A New Method for Causality Enforcement of DRAM Package Models Using Discrete Hilbert Transforms
OTT Case 13-008| Patent Pending
One of the main steps in the process of designing and fabricating high speed, high performance and complex microelectronic systems is to create an accurate and reliable electric package macromodel that truly represents these digital systems. These macromodels are used in electronic circuit simulators to check the signal and power integrity of circuit designs, predict circuit behavior in the system level testing step and facilitate modeling and co-simulation of signal distribution network and power distribution network. An important step in the process of creating these macromodels is to ensure the stability, passivity and causality of the data that will be used to create them and system causality verifying is essential for extracting reliable and correct equivalent macromodels.
Verifying causality using frequency domain approach is a preferred method since the data are usually given in the frequency domain but this method has its drawbacks and potential errors. These errors arise from the fact that the data set used in this process is a set of system parameter values that have been measured or simulated over a set of discrete frequency points that covers a band-limited frequency range. In order to deal with approximation, truncation, and discretization errors associated with the conventional procedures, a new method for causality verification and enforcement was developed by researchers in the University of Idaho.
The new method is based on verifying and enforcing causality by applying the Discrete Hilbert Transforms integration pair (DHT) on a periodically extended version of the real or imaginary parts of the system parameter. The new method utilizes Fast Fourier Transform (FFT) and the Inverse Fast Fourier Transform (IFFT) to compute DHT after periodically extending the system parameter measured or simulated set of points using for example 3rd or 5th order periodic polynomial extension that employ Richardson Extrapolation to calculate the 1st and 2nd derivatives at the end points with different error accuracy order or using cubic and quantic periodic spline of the raw data as well as B-splines.
The new work is capable of verifying and enforcing causality of the measured or simulated set of points that represent system parameter which facilitate creating electric package macromodels.