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   Linear Electrical Discrete Time Simulation with Convolution       


Linear Electrical Discrete Time Simulation with Convolution

During signal analysis, all electrical components and sub-designs are converted to time domain behavioral models (i.e., unidirectional models). This time domain model is extracted from the corresponding frequency response evaluated during the course of the simulation. For example, the linear electrical sub-design for the PLL example project shown previously is identified on the schematics in Figure 4.

The extracted time domain behavioral models will typically contain the transient, steady state, and noise responses of the electrical sub-design (all in accordance with the frequency-domain signal and noise response of the electrical sub-design as well as impedance mismatches within the sub-design). Therefore, the processing of modulated signals through electrical components/sub-designs will include the transient, steady state, group delay, and noise effects.

There are two techniques available for discrete time simulation of linear electrical components and sub-designs: Convolution and Impulse Invariance. Convolution analysis, which will be discussed in detail in this section, is a general technique for simulating mixed mode systems. Impulse Invariance analysis, discussed in the following section, is at least an order of magnitude faster than convolution, but it is limited to solving systems that can be represented with a finite number of poles.

Consider a multi-port linear electrical sub-design with the functional component connections shown in Figure 5 below. Note that the assumptions discussed above regarding a functional-electrical connection are reflected on the figure. In addition, assume that the system has N input ports and M output ports as shown below.

 

The topics for this section include:

Step 1: Evaluating the Frequency and Noise Responses

Step 2: Extracting the Discrete Time Impulse and Noise Responses

Step 3: Computing the total (signal plus noise) discrete time output voltages of an electrical sub-design

 




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