Analysis and modeling of interstacked transformers for mm-wave applications

Abstract

The analysis and modeling of monolithic interstacked transformers for mm-wave applications is addressed. The performance advantages of the interstacked structure are demonstrated by using the most important figures of merit for integrated transformers and a physicbased scalable lumped model is proposed. The model components are calculated with closed-form expressions that make use of geometrical and technological parameters. The accuracy of the proposed model is demonstrated by comparison with electromagnetic data in a wide frequency range. Maximum errors are below 5, 7.5, and 2% for magnetic coupling factor, quality factor, and self-resonance frequency, respectively. High accuracy is also achieved in the modeling of S-parameters up to the self-resonance frequency.

Interstacked Transformer Quad-Core VCOs

“…As a first but effective design of an interstacked transformer, a simple lumped model has been proposed in [30]. For the sake of completeness, the model schematic is reported in Figure 2, along with main design equations and geometrical parameters.…”

“…Coupling factors k m , k S, , and k IN could be drawn from EM simulations of open-air coupled spirals (i.e., without the silicon substrate beneath) separated by silicon dioxide of proper thickness, as proposed in [30]. Finally, capacitive effects are taken into account by means of the port-to-port inter-metal (C OXM ) and port-to-substrate (C OXS ) capacitances that mainly arise from the area contributions.…”

“…Ideally, the greater the coupling factor, k, between the coils, the greater the area reduction and the better the coupling between the cores. Interstacked transformers-which exploit both the interleaved and stacked magnetic coupling between the coils-have proven to be a good solution for achieving high k values [28][29][30]. Compared to commonly used stacked transformers, they provide comparable or even higher k-factors and are intrinsically symmetrical.…”

A Comparative Analysis between Standard and mm-Wave Optimized BEOL in a Nanoscale CMOS Technology

“…Due to fabrication issues, the top Al layer, LB, exhibits a hole in transformer coils, as is visible in Figure 3. It is worth mentioning that the adoption of highly involved inter-stacked configurations to maximize the magnetic coupling is mandatory only in presence of very thick intermetal oxides [18,31]. No patterned ground shield (PGS) was included since it would have a detrimental effect on the Q-factor at W-band frequencies.…”