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# Find L, Q, & mutual inductance of two close inductors.

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#### MustafaSami

##### Newbie
Hello, all.
This is my first post here so I'm sorry if there's any inconvenience.

I'm designing a (very well known) degenerated LNA that contains inductors at both Gate&source of the input core MOS, indicated as LG&LS, respectively.

I did layout both inductors in the virtuoso and used sonnet as shown to extract them and successfully managed to generate .s4p file:
Port 1&2 for Ls,
Port 3&4 for Lg.

I was wondering how to simulate them using cadence in order to extract:
Lg, Ls, Q, and mutual inductance between them.
My test bench is shown here.

Simulate the coils independently then simulate both inductors are close each other.
The difference between two simulation will give you an aspect about Mutual Inductance.

I think that Cadence Virtuoso itself cannot do EM simulation, but can connect to EMX 3D, or Clarity 3D Solver, or to AWR Microwave Office.
If you have access to AWR, would be the simplest way to do the simulation.
You have to connect one port of each inductor to the ground (e.g. port 2 and port 3), and in a rectangular plot click on Linear, and choose L_SRL for Port index 1 and 4, and you get series inductance for each inductor.
On other rectangular plot, also on Linear, choose Q_IN2, which is Q factor with other port grounded. Do for both, Port index 1 and 4.
On a third rectangular plot , Linear S parameters, do S41 in dB, which will be the coupling (in dB) between the two inductors.

Simulate the coils independently then simulate both inductors are close each other.
The difference between two simulation will give you an aspect about Mutual Inductance
This is an interesting idea. Will try that.
But can you tell me how to properly extract L&Q for LG&LS from the .s4p that I talked about? I know how to run sp simulation in cadence but not sure how to extract L&Q.

I tried to plot the imaginary part of Z11&Z33 to extract XL value.. But I found it to be negative value (which means Z11&Z33 are capacitive not inductive.. Not sure though)
I think that Cadence Virtuoso itself cannot do EM simulation, but can connect to EMX 3D, or Clarity 3D Solver, or to AWR Microwave Office.
If you have access to AWR, would be the simplest way to do the simulation.
You have to connect one port of each inductor to the ground (e.g. port 2 and port 3), and in a rectangular plot click on Linear, and choose L_SRL for Port index 1 and 4, and you get series inductance for each inductor.
On other rectangular plot, also on Linear, choose Q_IN2, which is Q factor with other port grounded. Do for both, Port index 1 and 4.
On a third rectangular plot , Linear S parameters, do S41 in dB, which will be the coupling (in dB) between the two inductors.
Unfortunately I don't have access to AWR, but I do have access to ADS. Do you know a way around with ADS to simulate this .s4p file to extract L, Q, & Mutual inductance?

As told, the OP did already a planar EM simulation with Sonnet. Provided the results are correct, the respective .s4p files contain all required coil data. Because you are not asking for capacitance values, it would be probably simpler to use a 2 port rather than 4 port setup. If you are operating clearly below inductor self resonance frequency, you can convert s-parameters to z-parameters and read the complex impedances as self- and mutual inductance with series R.

Presume that Sonnet can output z-parameters in addition to s-parameters.

You have to define ADS view in Virtuoso then simulate your coils.

What is going on here?

There is absolutely no reason to switch to AWR or ADS! Sonnet is perfectly fine for this task.

Regarding L and Q, you can re-simulated the single inductors, or use Sonnet netlist to reduce the 4-port simulation into a 2-port model for one inductor. Then you can use Sonnet built-on equations for L and Q, using "Inductance2" and "Untapped Qdiff".

To get mutual inductance, you can evaluate the change in extracted inductance if you short the other coil, instead of leaving it open. Again, that could be done using the Sonnet netlist.

Long ago I had created Sonnet custom equations to extract M and k factor from 2-port simulations, where each inductor is connected by one differential port. That is attached, but you should double check with test data if that really works for you.
--- Updated ---

I tried to plot the imaginary part of Z11&Z33 to extract XL value.. But I found it to be negative value (which means Z11&Z33 are capacitive not inductive.. Not sure though)

Z11 is impedance into port 1, with all other ports open. In your case, each inductor is simulated with 2 ports, so Z11 evaluation is wrong: one side of the inductor would be floating.

For single 2-port inductors, you would evaluate 1/Y11 instead. That is impedance with the other ports shorted, i.e. the second inductor terminal is connected to ground. HOWEVER, in your case you have two inductors and these are coupled by mutual inductance, so the open/shorted state of that other inductor would change results also. For this reason, you better evaluate individual inductances from 1/Y11with a testbench where the other inductor is open (unconnected).

All these basics are applicable to all EM solvers, no matter if that's Sonnet or Momentum or AWR.

#### Attachments

• Sonnet_xfmr.zip
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