Hierarchical Electromagnetics

High Frequency Packaging

The Hierarchical Electromagnetic Modeler provides an accurate modelization of RF circuits composed of active devices and a connecting network. The Hierarchical Electromagnetic Modeler can be used to generate an equivalent circuit which represents the electrical response of the passive parts and includes a set of ports aimed at the connections of electrical circuits associated with the active devices.

This capability is demonstrated in a test case consisting of a small monolithic circuit (realized on a GaAs substrate) that is mounted on the top layer of a LTCC circuit which, in turn, is mounted on a PCB.

The bottom layer (GND) of the monolitic circuit is soldered on a metallic pad of the LTCC circuit. This pad is connected to the bottom side (a GND layer) of the PCB trough a series of staggered via holes that transverse the internal layers of LTCC and the PCB substrate. The electrical connections between LTCC and PCB conductors are provided by a Ball Grid Array. The connection between the signal conductors of the monolitic circuit and LTCC circuit are realized by a couple of bonded micro-wires.

The simulated electrical structure is shown in the figure 1. The small box depicted in the center of the image is enclosing the monolitic device and is used to separate the active part (the monolitic circuit) from the passive part (the exterior of the box).

In the electromagnetic simulations the active circuit has been replaced by a simple micro-strip line on the top layer of the GaAs substrate. The electrical response obtained with a full wave simulation of the whole structure was compared with the response of the assembled subcircuits associated with two parts. The result of this comparison is shown in figure 2 .

The figure 3 shows the same kind of comparison between the full wave and assembled responses computed using a commercial EM solver (CST Microwave studio). It can be seen that in this test case the agreement of the two responses shown in figure 2 is much better than in figure 3. This results demonstrates that Hierarchical Electromagnetic Modeler provides a better modelization of passive networks connecting active devices. This capability is very important in the design, in example, of MCMs (Multi Chip Modules) and SIPs (Systems In a Package) operating at very high frequencies.

Accurate Reconstruction Through Multimodal Internal Ports

In both EmCAD and CST test cases, the structure was analyzed via two simulation strategies: a full-wave simulation of the complete structure and a simulation obtained by reassembling the circuits extracted from the two separated parts (the passive portion and the chip).

Ideally, in the absence of modeling errors, the response of the reassembled simulation should match the full-wave response. However, discrepancies arise — and they are significantly more pronounced in CST's case.

This difference demonstrates the superior ability of Hierarchical Electromagnetic Modeler to capture electromagnetic interactions across internal ports, thanks to its multimodal modeling capabilities.

Why EmCAD Outperforms Traditional Simulators in Internal Port Modeling

EmCAD's edge lies in its multimodal treatment of internal ports — especially crucial in modern high-frequency packaging:

• Conventional tools typically model only the fundamental TEM mode at internal microstrip ports.
• EmCAD captures higher-order mode interactions, which become significant in practical designs — e.g., when an LTCC module sits atop a PCB with misaligned ground planes.
• In de-embedding of internal components EmCAD disconnects only TEM modes at internal ports, while keeping higher-order interactions intact.

This yields a more physically consistent model of the passive section, allowing better integration with active components.

The equivalent circuit generated with this strategy may include cross-coupling terms between de-embedded pars. These terms have to be removed but this approximation is significantly more accurate than approximations introduced in conventional simulators produce — since they ignore higher-order coupling entirely.