e-002 2.7751555162e+002 9.0000000000e-001 3.6840589578e+000 4.2893582985e+000 5.0447878658e+000 1.8479945086e-002 4.0333884663e+002 2.7992224579e-002 2.7742769909e+002 1.0000000000e+000 3.7155917127e+000 4.2830839143e+000 5.3524113018e+000 1.8874032028e-002 4.0338369214e+002 2.7451753958e-002 2.7735051049e+002 1.1000000000e+000 3.7104536428e+000 4.2767698582e+000 5.6879961796e+000 1.9168834996e-002 4.0341359610e+002 2.7042986298e-002 2.7727940992e+002 1.2000000000e+000 3.6779053964e+000 4.2704203078e+000 6.0512765400e+000 1.9398397124e-002 4.0343097980e+002 2.6728271311e-002 2.7721107960e+002 1.3000000000e+000 3.6253743664e+000 4.2640362331e+000 6.4419974737e+000 1.9583563237e-002 4.0343645119e+002 2.6482590984e-002 2.7714297840e+002 1.4000000000e+000 3.5586854764e+000 4.2576168344e+000 6.8599134267e+000 1.9737402557e-002 4.0342971969e+002 2.6288592239e-002 2.7707311492e+002 1.5000000000e+000 3.4823301179e+000 4.2511603777e+000 7.3047871466e+000 1.9868269321e-002 4.0341013762e+002 2.6133814485e-002 2.7699993320e+002 ….

6-34 Section 6.15 Modeling True Thickness of the Spiral Inductor

Step 1 Run MGRID. Open .\ie3d\practice\spiral1.geo. Please select Parameters->Basic Parameters to see the strip thickness. It is 1.5 microns. Select Cancel. Click at the No. 3 Layer at Z = 275 to focus on the layer. Select Edit->Layer->Grow Thickness on Layer. The dialog comes up (see Figure 6.46). Make sure the Thickness Growing Direction is Positive Z-Direction and the Ports on All Edges are checked. Select OK to accept the default setting of 2^nd Degree Compensation with Pre-Processing. This is the best setting for accurate modeling of loss. The Positive Z-Direction for the Thickness Growing Z-Direction means that we want the thickness spans from Z = 275 to Z = 276.5. The Ports on All Edges will guarantee an extension port will be on all the edges of a thick trace for high accuracy results.

Figure 6.46 The Grow Thickness on Layer dialog.

Figure 6.47 The spiral with true thickness built.

Step 2 Select OK. MGRID will prompt you for removing the existing s-parameters. Please select YES because the results are saved. The thickness is built. Please save the file as:

.\ie3d\practice\spiral1_tk.geo. The top view and the 3D view are shown in Figure 6.47. You can see the connection markers on the supposed open edges in the top view and the true thickness in the 3D view. The current on the four sides of the trace will be accurately modeled. At low frequency, current is not concentrated on the surface. You may wonder whether the model is

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accurate enough at low frequency. In fact, the model is good from very low frequency to very high frequency. More explanation is included in Appendix S on modeling thickness.

Simulation on spiral1_tk.geo takes couple minutes only. A comparison in the s-parameters between the Thin Model (spiral1.geo) and Thickness model (spiral1_tk.geo). is shown in Figure 6.48. There is some slight difference. Figure 6.49 shows the comparison in the Q-values. There is about 5% difference in the L value while the differences in R and Q are smaller. The difference in the calculated L is expected because the thin model is an approximation while the thick model is closer to the reality. Both models should be accurate results while the Thickness model should be more accurate.

You may notice that the meshing for the Thickness model does not have edge cells. This is due to the fact that the vertical polygons along the edges already model the edge effects very well.

There is no need to use edge cells unless very high accuracy is required. More discussion can be found in Appendix S.

This spiral does not have very high Q-value and it should not be a good design. We use this example to demonstrate to you how to accurately and efficiently simulate spiral and transformer circuits in RFIC. How to improve the Q-value is beyond the topics of this manual.

All the examples we demonstrated here are simple ones. It takes minutes to simulate. More complicated structures can be simulated in the same way. IE3D is the most accurate, efficient and capable EM simulator for MMIC, RFIC and PCB applications. You can use it to solve much tougher EM problems.

Figure 6.48 The comparison in s-parameters between Thin Strip and Thick Strip models.

Figure 6.49 The comparison in Q-values between Thin Strip and Thick Strip models.

6-36 Section 6.16 Automatic Run-Time Thickness

In the above example, we have demonstrated how we can use thickness model for structures with thick traces. Thickness model can include all the effects of thickness precisely. It should be the model we should use when the strip thickness is no longer much smaller than strip width and high accuracy is required. However, as you can see, the thickness model creates many more polygons. Further editing of the structure will be much more difficult. We suggest users to keep the thin model before “growing” thickness so that you can do the editing based upon the thin model and re-grow the thickness after change.

Another option is to use the Automatic Run-Time Thickness (ARTT). ARTT allows you to keep the thin strip model while it will automatically create the thickness model in run-time. It allows you to do editing on the thin model while you do the simulation on the thickness model transparently. Let’s use the spiral structure as our example to demonstrate the ARTT feature.

Step 1 Run MGRID. Open .\ie3d\practice\spiral1.geo. Select Parameters->Basic Parameters to check the strip thickness. It is 1.5 microns. The spiral is on Z = 275 microns. Please select the Insert button in the Automatic Run Time Thickness group (see Figure 6.50). MGRID will prompt you for the z-coordinate where you want to create thickness (see Figure 6.51). You also have the choice to choose the thickness growing in +z or –z direction. Enter the Layer Z-Coordinate as

“275”. Choose the option of Positive Z-Direction because we want the thickness growing in +z.

Select OK to close the dialog. Select OK to close the Basic Parameters dialog. MGRID may prompt you for multiple thin layers. You should select not to merge the thin layers. Merging thin layers normally can make the simulation faster but a little accuracy decrease might occur. For this example, the simulation is quite fast and you don’t need to worry about it.

Figure 6.50 The Insert button of ARTT in Basic Parameters.

Step 2 Save the file as: spiral1_artt.geo. The structure looks exactly like the thin model. However, the structure being simulated should be like the thickness model. How can you know it is like the thickness model?

Step 3 Please select Process->Create Run-Time Thickness Model. MGRID will prompt you for the new geometry file name. The default is: derived.geo. Select Save and MGRID will create the

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thickness model into derived.geo and open another instance of MGRID for it. The derived.geo will be a thickness model with polygons for the 4 sides of the traces. If you check the Basic Parameters, you will see the ARTT list box is empty in derived.geo. Certainly, ARTT is no longer required and should not be defined for the thickness model. The derived.geo is the exact structure you simulate if you select Process->Simulate on sprial1_artt.geo. If you simulate it and save the current distribution, you will also see the thickness on the spiral1_artt.cur file.

Figure 6.51 The ARTT dialog inside Basic Parameters dialog.