# Design the best interconnect for your next RF or microwave circuit

Microwave designers have long been aware of the importance of proper interconnect design as a critical step to successful circuit performance. As a matter of fact, one of the distinguishing features of microwave design is to use the interconnect to advantage by creating desired phase changes of the signal in the desired frequency band. Interconnect design can be efficiently carried out only if the circuit design software is capable in three important areas:

*Models:*Designs are only as good as the models used to make up the circuit. It is important that the various parts of the interconnect can be accurately and efficiently modeled. Remember that accuracy is only part of the story. It does little good to have the world's most accurate model if it is difficult to use, slow to simulate, or too limited in its range of validity.*Layout and Model Interaction:*By necessity, interconnect design involves working with the layout of the critical nets, and modeling the resulting structures. It is important that the designer be able to quickly layout the necessary nets, and obtain (extract) the corresponding models. Often this involves sending the interconnect layout to an electromagnetic simulator or extraction tool.*User Interface and Simulation*: It is important that the designer be able to simulate the design efficiently, in order to see how the interconnect affects the performance. This often involves switching between different simulators, annotating schematics, and updating graphs. A poorly designed user interface will make it difficult to carry out these tasks easily.

There have been a number of exciting new developments in these three areas in the past few years. It is now possible to account for the interconnect effects in the circuit much more efficiently and accurately. Part of this is due to increased computer power. For example, electromagnetic simulations can be carried out on much larger structures than before. Less well known are improvements made in the areas listed above. This paper describes these recent developments.

**Figure 1** summarizes new interconnect modeling software ideas. The figure is broken up into two regions, the microwave region and the radio frequency IC (RFIC) region. Each of these two design regimes has its own set of requirements. The classic microwave type of design process, be it for a package, board, or microwave IC (MIC), is typically frequency centric. The interconnect is long enough that distributed models are required. Well-defined ground planes make it useful to use S parameter descriptions of elements. Either planar or 3D EM simulators are used to help develop models. The RFIC designer usually works both in the time and frequency domains. The interconnect structures are small compared to a wavelength, and therefore can be modeled with lumped elements effectively.

**Interconnect Model Basics**

In its most general sense, a model is any mathematical description of a portion of the interconnect. Models for interconnect components come in three basic varieties: closed-form models, quasi-static electromagnetic models, and data-based models.

Closed form models are the traditional models we have all grown to know and love. They consist of formulas describing the electrical properties of the object. For example, microstrip line models give formulas for the either the line's impedance and propagation characteristics, or its electrical parameters (R,L,C,G) per unit length. The formulas are either analytically derived from a simplified geometry, or they are the result of curve fitting to numerical data. Closed form models have significant advantages. They can be moderately accurate (errors of a few percent, typically) and are extremely fast to calculate. As a result, they are ideal candidates for tuning and optimization studies.

Quasi-static electromagnetic based models get their electrical parameters for the transmission lines from a quasi-static solution of the cross sectional geometry of the line and its ground plane. Quasi-static solutions can more accurately predict the line parameters over a larger range of physical parameters (width, dielectric constant, line thickness, etc.) than can closed form models.

There are different methods used to solve for the parameters, with the most popular ones being based on moment method or boundary element methods. In this approach, the charge is solved on the surface of the conductors, and the capacitance and associated parameters are derived. The method assumes that the conductor loss increases in frequency as the square root of frequency, which is usually called the "skin depth approximation." This approximation is valid for boards, packages, and MIC technologies. It falls down, however, for RFIC technologies in silicon. Fortunately, alternative methods now exist using the finite element method, which can account for the more complicated loss behavior in silicon due to the lossy silicon substrate and small cross sectional dimensions of the line.

Data based models are often the network dataset of the element (S, Y, or Z parameters). The data typically come from either measurements or electromagnetic simulations. The main advantage of these models is that they are extremely accurate (assuming the measurements and/or simulations have been carried out carefully). There are, however, some disadvantages. First, the models must be interpolated and extrapolated in frequency if data do not exist at needed points. (Typical situations where this occurs is when a DC bias point is needed for the circuit, or harmonic frequencies are needed for a harmonic balance simulation.) Second, S parameter models are straightforward to use for frequency domain simulations, but are awkward for time domain ones. (This limitation will be discussed later in the user interface and simulation section of this paper.)

**Recent Developments in Interconnect Models**

So what is new in interconnect models? Much work has been done to increase the generality and robustness of cross-sectional electromagnetic based line models. New methods have removed the skin depth approximation, which is not valid for silicon RFIC lines. Sophisticated substrate effects can be included, such as accurate modeling of the frequency dependent capacitive coupling to the silicon substrate.