Shulou(Shulou.com)06/01 Report--

In this issue, the editor will bring you an example analysis of DC Analysis and Newton-Raphson iterative method. The article is rich in content and analyzed and described from a professional point of view. I hope you can get something after reading this article.

The following figure is an example

The solution or working point of the circuit is the intersection of the load line and the diode IV curve.

Where the load line current equation is

The Diode current equation is

At the work point

Because diode's equation is a nonlinear equation, it is almost impossible to calculate it directly.

The Newton-Raphson iterative algorithm can be used to solve the above nonlinear equations.

Its principle is roughly shown in the following figure.

First of all, start with Vd1 (First-guess), and linearize the Diode I-murv curve at Vd1.

Among them

Geq1 is the slope at Vd1.

By rearranging Idlin1's equation, we can get

Among them

Idlin1 is the expression of the red line shown above. When it intersects with the load line, it can be found that the intersection point is not close enough to the working point. However, the value of Vd2 can be obtained, and then the same linearization operation as Vd1 is carried out on the Diode IV curve at Vd2, that is, the blue straight line shown above is obtained. The intersection of the blue line and the load line is closer to the working point than the previous intersection, but it is not a working point. The Diode IV curve can be linearized again at the second intersection (i.e. Vd3), and the third intersection is expected to be closer to the working point than the second intersection.

With the increase of the number of iterations, the intersection of the linearized line and the load line will be closer and closer to the Vd of the working point. If it is not controlled, the iterative process will go on forever. That is, the iterative process will not converge.

General simulators define tolerance options such as reltol/abstol to control the iterative process.

Simulators such as SPECTRE series will judge the convergence of Newton iteration according to the following three criteria

Different types of simulation will be different. And there are usually more judgment conditions, here are only examples.

The first criterion is to judge the Sigma-I in the second picture.

The second criterion is to judge the delta-V in the picture in Chapter 2.

The third criterion is used to determine whether the circuit node current satisfies KCL's law.

If the above three criteria are true, then convergence.

As a result, it can be known that the smaller the retol/abstol value is, the more iterations are, and the longer the simulation time is, the more accurate the result is and the higher the possibility of non-convergence is. On the contrary, the shorter the simulation time is, the less accurate the result may be and the greater the possibility of convergence is.

From the above iterative process, we can see that the selection of the initial value Vd1 is very critical, and the simulator will select it automatically. If the selection is not good, it will be difficult to converge or not to converge. For example, in the actual multi-corner simulation, we will encounter some cases of corner non-convergence and some corner convergence, in which the unconvergent points may not be selected well, then we can try to use options such as readns to call the solution of the converged point as the initial value to simulate the current non-convergent corner.

However, in most cases, these values do not need to be changed when using SPECTRE series simulator.

Generally speaking, it is only necessary to select conservative/moderate/liberal among each Analysis type errpreset according to the circuit type and the expected results. That is, high precision / medium precision / low precision.

In the process of practical circuit simulation, it is difficult to converge only by Newton Method, for example, when an equation is non-differentiable, the iteration cannot be carried out.

Simulations like DC also require Continuation Method, that is, homotopy, which you will see in spectre.out.

Homotopy has six values, namely none/gmin/source/dptran/ptran/all. The default is gmin, if gmin stepping fails, source is used, and if it is still fails, dptran is used until ptran.

If it is set to all, it is simulated from Newton- > gmin- > source- > dptran- > ptran to convergence.

Gmin Stepping means that all nonlinear devices are connected in parallel with a 1Ohm resistor at the beginning of the simulation to linearize the circuit, making it easier for the simulator to calculate the voltage. If it does not converge, gmin will decrease until 1mOhm. If it does not converge, then gmin Stepping fails. If convergent, the simulator increases the resistance one by one and uses the result of the previous Stepping as the initial value of the current Stepping. The number of iterations of each Stepping is adaptive and automatically adjusted according to the current inserted resistance and iteration limit. Each time stepping converges, the spectre simulator will stepping all the way to the value set by gmin (default 1e-12).

Therefore, in some cases, reducing gmin can improve the accuracy of DC simulation. Increasing gmin makes it easier for DC to converge. However, in most cases, changes are not recommended.

Source Stepping is according to the stage "powering up" circuit. All voltage sources are multiplied by a constant, and then the constant decreases gradually until it converges.

PseudoTransient Ramping, namely dptran and ptran, this method gives each non-linear device a 1 Farad capacitor in parallel, and then pseudo-time is swept to infinity until convergence. If the circuit oscillates because of the added capacitance, the method fails.

On the other hand, the current simulators such as SPECTRE APS/X are basically automatic in setting the above content. In most cases, you only need to select conservative/moderate/liberal or CX/AX/MX/LX/VX to set the number of multithreads or automatically multithreading.

The above is the example analysis of DC Analysis and Newton-Raphson iterative method shared by Xiaobian. If you happen to have similar doubts, you might as well refer to the above analysis to understand. If you want to know more about it, you are welcome to follow the industry information channel.

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