In addition to the above elements mentioned, a mixed SC/D network may contain comparators and logic gates such as AND, OR, NOT, NAND, NOR, XOR, and XNOR. The ON-OFF switches in a mixed SC/D network may be controlled not only by periodic waveforms but also by nonperiodic waveforms from the output of comparators and logic gates.
The other time-domain analysis applies to mixed SC/D networks as well as linear SCN's. It computes the transient response of networks without computing the steady-state values as initial conditions. A set of the initial condition of analog and digital nodes at may be specified by user.
Frequency-domain group delay and sensitivity analyses are also provided.
Operational amplifiers with limited frequency response may also be simulated. The frequency response may be modeled with an RC network and then simulated with the R's replaced by equivalent SC networks.
Clock feedthrough from switch parasitics may be simulated in both the time and the frequency domains. The frequency-domain simulation of this effect is particularly efficient using the dc steady-state analysis capability of the program which does not require the direct computation of the Fourier components of any clock waveform.
To incorporate these higher order effects in a simulation, the subcircuit facility of the program may be used to advantage. A circuit can be simulated with, say, ideal elements at a high level of abstraction, or complex subcircuits including parasitics and nonidealities can be substituted for ideal elements to carry the simulation to a lower level. However, it must be warned that the simulation of these nonideal effects is computationally time consuming due to the need for higher switching rate to model the nonideal effects.
Internally, SWITCAP2 consists of several different algorithms depending on the type of desired analysis. For time- and frequency-domain analyses (excluding group delay and sensitivity analyses) of linear SCN's, SWITCAP2 uses an algorithm based on the formulation published in [1, 2, 3, 4, 5, 6, 7, 8, 9]. This formulation, which was incorporated in the original SWITCAP [6, 7], uses a set of charge variables as the network variables for computation. The number of charge variables is typically very small. For example, an nth order filter implemented in a leap-frog configuration wherein the number of integrators is the same as the order would have n charge variables per switching interval. As a result of the small number of network variables, the iterative steps in the computation are very efficient. The most memory-intensive portion of the computation is in the preprocessing stage during which the network matrices to be used in the subsequent iterations are computed and stored. Because of this memory requirement, a dynamic memory allocation scheme has been implemented. With this allocation scheme, the maximum complexity (number of elements times the number of unique switching intervals) of an SCN that can be simulated is limited solely by the user's computer memory size.
The analytical expressions that allow exact analyses of group delay and sensitivity for many-phase linear SCN's are derived from the above mentioned state charge variable formulation [10, 11]. The analytical expressions not only lead to efficient algorithms for computing the group delay and sensitivity but also retain efficiencies similar to those that were realized for simple time- and frequency-domain analyses using the state charge formulation.
The transient analysis of mixed SC/D networks is formulated in such a way that separate algorithms are used for analog, digital, and interface subgroups to take full advantage of their own properties. Detailed technical discussions of the algorithms and their applications can be found in [11, 12, 13].