Current Mode Logic Active Inductor Load

Active inductor load can be designed by applying a negative voltage feedback from drain of an active current load to the gate of the active load. The feedback has a time constant that depends on the size of gate resistor and Cgs of the active load. Overall, feedback makes the load to behave like an inductor where $L=\frac{R_g C_{gs}}{g_m}$. For more details refer to page 68 of this Master's thesis. The following image is also captured from the thesis.

Spectre Simulation (Fundamental)

"Simulation of Analog and Mixed-Signal Circuits by Ken Kundert" slides are a quick review of the book, "The Designer's Guide to SPICE and Spectre". The book goes through the details of spice simulation and explains the trad-offs.

CMOS chopper amplifier to reduce 1/f noise

The paper reviews CMOS chopper amplifier theory and actual circuit. The theory is simple: modulate the input signal to F_chopper where 1/f noise is not significant, amplify the modulated signal. and finally demodulate and reconstruct low pass signal at the output. Also, found this work interesting: using CMOS devices in lateral bipolar mode to decrease 1/f noise (see figure 14).

Noise Sources in Bulk CMOS

A nice summary on CMOS noise sources(flicker, shot, thermal).

Voltage Mode R-2R DAC: Theory of Operation

This document is about "how voltage mode R-2R DAC does work?". A major goal is to extract the math behind R-2R DAC intuitive structure.

Random DC Offset of Comparators

These slides review Flash ADC circuits. The source of random DC offset is the random fabrication mismatch. The reference paper, "Matching Properties of CMOS Transistors" (1989) divides the mismatch to two models: local and global.

Charge Injection in CMOS switches

"Charge Injection in Analog CMOS Switches" (1987) presents a model for charge injection. It also proposes some methods to alleviate charge injection by design.

Serial Charge Redistribution DAC

The slides introduce ABC of charge redistribution DAC.

Fractional Frequency Divider by Delta-Sigma Modulator

"Delta-sigma modulation in fractional-N frequency synthesis" (1993) compares pulse swallowing, phase interpolation, and Wheatley random jittering methods with Delta-Sigma jittering technique.

CMOS Capacitance and Delay

handy notes on CMOS delay. Analyse the capacitance and connect it to delay of circuits (driver load and total load capacitance).

PLL close loop bandwidth

The slides cover PLL analysis from a system point of view.

A tutorial on Phase Locked Loops

This tutorial is recommended by a senior member of my team: "Design of Monolithic Phase Locked Loops and Clock Recovery Circuits: A Tutorial".

Are uncorrelated normal random variables necessarily independent?

Professor Rosenthal nicely explained this questions by giving two clear examples. The golden quote is "What is true is that if the random variable pair (X,Y) follows the bivariate normal distribution, and Cov(X,Y) = 0, then X and Y must be independent. But what is not true is that if each of X and Y is normally distributed, and Cov(X,Y) = 0, then X and Y must be independent".

An Overview of Boundary Scan Test Methodology

An abstract review of boundary scan test methodology is available here. Pros and cons are introduced as below:

Benefits:

• Reusable Test Vectors
• Reduced Test Time
• Reduced Time to Market
• Faster ROI
• Reduced Design Iterations
• Efficient and Economical Production
• Functional Test

Challenges:

• Area Overhead / Additional Circuits
• Additional Pins
• Higher Design Effort
• Performance Degradation
• Power Consumption

Digital Signatures Verification

Heartbleed bug and stories around it motivated me to review the SSL security. Here is a good review of Digital Signature. It provides graphical flow charts of the procedure that eases the review ....

Multivariate Mutual Information

Here is a useful review on "Multivariate Mutual Information". I'm working on the negative interaction in a tri-variate problem. The definition of semi-independent distribution caught my attraction. From [Han'80: Multiple Mutual Informations and Multiple Interactions in Frequency Data], a tri-variate distribution (U,V,Y) is semi-independent if

Pr{U V Y} = Pr{U} Pr{V Y} + Pr{V} Pr{U Y} + Pr{Y} P r{U V} − 2 Pr{U} Pr{V} Pr{Y}

DFT and windowing

Recently, I was working on a feasibility study of measuring/detecting IM3s of an ADC output by capturing only 512 samples, where the sampling rate is about 300MS/sec. During this research, I came across "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform", by F. Harris (1978). This paper is a must-read for signal processing folks.
The concepts such as spectral resolution, the window processing loss (gain), 6-dB BW of the window, etc. need to be considered in any DFT design/analysis. As the figure below, with 512 samples, the signal intermods are not detectable if we do not use a proper window.

 

Gilbert Mixer: Secod order order (IM2/HD2) nonlinearities

In one of our tests, we noticed a significant HD2 at the output of a differential passive Gilbert cell mixer (the mixer performance was supposed to be at least 20dB better than what we measured in the lab). I was looking for a systematic methodology to link this problem to load mismatches on P and N paths. In my research, I came across this paper [this webpage includes better quality images] that categorizes second order nonlinearities of a Gilbert cell. My take on this work is Eq. (16), where the IM2 output voltage is extracted by i_im2_diff (differential current IM2) and i_im2_cm (common mode current IM2). The equation express the relation between the overall IM2 and internally+externally generated IM2. In other words, if the output load is matched (load of path N and P are equal in terms of phase and amplitude) then i_im2_cm's impact will be canceled by teh balance between the loads (P&N) , i.e. delta_Rload*i_im2_cm becomes almost 0. On the other hand, i_im2_diff (generated by internal transconductance/timing mismatches) will be signified by sum_Rload (Rload_P+R_load_N). In my case, I guessed that the strong HD2 would have been generated by P&N load mismatched; however, later we found out that the input signal to the mixer was imbalance!!!

LNA linearization methods

This presentation reviews the analog techniques to linearize LNAs.

On oversampling of quantization noise

This is about Eq.(3) of [Candy'92]. Basically, I keep asking myself why the sampled quantized noise spectral density is given by


where the quantization noise is a white process with the following RMS value:


[Candy'92] explains that due to sampling, the noise power folds into the frequency band

However, I have to find a self-convincing explanation.

Here is how I understand the impact of oversampling on quantization noise:

1- we should consider a LPF with the bandwidth of

2- the sampling/quantization system is as follows [x denotes the instantaneous quantization noise]:

x--|sampler|--|LPF: h[n]|--y



3- Auto-covariance of LPF output is given by:


4- for a ideal LPF with f_0 = f_s/2, we have



5- Consequently the density of the quantization noise, which spreads over

is given by