## Linearity Improvement Techniques

Linearity Improvement Techniques for on-chip Amplifiers The Fantastic Four of Linearity Improvement Techniques Linearity is one of the most, if not THE most, important metric in circuit design. All analog circuits are inherently non-linear mainly because of non-linear behavior of transistors. Many linearity improvement techniques have been discovered or invented in literature yet we only […]

## Impedance Matching and Quality Factor

A Journey from Resonance to Impedance Matching Chp. 7: Quality Factor and Impedance Matching One Must Not Tell Lies. We have reached the finale of this saga. We have discussed how quality factor of a resonator led to signal gain and how did RF designers used that gain to boost impedance. Today we will look […]

## Quality Factor and Bandwidth

A Journey from Resonance to Impedance Matching Chp. 6: Quality Factor and Bandwidth Q-factor is Inverse of 3dB BW. Design or Coincidence? You have seen this $$ Q = frac{1}{FBW}$$ where FBW is fractional bandwidth (dfrac{Delta omega}{omega_o}) and (Delta omega) represents 3dB bandwidth around your resonance frequency (omega_o). We tried looking this up on internet […]

## Transient response of LC Tank

A Journey from Resonance to Impedance Matching Chp. 5: Quality Factor and LC Tank Behavior in Time Domain To develop further intuition in Q-factor and extend its application to matching and bandwidth, it is prudent to study time domain behavior of LC tank. We show how an LC tank starts up, how the voltage developed […]

## Quality Factor and Gain – Passives Can Amplify Too

A Journey from Resonance to Impedance Matching Chp. 3: Passive Amplification using Quality Factor The Story of Unsung Hero Passives have been such an underdog. All they ever did was taking your signal away from you. A resistor dissipated it away in heat. An inductor and a capacitor exchanged it back and forth. You always […]

## Quality Factor Formula – Inductor vs Resonator

A Journey from Resonance to Impedance Matching Chp. 2: Inductor vs Resonator Quality Factor The Ultimate Truth Teller The idea of quality factor originated from resonators and was ported to inductors later on. It was observed that a nice pure LC tank could not sustain oscillations because inductor degraded the quality of resonance. So instead […]

## Quality Factor – How it All Started

A Journey from Resonance to Impedance Matching Chp. 1: Origin of Q-Factor The Deadly Beginnings #1 When a Capacitor discharges through Resistor Let’s start from a capacitor C. Charge it to 1V. Now connect it to a resistor R. What will happen? Capacitor will lose charge exponentially. You would say, ok, my time constant (tau) […]

## Baseband Tones Intermodulation

Intermodulation of Two Baseband Tones This is part 3 in series of two tone intermodulation distortion. When we usually talk about two tone intermods, we mean it for two RF tones for which 2nd harmonics or even order terms fall far away, and we say we only care about IM3 and IM5 because they are close […]

## Intermodulation Distortion Analysis

Advance Intermodulation Distortion Analysis This is part 2 in series of two tone intermodulation distortion analysis. Whether you are optimizing linearity or debugging it, you want to understand what are different distortion products, how do they get generated and what are they made of. For example, IM3 is made of odd order non-linearities: 3rd order has […]

## RFIC Transformer Model

Integrated Transformer Models We decided to write this article because there are only so many different models of a transformer that exist. Analog IC designers, RFIC designers and mm-wave IC designers – they all understand transformers a little differently. Enough is enough. We are putting together a list of different models (with derivations of course) […]