Steady state (electronics)

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In electronics, a steady state (S.S) occurs in a circuit or network when all transients have died away. It is an equilibrium condition that occurs as the effects of transients are no longer important. DC steady state is that state, if it exists, of a circuit described by a differential equation where the transient(s) have decayed away--typically the solution as time goes to infinity.

Steady state determination is an important topic today, because many of design specifications in a power electronic system are given in terms of the system’s steady-state characteristics. Periodic steady-state solution is also a prerequisite for smallsignal dynamic modeling. Steady-state analysis is therefore indispensable component of the design process. In some types of circuits, such as lightly damped systems this integration could extend over many periods making the computation costly. The same happens for the so-called "stiff" circuits, and for circuits were a high frequency carrier is modulated by a much slower signal (e.g. Cellphone mixers): such circuits, for example, require a computational-costly integration over a wide span of time, with much smaller integration step. Faster numerical methods than the classical brute force integration are available to find the steady state (periodic, quasiperiodic) of non-autonomous and autonomous circuits(such as, the period T is not known a priori). Such methods are often referred as fast steady state algorithms. Steady state algorithms can be sorted into:

TD Time domain algorithms (Time domain sensitivities,Shooting)
FD Frequency domain algorithms (Harmonic Balance)

Harmonic balance methods, are the best choice for most microwave circuits excited with sinusoidal signals (e.g. mixers, power amplifiers). Time domain methods can be further divided into:

One step methods (Time domain Sensitivities)
Iterative methods (Shooting methods).

One step methods require Derivatives to compute the S.S; whenever those are not readily available at hand or at the output of the simulator involved, iterative methods come into focus. SPICE, for example, doesn't output derivatives, and it's not readily suitable to be the simulator of choice to compute SS thru time domain sensitivities. There's the slight option to rebuild derivatives numerically, but iterative methods are often preferred.

Many commercial and non-commercial simulators embed a fast steady state algorithm: For example:

Books: