# analog synthesis

Even a digital-radio system requires analog elements, however. On the transmitter side, DACs convert a digitally modulated signal to an analog format. This conversion takes place before the signal can be further upconverted in frequency and then amplified and transmitted through the antenna. On the receiver side, ADCs convert the analog signal that’s coming from an antenna through a low-noise amplifier (LNA) and mixer (the IF signal). Clearly, the dataconverters’ performance is key to obtaining the final bandwidth, sensitivity, and power specifications of the overall system.

To achieve the best system performance, dataconverters must be carefully tailored to the application at hand. Sometimes the sampling rate is key, while other times it’s the dynamic range. Low power consumption also may become the top priority. Such varying requirements make it difficult to use one converter design for many different applications. Similarly, it’s often impractical or suboptimal to use a design from an intellectual-property (IP) library.

To mitigate these concerns, consider the use of analog synthesis as an option. For a dataconverter, the user inputs high-level specifications like required sample rate, dynamic range, and linearity. The system then produces a circuit that automatically defines all transistor sizes, bias currents, and other design variables.

With analog synthesis, a synthesized design can be truly optimized for an application. This approach also can reduce design time by orders of magnitude. It may take days or even hours to run the synthesis tool, as opposed to the months that are normally required to do a design by hand.

Several approaches have been proposed for analog synthesis. They include:

Simulation-based methods: These methods bear a lot of similarity to hand design. To modify device sizes and improve circuit performance, they utilize circuit-level simulations. An automated process is used to run simulations, evaluate the circuit performance, and refine the design variables.

Equation-based methods: With this approach, the relationship between circuit performance and design parameters is described using mathematical expressions. The circuit design is then cast as an optimization problem. That problem is solved using a numerical algorithm. The “solution” finds the one particular combination of device parameters that result in the best circuit performance (like the lowest possible power). At the same time, it satisfies all of the constraints that are defined by the user specifications.

Note that the simulation-based methods run a circuit simulator. They may require very long simulation times. These methods tend to be appropriate for smaller circuits. Often, they require an experienced analog designer to run them. Typically, they’re design “tools” rather than complete synthesis systems.

Recently, the equation-based methods have found increasing acceptance. They’re usually more automated and can handle larger systems. The use of efficient numerical solvers can be credited as their main breakthrough. Such solvers enable the equation-based synthesis of larger systems, in which the design space can consist of hundreds or thousands of variables.

One particularly powerful approach relies on geometric programming. A geometric program (GP) is an optimization problem that involves a special class of nonlinear functions, which are called monomials and polynomials. Most circuit equations can be written in GP form fairly easily. The problem can then be solved numerically in an extremely efficient manner. The notation lends itself to hierarchical expansion, which is well suited to the hierarchical approach that’s commonly used for analog design.

GP-solution techniques ensure that if there’s an optimum solution, it will be found. Furthermore, that solution is guaranteed to be globally optimal (i.e., no better design is possible). If no solution exists, the software will say so.

New synthesis approaches go one step further by automatically generating the circuit layout. The combination of schematic and layout synthesis results in truly one-step, analog-synthesis engines “from spec to GDSII.”

The layout problem commonly consists of placing and routing the various components. Aside from using graph-theoretic algorithms, this step serves as somewhat of an optimization problem. Area and interconnect parasitics need to be minimized while accounting for special constraints, such as symmetry and matching.

Modern, highly digital wireless systems require the careful optimization of dataconverters. This very time-consuming process usually demands specialized analog designers. Meanwhile, relying solely on analog libraries results in suboptimal systems. This dilemma can be addressed with analog synthesis. While simulation-based approaches seem most useful for smaller subsystems, equation-based synthesis lends itself to larger analog systems. The latter approach is able to handle complexity through efficient optimization techniques.

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