From Robert A. Wannamaker’s Paper 1. Introduction A. The Classical Model of Quantization For Mid-tread quantization [Q(w) = \Delta \lfloor \frac{w}{\Delta} + \frac{1}{2} \rfloor] where $\lfloo...
Fourier Analysis 001 Introduction
From book Fourier Analysis Introduction Suppose \(f\) is a Riemann integrable function from \(0\) to \(2\pi\). [\int_{0}^{2\pi} f(t)dt \quad \text{exists}] Then we define the Fourier coefficien...
Paper A -58dBc-Worst-Fractional-Spur and -234dB-FoM, 5.5GHz Ring-DCO-Based Fractional-N DPLL Using a Time-Invariant-Probability Modulator, Generating a Nonlinearity-Robust DTC-Control Word
ISSCC 2020 17.3 From Jaehyouk Choi’s Paper The concept of this work is from Micheal Peter Kennedy’s Paper that showed that if the expected value of an arbitrary analog or digial signal \(X\), \(E...
Paper Design of Crystal-Oscillator Frequency Quadrupler for Low-Jitter Clock Multipliers
From Karim M. Megawer’s Paper integer-N 54-MHz-4.752-GHz RO-based ILCM 366fs 6.5-mW. Introduction Assuming reference clock is generated by a low-noise XO, the in-band noise is typica...
Paper Clock Multiplication Techniques Using Digitial Multiplying Delay-Locked-Loops
From Amr Elshazly’s Paper Introduction A classical digital PLL composed of TDC, digital loop filter (DLF) and DCO (possibly DAC followed by VCO). Digital Multiplying DLL is different from classi...
Applied Electromagnetics For Engineers 01
Index Lecture 01 Lecture 02 Circuit Model of Transmission Line Lecture 03 Solution of Wave Equation Lecture 04 Reflection Coefficient and Transmission Coefficient Lecture 05 Circuit Par...
High-Frequency Design Techniques 03
Quality Factors The Q of an inductor or capacitor is the ratio of its reactance to its resistance. Example 01 A inductor and a resistor in series [Q = \frac{\omega L}{R}] Example 02 A capacit...
Phase Noise in Signal 01
Chapter 0 Signal’s Spectrum and Power consider a periodic signal \(x(t)\) with period \(T_0\) [\begin{align} a_n &= \frac{1}{T_0} \int_{T_0} x(t) e^{-jn\omega_{0}t}dt x(t) &= \sum_{k=-\in...
Trigonometry
Remember [\begin{align} \sin(\alpha + \beta) &= \sin\alpha\cos\beta + \cos\alpha\sin\beta \sin(\alpha - \beta) &= \sin\alpha \cos\beta - \cos\alpha \sin \beta \cos(\alpha + \be...
An Introduction to Cyclostationary Noise
from resources paper introduction to cyclostationary noise. Introduction This paper introduces the noise analysis for mixers, oscillators, samplers, and logic gates. Ensemble Average Noise free...