# 电气工程代写|模拟电路代写analog circuit代考|ECE511

## 电气工程代写|模拟电路代写analog circuit代考|Matrix Equations

Matrix equations and their solutions were mentioned in Chap. 1. It is a key to many modern simulation methods, and a good knowledge on how one can set up and solve them is an essential piece of knowledge for the working engineer. This section will discuss the setup of such equations given an electronic circuit topology. Most students learn in elementary classes on circuit analysis how to analyze fairly simple circuit topologies, and this section will show how to systematize such methods when building simulator matrices. We will start with the fundamentals of passive elements and from a simple passive network build a full matrix equation. This should be familiar to most readers. We will then use that exercise to motivate a common way to set up simulation matrices. Much of the mathematical details and formal proofs we leave as references and outline in Chap. 7 for the interested reader to investigate further. Once such a methodology has been employed, we will use it to build a simple Python code that can be used to read in circuit netlists and set up matrix equations. Thereafter, we will use the built-in matrix solver in Python to solve the system of equations and compare to other SPICE implementations. The main motivation is to show that the methodology is fairly straightforward and dispels any mystery that might surround a circuit simulator. Naturally a fully professional simulator has many more optimization tricks, and details in the implementation can easily be differentiated between various products.

After showing a simple simulation setup with passive devices, we will then continue by defining active devices and show how they can be implemented in a similar fashion to the passive devices in building a full matrix.

## 电气工程代写|模拟电路代写analog circuit代考|Passive Element

A passive circuit element is a component that can only dissipate, absorb, or store energy in an electric or magnetic field. They do not need any form of electrical power to operate. The most obvious examples are resistors, capacitors, and inductors that we will be described in this section.

Let us first review the basic equation governing passive devices. Any device can be described by its current-voltage relationship:
$$i(t)=f\left(v(t), \frac{d v(t)}{d t}\right) \text { or } v(t)=f\left(i(t), \frac{d i(t)}{d t}\right)$$
An element is called linear if $f$ is linear. A device is called a resistor if the relationship is set by
$$v(t)=i(t) R(t)$$
where $R$ is the resistance we consider constant for now. Nonlinear resistors are an important circuit device, but we will not discuss them here. We also have inductors
$$v(t)=L(t) \frac{d i(t)}{d t}$$ and capacitors
$$i(t)=C(t) \frac{d v(t)}{d t}$$
The last two are often referred to as dynamic elements, and we assume for now the variables $L, C$ are independent of current and voltage. Lis called the inductance and $C$ the capacitance. The fact that there is such a thing as nonlinear capacitors, for instance, in CMOS devices can significantly complicate the solution and accuracy and convergence of a simulator, and we will discuss a few examples of this later in Chap. 5. A network consisting of resistors only is referred to as a resistive network, and one that contains capacitors and inductors is often called a dynamic network. If the network only has passive devices, it is called a linear network.

# 模拟电路代考

## 电气工程代写|模拟电路代写analog circuit代考|Passive Element

$$i(t)=f\left(v(t), \frac{d v(t)}{d t}\right) \text { or } v(t)=f\left(i(t), \frac{d i(t)}{d t}\right)$$

$$v(t)=i(t) R(t)$$

$$v(t)=L(t) \frac{d i(t)}{d t}$$

$$i(t)=C(t) \frac{d v(t)}{d t}$$

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