From Dr. Chun-Yao Wang’ Lecture Interesting Formula [\dfrac{1-x^N}{1-x} = 1 + x + x^2 + \dots + x^{N-1}] gong bi ci fang jian yi, chu yi gong bi jian yi [\sum_{n=0}^{N-1} e^{jk(2\pi/N)n} = 0, \...
Advanced Differential Equations 003
From Prof. J. Nathan Kutz’ Lecture 003 Linear Operators And Thier Adjoints Fredholm Alternative Theorem Given a matrix \(\mathbf{A} \in \mathbb{C}^{m\times n}\), then the vector \(\mathbf{Ax}\),...
Advanced Differential Equations 002
From Prof. J. Nathan Kutz’ Lecture 002
Advanced Differential Equations 001
From Prof. J. Nathan Kutz’ Lecture 001 Phase-Plane Analysis For Nonlinear Dynamics We begin by reviewing linear system [\mathbf{x}’=\mathbf{Ax}] where [\mathbf{x} \in \mathbb{R}^{2}, \mathbf{A...
Computer Aided Circuit Analysis 002
In this post, the detail of linear DC nodal analysis is discussed. The material is from Book: Electronic Circuit and System Simulation Methods. Most of the content are from chapter 2 in the book. ...
Computer Aided Circuit Analysis 001
In this post, the principle of DC analysis, AC analysis and transient analysis are explained. We will focus on the minimum examples, such that the algorithms can be simplified as much as possible. ...
5T OTA Design
Assume we need to design an amplifier with the following specification. Load capacitance \(C_L\). Gain-bandwidth product \(f_u\). Choose The Topology Assume we choose the simple 5 transist...
Delta Sigma Modulator
Reference slides_an_introduction_to_digital_delta_sigma_modulators paper a multiple modulator fractional divider paper A Calibration-Free Fractional-N Analog PLL With Negligible DSM Quantization...
Calculus 006
From Zhenyu Qi’ Lecture 006 Seperated Sequences Given a sequence \(a_n (n \in \mathbb{N})\), we can seperate all terms into two sequences: [a_{n_1}, a_{n_2}, \dots \text{ and } a_{n_1’}, a_{n_2’...
Calculus 005
From Zhenyu Qi’ Lecture 005 Series Convergent Criterion [\sum_{n} a_n \text{ converges} \iff s_{n} (n \in \mathbb{N}) \text{ converges } \iff s_n (n \in \mathbb{N}) \text{ is Cauchy}] [\forall \...