Understanding the effects of process and component variations can help in constructing LTCC circuit designs that deliver desired performance levels in spite of those variations.

Low-temperature-cofired-ceramic (LTCC) circuit technology supports compact, multilayer designs and is now widely used in wireless applications, especially in RF modules and system-in-package (SiP) designs. It has a number of advantages over laminate technologies, although the process is similar to those used for laminated printed-circuit-board (PCB) materials. Typical advantages are lower dielectric loss, higher packaging density, and integrated/embedded passive components (resistors, inductors, and capacitors). There are a wide range of tape materials and processes available for LTCC designs.

A multilayer LTCC structure generally shrinks during the low-temperature cofiring process. However, there are some manufacturers who offer "zero-shrink" materials, where shrinkage is restricted only to the z-dimension. These materials may cost more than standard LTCC tape materials and processes. Shrinkage has added a challenge to achieving high performance with LTCC designs and limited the yield of LTCC components or subsystems. As a result, it may prevent the use of LTCC for applications requiring high performance and high yield. Still, the use of a Design for Manufacturing (DFM) methodology can help to achieve first-pass design success with LTCC, even accepting the shrinkage.

The DFM approach for LTCC involves the development of a design flow to generate broadband models for embedded passive components in LTCC. Those models, which are used for first-pass design success, will be presented along with several passive LTCC circuits developed from the DFM technique. The passive circuits were developed with the help of the Advanced Design System (ADS) and Momentum software tools from Agilent Technologies (www.agilent.com/find/eesof). ADS is a popular electronic-design-automation (EDA) software tool that includes circuit/system simulators and layout tools for RF integrated circuits (RF ICs), monolithic microwave integrated circuits (MMICs), SiPs, modules, and circuits. ADS can also perform statistical design studies, such as Monte Carlo analysis. (Momentum is a three-dimensional (3D) planar electromagnetic (EM) simulation tool that can study current flow and planar field behavior for a wide range of 3D planar high-frequency structures.) Momentum accepts arbitrary design geometries such as multi-layer structures, and then it accurately simulates complex EM effects such as coupling and parasitics. Multilayer LTCC is well suited to simulation with a 3D planar tool like Momentum.

The typical front end found in a wireless handset includes a transmitter section with a directional coupler for power-control measurements . The purpose of the power control is to assure that transmit power is within the regulatory limits for a given handset. Maintaining transmitter power within these limits is essential for spectral mask compliance since the operating range of the unit's RF power amplifier must be maintained in its linear range for amplitude-modulated (AM) signals. The power control loop relies on the directional coupler for sensing incident power; any other-than-specified directivity in the directional coupler may lead to erroneous readings in the measured power. Because the handset power amplifier can generate unwanted levels of harmonic energy, an additional lowpass filter is added to the transmitter architecture to maintain spectral emissions within regulatory limits.

To ensure handset compliance within regulatory limits, a robust design technique is needed for both directional coupler and lowpass filter. The two components will be used as examples of how to apply a DFM methodology in studying the process variations and layout parameters of LTCC and its impact on certain output parameters such as insertion loss. Some variations are to be expected in designing passive circuits with LTCC; typical variations include changes in dielectric constant, substrate thickness, transmission line width, and layer alignment. Such variations are expected to be monitored and controlled during the manufacturing process but, nevertheless, must be accounted for in order to achieve first-pass design success with LTCC.

The flow chart in Fig. 1* *illustrates the cross-interaction of these parameters to some of directional coupler's output parameters, insertion loss, directivity, and coupling ratio. In this chart, ε, T, W, and AL represent dielectric constant, substrate thickness, trace width, and alignment, respectively. Also, the "plus" and "minus" signs denote the extreme case of the upper and lower specifications, respectively. Based on the LTCC material supplier's data, variations in dielectric constant are minimal, hence the other three parameters, the substrate thickness, trace width, and alignment should be taken into consideration.

The directional coupler used as an example here has broadside embedded coupled lines. The coupler has four ports: RF input, coupled port, isolated port, and RF output. Figure 2* *shows the layout (with port definitions). The performance of the directional coupler was simulated with Momentum; Fig. 3

*shows the measured versus simulated results for the coupler's insertion loss and coupling ratio. The simulation data agrees closely with the measured results. To demonstrate this approach, it will also be applied to the design of an example lowpass filter (Fig. 4).*

Such variations in process and layout parameters may be unavoidable in the course of the design cycle. Circuit components can even suffer variations in value, typically expressed as component tolerance. Such changes in component values, manufacturing process variations, and related layout parameter variations are usually difficult to fix later in the design cycle. Consequently, taking them into consideration at the early stages of a design will help ensure high-yield first-pass design success.

Among all possible variations in process and layout parameters, some are more critical than others to affecting output parameters. Understanding the sensitivity of output parameters to those critical parameter variations is a simple but effective first step for a DFM methodology. For example, insertion loss may be affected differently by variations in trace width or substrate thickness. In order to achieve less performance variations in a design, it is critical to understand and control the most sensitive parameters first. Sensitivity analysis in simulation software involves taking partial derivatives of the performance response with respect to a design variable of interest. This can help pinpoint variables that contribute disproportionately to performance variances. The ADS software provides sensitivity analysis as a part of its basic statistical package.

The directional coupler's insertion loss, directivity, and coupling ratio vary as a function of three different cases of substrate thickness, trace width, and alignment. The three cases represent the nominal, lower, and upper extreme. For instance, W0 stands for the nominal value of trace width and W0+ for the upper extreme case. Momentum EM simulations were used extensively to collect the variation data for this case study.

Although designers can make some analogical conclusions about the sensitivity from these charts, it is much easier and more useful to use a graphical display of the results, such as in a Pareto chart showing the percentage ratio of certain parameter variations to performance. Figure 5* *shows a Pareto chart for the parameters or factors that contribute to the directional coupler's performance variations. The chart shows that variations in substrate thickness are more influential in the insertion loss performance than any other parameters or their combinations. For instance, 60 percent of the variations in performance stem from the effects of substrate thickness variations.

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The example lowpass filter in this article is a third-order elliptic design with a single inductor to minimize insertion loss. In fact, the primary cause of loss in the filter is the inductor resonance or quality factor (Q). All of the filter's components are realized as LTCC layers with embedded passive components.

Any design starts by establishing the performance requirements. This is followed by a feasibility study during which possible circuit topologies can be developed. For filters, designers often rely on filter synthesis tools for different topologies. Following this step, baseline circuit models are determined with appropriate ideal lumped-element component values. Since a designer must create an individual embedded passive component for LTCC that will replace the ideal lumped-element component, an EM simulation is needed to accurately model and simulate the embedded passive components.

Using the S-parameters generated by the EM simulation, a broadband lumped passive model with parasitic circuit elements can be extracted. The extraction process has numerical optimization routine by the aid of analytical expressions to compute initial values for the circuit model. This broadband lumped passive model helps perform statistical analysis including yield optimization faster than directly dealing with an EM simulator.

The extracted broadband model replaces the simple lumped-component model. Then, the new baseline circuit is optimized one component at a time with a circuit simulator to find the best component values for a set of performance conditions. This process is repeated until all of the formerly ideal components are replaced with embedded physical components. Once a design meets its set of performance requirements, it may be time for Monte-Carlo analysis in order to understand the statistical aspects of performance as a function of the manufacturing process.

The final layout for the example lowpass filter with extracted broadband models for the embedded capacitor and inductor is shown in Fig. 4. Figure 6 compares the EM simulation versus the extracted lumped-component model results for the filter's insertion loss, with good agreement between the lumped-component model and the EM model. The EM simulated responses are compared to measured data in Fig. 7, again with close agreement.

Statistical analysis (based on MonteCarlo analysis) is the process of varying a set of parameter values within a design, using specified probability distributions, to determine how performance will change as the parameters vary. Such analysis is often used to project yield, which is defined as the ratio of the number of items that meet or exceed performance expectations (specifications) to the total number of items that are analyzed during a statistical analysis. Yield is also the probability that a given design sample will pass the performance specifications. Because the total number of designs to be manufactured may be large or unknown, yield is usually estimated over a smaller number of samples or trials, a function known as yield estimation. As the number of trials becomes large, the yield estimate approaches the true design yield. Yield optimization minimizes the sensitivity of a design's performance to component variations. Yield optimization estimates yield and yield sensitivities and changes the circuit statistical parameter nominal values in order to simultaneously minimize statistical sensitivity and maximize circuit yield.

The first step in the statistical design flow is to collect the supplier's process variation data. With this data, statistical parameters for the extracted circuit models can be developed. Then, statistical analysis is applied to the design with associated statistical parameters. If the design meets the yield specification, the analysis process is ended and the manufacturing process can begin. Otherwise, yield optimization can be applied to extracted circuit models to modify the design for a given yield specification. The optimized component value for the extracted model must be realized as embedded passive physical components. Thereafter, a broadband circuit model is re-extracted from redesigned embedded passive physical components and statistical analysis is performed again until the yield specification is met. The LTCC design process can be depicted as a flow chart (Fig. 8).

A Monte-Carlo/yield analysis (Fig. 9)* *was performed for 6000 trials of the example lowpass filter circuit. The results (not shown) of statistical analysis of lowpass filter for insertion loss, second-harmonic rejection, and third-harmonic rejection indicate those cases where the design doesn't meet specifications, and reveal that the design delivers a 100-percent yield across 6000 trials.

Figure 10* *shows a total of five measured samples versus data from a single EM simulation. Parameters S11 and S21 in the graph are EM simulation results while the remaining curves show measured data. The data from the measured samples show good agreement with the simulations.

The two examples show that DFM offers a practical means of achieving first-pass design success even with a process like LTCC with inherent variations. Success depends on a well-thought-out design flow, especially with the use of broadband models. Applying DFM throughout the design process improves the odds of first-pass design success. Although the examples for DFM were based on LTCC, the design flow can be applied to other processes.

REFERENCE

- Jean-Pierre Cazenave, Jacky Cerisier,
*et al.*, "Improved RF Circuit Performance with an enhanced and expanded LTCC System," 14th European Microelectronics and Packaging Conference & Exhibition, Friedrichshafen, Germany, June 23-25, 2003.