Exponentially Shaped Memory Delay Profile Memory Polynomial Model

The memory polynomial based shaped delay (MPSD) model was presented in [9]. In this model, each branch is assigned a different memory depth to include both thermal and electrical memory effects of the system. Hence, the delay is an exponential function rather than a uniform function in which equal delay steps is incorporated in all the branches. The mathematical representation of the MPSD model is given in Equation 5.15:

where the delay values are defined as:

In Equation 5.16, Д_{0} is the maximum delay, a is a coefficient describing the exponential decrease of the memory depth value, and avg is the average delay value that is related to the drain-source average channel length. The value the parameter avg of depends on the average power applied to the transistor.

Figure 5.5 Block diagram of the non-uniform memory polynomial model

The advantage of the MPSD model is that there is no need to keep adding branches as in MP model in order to increase the over-all memory depth of the model. In contrast, if a higher delay value is needed in the memory polynomial model with unit delay, extra delay branches are needed, resulting in much greater complexity. The MPSD model extraction requires the calculation of delay coefficients and the model coefficients extraction simultaneously. Experimental validation of this model demonstrated that as the value of M is changed from 0 to 3 the accuracy of the model is substantially enhanced [9].