Understanding Transient Modeling

The Laplace transform method also provides an easy way of relating a circuit's behavior in time and frequency-domains, facilitating simultaneous work in those domains.

The performance of the algorithm Star-Hspice uses for Laplace and pole/zero transient modeling is better than the performance of the Fast Fourier Transform (FFT) algorithm. Laplace and pole/zero transient modeling is invoked by using a LAPLACE or POLE function call in a source element statement.

Laplace transfer functions are especially useful in top-down system design, using ideal transfer functions instead of detailed circuit designs. Star-Hspice also allows you to mix Laplace transfer functions with transistors and passive components. Using this capability, a system may be modeled as the sum of the contributing ideal transfer functions, which can be progressively replaced by detailed circuit models as they become available. Laplace transfer functions are also conveniently used in control systems and behavioral models containing nonlinear elements.

Using Laplace transforms can reduce the long simulation times (as well as design time) of large interconnect systems, such as clock distribution networks, for which you can use methods such as asymptotic waveform evaluation (AWE) to create a Laplace transfer function model. The AWE model can represent the large circuit with just a few poles. You can input these poles through a Laplace transform model to closely approximate the delay and overshoot characteristics of many networks in a fraction of the original simulation time.

Pole/zero analysis is important in determining the stability of the design. The POLE function in Star-Hspice is useful when the poles and zeros of the circuit are provided, or they can be derived from the transfer function. (You can use the Star-Hspice .PZ statement to find poles and zeros. See .PZ (Pole/Zero) Statement for information about the .PZ statement).

Frequency response, an important analog circuit property, is normally specified as a ratio of two complex polynomials (functions of complex frequencies) with positive real coefficients. Frequency response can be given in the form of the locations of poles and zeros or can be in the form of a frequency table.

Complex circuits are usually designed by interconnecting smaller functional blocks of known frequency response, either in pole/zero or frequency table form. For example, you can design a band-reject filter by interconnecting a low-pass filter, a high-pass filter, and an adder. The designer should study the function of the complex circuit in terms of its component blocks before designing the actual circuit. After testing the functionality of the component blocks, they can be used as a reference in using optimization techniques to determine the complex element's value.