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# What is discrete time domain simulation of switching power s

What is discrete time domain simulation of switching power supply? This problem sounds difficult to understand. In essence, the switching power supply is a discrete nonlinear system. If the piecewise linear equations of the nonlinear system listed in the state space are solved by computer, the analysis and research can be performed more accurately. This is the so-called discrete time domain simulation method.

The discrete time domain method can simulate multi-loop control systems to achieve different control laws, and to quickly, accurately, and efficiently study circuit changes and / or component parameter changes that affect the transient characteristics of the system. It can be used to simulate the steady-state process (such as voltage and current ripple, etc.), large signal response (such as startup process, etc.) and small signal response (such as calculating the characteristic value of the switching power supply, stability analysis, and verification of the design of the control circuit Wait).
Discrete time-domain simulation method also has shortcomings, that is, this simulation method can not get the mathematical equation in analytical form, and it must rely entirely on the numerical calculation and analysis of the computer, and the physical concept is not clear. When applying discrete time domain simulation, an equivalent nonlinear iterative time domain model should be established first. The basic method is:
List the piecewise linear state equation of the system, and then find the state transition law, and derive the nonlinear difference equation from this. The Newton iteration method can be used to find the precise equilibrium point. When solving nonlinear difference equations, it is necessary to determine the switching time of the switch, that is, the boundary conditions of each piecewise linear network. The time-domain solution of the nonlinear difference equation is the large signal transient response.
When performing small-signal analysis, the switching power supply must be linearized near the equilibrium point to obtain a linear difference equation. The z-transform can be used to analyze small-signal characteristics such as stability and transient response in the Z domain. Existing simulation algorithms, the speed and accuracy are a big contradiction, the conventional fixed-step integration simulation method is difficult to use in switching power supplies;
There are two main reasons:
1. The amount of calculation is large. For example, in order to ensure sufficient accuracy, it is often required to solve hundreds of differential equations to thousands of differential equations in one switching cycle, and the number of multiplication operations is very large;
2. The precision is low, and the limited integration step will cause a large calculation error (cutoff error) at the switching time of the switching power supply. The occurrence of this error has a great influence on the transient process of the switching power supply. If the step size is too small, not only the calculation time is long, but during the state transition process, the numerical calculation will also cause a large accumulation error.