SIwave is a power integrity and signals integrity tool. The focus in this article is on the Resonant mode solver.

The main reason for doing resonance calculations is to identify the best location(s) for decoupling caps in powerplanes. The size of a powerplane is determined by the maximum expected current and the allowed maximum voltage drop. However, even the best design does not have enough capacitance to keep the impedance at low values for a broadband spectrum. The spectrum of the power plane is derived from the current pulses. Powerplanes need decoupling caps to extend their bandwidth beyond.

Figure 1: Rosanant modes solver icon

SIwave should not be used to build PCBs. While this is possible, it is not the best way to utilize SIwave. SIwave can import the following type of CAD files:

Figure 2: Import dialog box in SIwave

SIwave extracts different information from the CAD file: for example, the stackup, the materials, the components, and the nets.

Any process in SIwave: DC, PI, SI, or radiation starts by selecting a solver. SIwave then generates a dialog box that looks like a form. The user needs to check the form and fill up the missing information.

For example, once the resonant mode solver is selected, a simple dialog box popup where the user enters the min/max frequency of interests and the number of modes. One can select other solver options to adjust the accuracy of the solver.

Figure 3: Resonant modes solver setup

From the PI analysis discussed in another blog, the Z11 plot exposes all the resonant modes. It is highly recommended when studying Z11 curves to include the effect of the VRM and read the impedance from the load side. That is the right way to study a powerplane.

In the plot below, there is a resonance at 0.2065GHz on the powerplane 1.2Volt. To suppress this peak, one needs to add decoupling caps. But where? And what values and how many? The resonant mode solver answers the first question.

Figure 4:PI results without the caps

The definition of Resonance is the frequency at which the impedance is very high, but physically what does it mean? For people working with antennas, it means that at this frequency, the power plane becomes a perfect antenna; it radiates lots of its energy out and also accepts any signal from outside at that frequency. Nothing you inject at that frequency will reach the other side. So if there is a sudden demand for lots of current, the system cannot deliver that. That is another reason why it should be suppressed.

- Examining the solution:
- Display resonance

Once the solution is finished, the user gets a list of all the resonances in the PCB in the band selected. The real part represents the resonant frequency, and the imaginary part stands for the losses of the Resonance or the decay factor. The k is the eigen number, equal to the resonance frequency times 2PI/ speed of light in free space, and it is around 20.954 times the resonant frequency in GHz. The wavelength is the wavelength in air, and the Q is a measure of how sharp the resonant is, and it is equal to the resonant frequency/ 2 times the imaginary part.

Some of these Resonance are strong, and others are weak. But which one of them belongs to the 1.2V power plane? The only way to know is to plot them all.

Figure 5: List of Resonance without caps

It is important to understand that the Resonance exists between the powerplanes and the grounds, the return path. SIwave plots the Resonance between layers only. So the user needs to select to plot the voltage between two layers: the one where the powerplanes are located and the one with the ground. Repeat that for every layer that has a ground. Repeat that for each layer that has powerplanes.

For each set, SIwave calculates the field of all the Resonance between the selected two layers. The user must then go through them individually to see to which powerplane they belong.

Figure 6: List of Resonance without caps and the fields

The second resonant at 0.2078 is red. This is a real resonance in a 1.2Volt powerplane. Go more, nothing and the sixth one is also a resonance but not in the 1.2Volt power plane, but in the other one 3.3Volt. This is how the user identifies the real Resonance.

Looking at the sixth one and doing animation, to see that the Resonance is reaching its max at the top and bottom left corners. Rotate to see things in 3D. Decoupling caps should be placed at the top and bottom left corners.

Figure 7: 3D plot of Resonance in the 3.3-volt power plane.

Back to Resonance number two. It matches the one in the Z11 plot. This Resonance covers the whole powerplanes. So decoupling caps need to be placed around inside the powerplane.

Figure 8: 0.2GHz Resonance in the 1.2Volt power plane.

Figure 9: 0.2GHz Resonance in the 1.2Volt power plane (3D plot).

Adding capacitors inside and around the powerplane, then rerun the PI. From plotting Z11, the Resonance at 0.206GHz was suppressed from 21Ohm down to 0.132Ohm. Mission accomplished

Figure 10: PI response with the caps

The resonance plot shows how small the red area is at 0.2GHz compared to the ones without the caps. Notice that the red area is always at 1Volt. So all the Resonances are normalized to 1Volt. That is why one cannot use the field plot alone to tell how aggressive is the resonant mode. The user needs to examine the Z11 plot.

Figure 11: The resonant modes in the PI plot and in the list

Notice that there are more resonant modes in the Z11 curves, So the decoupling caps added more, but they are so small. Solving the resonant mode solver again but selecting the low band, one will see these new modes. But from the Z11 and field plots, one can tell they are small.

Figure 12: The resonant modes in the PI plot and the list at low frequencies

We see in the list of Resonances some very close values. Remember, the Resonance does not always match the Z calculations. There is always a small delta because they use two different techniques to derive them. That is why one needs to look at both of them.

The Resonant Mode solver exposes the powerplanes and determines where is (are) the best place(s) to put decoupling caps.

June 26, 2023