电气工程代写|模拟电路代写analog circuit代考|AC Simulation

Traditionally, AC simulations are single-tone frequency analyses where a certain stimulus frequency is varied and the systems response is calculated. The circuit for these simulations is linear. If the underlying circuitry contains nonlinear elements, these have been simply linearized around some bias point. This section will look at such a simulation using the circuit from the previous section as a specific example. We will also describe how the analysis from this circuit suggests how to set up the matrix from an arbitrary circuit topology with some surprisingly simple rules. We will describe these rules for passive elements and also how they work for various sources (voltage/current) and multi-port controlled sources. We will then implement these rules in a Python code script and run it for a couple of circuit examples. The reader is then encouraged to explore more using the exercises at the end of this chapter.

If the system is linear and driven by a single frequency, $\sim e^{j \omega t}$, we can replace the derivatives $\frac{d e^{j \omega t}}{d t}=j \omega e^{j \omega t}$ with a product:j $\omega$ (the exponential term is the same everywhere and can be eliminated). We then have the three basic passive elements:
$$v(\omega)=i(\omega) R \quad v(\omega)=j \omega L i(\omega) \quad i(\omega)=j \omega C v(\omega)$$
Consider again the simple network in Fig. 4.1.
We can exchange the derivative operator in Eq. $4.8$ and end up with
$$\left(\begin{array}{cccccc} 0 & 0 & 1 & -1 & -1 & 0 \ 0 & 0 & 0 & 1 & 1 & -1 \ 1 & 0 & j \omega L & 0 & 0 & 0 \ -1 & 1 & 0 & R_1 & 0 & 0 \ -j \omega C & j \omega C & 0 & 0 & 1 & 0 \ 0 & -1 & 0 & 0 & 0 & R_2 \end{array}\right)\left(\begin{array}{c} v_1 \ v_2 \ i_1 \ i_2 \ i_3 \ i_4 \end{array}\right)=\left(\begin{array}{c} 0 \ 0 \ v_{\text {in }} \ 0 \ 0 \ 0 \end{array}\right)$$
Before we get into the solution mode, let us take a step back and rewrite this matrix slightly. We see in Eq. $4.10$ terms that look like an impedance, for example, $j \omega L$ or an admittance, $j \omega C$. This can in fact be shown to be quite general $[4,5,10]$, and one can write the branch equations in either an impedance or admittance matrix form. To highlight this further, we can write the matrix in Eq.

电气工程代写|模拟电路代写analog circuit代考|Active Elements

An active circuit element is an electronic component that supplies energy to a circuit. This includes voltage and current sources of various flavors and of course transistors. In this book, we will model transistors using voltage sources, so we will limit the discussion of active elements to voltage and current sources.
An element is called active if one of the following conditions is met:

1. The voltage or current is a constant or a function of time, $v(t), i(t)=f(t)$. It is then called an independent voltage or current source.
2. The voltage or current is a function of the current through an other network element or a function of the voltage across an other network element. It is then called a dependent voltage or current source.

There are two varieties of voltage-controlled devices, namely, voltage-controlled voltage source (VCVS) and voltage-controlled current source (VCCS). Likewise for current-controlled devices, we have current-controlled voltage source (CCVS) and current-controlled current source (CCCS). In this section, we will go through both the independent and dependent sources.

模拟电路代考

电气工程代写|模拟电路代写analog circuit代考|AC Simulation

$$v(\omega)=i(\omega) R \quad v(\omega)=j \omega L i(\omega) \quad i(\omega)=j \omega C v(\omega)$$

电气工程代写|模拟电路代写analog circuit代考|Active Elements

1. 电压或电流是常数或时间的函数，在(吨),一世(吨)=F(吨). 然后它被称为独立的电压或电流源。
2. 电压或电流是通过其他网络元件的电流的函数或通过其他网络元件的电压的函数。然后将其称为相关电压或电流源。

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