User:Jakub.duchon

Low Noise Amplifier Design
Tutorial - resources :

May - 2009

LNA for CDMA

Circuit Examples LNAa - different frequency ranges :

BFP740F

June - 2009

Modelithics

Infineon Trasistors for LNA

Infineon BFP620 app Note 60

LNA Design Queen's Wiki

IEEE CMOS LNA Design

A Scalable High-Frequency Noise Model for Bipolar Transistors with Application to Optimal Transistor Sizing for Low-Noise Amplifier Design

A new calculation approach of transistor noise parameters as afunction of gatewidth and bias current

ADS Tutorial Files - ECE Department University of California Santa Barbara

Tutorial 

Neste 

Thesis 

AT 41533 + biasing 

Criteria for the Evaluation of Unconditional Stability of Microwave Linear Two-Ports: A Critical Review and New Proof 

Modified determinations of stability criteria for accurate designing the linear two-port amplifiers 

A New Criterion for Linear 2-Port Stability Using a Single Geometrically Derived Parameter 

White Paper - Overview of the 3GPP Long Term Evolution Physical Layer 

Specification
The amplifier is usually part of a system which is composed of many blocks. Such a system can be connected in a cascade and when connecting many blocks together behavior of each block must be described. This description is called specification. The specification is set of parameters specifying behavior of particular block. Parameter in specification care for example an operating point, input and output parameters, extreme working conditions, supply. Specification is a language how engineers communicate between each other. Specification sets a course of the product development.

All parameters should be satisfied within the whole bandwidth.

Transistor Selection
Transistor selection affects the whole process of design. This part is very important and special attention has to be paid. Transistor selection can make whole design procedure succeed or fail. The question is from where and how to start finding the best fitting transistor to the specification. Well, it pretty much depends on the specification. Good start can be making a set of priorities and start from the most demanding parameters. It may be a good practice to be a bit pessimistic. Choosing better performing transistors can pay off during the finalization of the design. Based on the specification a priority list can be made.

Selection

 * 1) Low consumption
 * 2) Low Noise Figure
 * 3) High Gain
 * 4) Price

Taking this selection list as an example, there is still one parameter missing. Operating frequency has to be considered in parallel with almost all parameters in the list. Operating frequency prompts a technology (BJT, FET, HEMT).

Manufacturers
Avago

Infineon

NXP

Transistor Models
Transistor model can be linear or non-linear.

Linear model
Linear model of a transistor is set of s-parameters within a frequency range and with specific bias conditions. Frequency range generally starts from 40 MHz and it ends close to the transient frequency. Bias conditions are typically chosen in a convenient manner. In order to be able analyze the noise properties, the transistor can be also described by noise data. The noise data specify minimum noise figure, optimal input impedance and equivalent noise resistance.

Linear models are used for simulation of stability, gain, noise figure.

Non - Linear model
BJT models can be represented by Ebers Mool and Gummel-Poon models. These models are usually described by so called SPICE model representation. SPICE is an acronym for Simulation Program with Integrated Emphasis. One of such a program is ADS (Advance Design Software). ADS is software developed by Agilent Technologies and this tutorial uses it as a tool for simulations.

Formula 1
Input reflection coefficient

$$ \Gamma_{S} = \left( S_{11} + \frac{S_{12} \cdot S_{21} \cdot \Gamma_L}{1-\left(\Gamma_L \cdot S_{22} \right)} \right)^{\ast} $$

Output reflection coefficient

$$ \Gamma_{L} = \left( S_{22} + \frac{S_{12} \cdot S_{21} \cdot \Gamma_S}{1-\left(\Gamma_S \cdot S_{11} \right)}\right)^{\ast}$$

Noise Figure of a device characterized by noise parameters

$$ F = F_{min} + \frac{G_n}{R_S} \left| Z_S - Z_{opt} \right|^2 $$

Stability factor K

$$ K = \frac{1- \left| S_{11} \right| ^2 - \left| S_{22} \right|^2+ \left| \Delta \right|}{2 \cdot \left| S_{11} \right| \cdot \left| S_{22} \right| } $$

$$ \Delta = S_{11} \cdot S_{22} - S_{12} \cdot S_{21} $$

Load and Source Stability Circles: radius and center

$$ r_L = \left| { \frac{ \left( S_{12} \cdot S_{21} \right)^\ast }{ { \left| S_{22} \right|^2 - \left| S_{11} \cdot S_{22} - S_{12} \cdot S_{21} \right|^2 } } } \right| $$

$$ C_L = \frac{ \left( S_{22} - \left( S_{11} \cdot S_{22} - S_{12} \cdot S_{21} \right) \cdot S_{11}^\ast \right)^\ast }{ \left| S_{22} \right|^2 - \left| S_{11} \cdot S_{22} - S_{12} \cdot S_{21} \right|^2 } $$

$$ r_S = \left| { \frac{ \left( S_{12} \cdot S_{21} \right)^\ast }{ { \left| S_{11} \right|^2 - \left| s11 \cdot S_{22} - S_{12} \cdot S_{21} \right|^2 } } } \right| $$

$$ C_S = \frac{ \left( S_{11} - \left( S_{11} \cdot S_{22} - S_{12} \cdot S_{21} \right) \cdot S_{11}^\ast \right)^\ast }{ \left| S_{11} \right|^2 - \left| S_{11} \cdot S_{22} - S_{12} \cdot S_{21} \right|^2 } $$

Unilateral Figure of Merit

$$ U = \frac{ \left| S_{12} \right| \cdot \left| S_{21} \right| \cdot \left| S_{11} \right| \cdot \left| S_{22} \right| }{ \left( 1 - \left| S_{11} \right|^2 \right) \cdot \left( 1 - \left| S_{22} \right|^2 \right) } $$

Formula 2
Simultaneous conjugate match

Matched source reflection coefficient

$$ \Gamma_{MS} = \frac {B_1}{2 \cdot C_1} - \frac {1}{2} \sqrt{ \left( \frac {B_1}{C_1} \right) - 4 \frac{C^{ \ast }_{1}}{C_{1}}} $$

$$ C_1 = S_{11} - S_{22}^{ \ast } \cdot \Delta $$

$$ B_1 = 1 - \left| S_{22} \right|^2 - \left| \Delta \right|^2 - \left| S_{11} \right|^2 $$

Matched load reflection coefficient

$$ \Gamma_{ML} = \frac {B_2}{2 \cdot C_2} - \frac {1}{2} \sqrt{ \left( \frac {B_2}{C_2} \right) - 4 \frac{C^{ \ast }_{2}}{C_{2}}} $$

$$ C_2 = S_{22} - S_{11}^{ \ast } \cdot \Delta $$

$$ B_2 = 1 - \left| S_{11} \right|^2 - \left| \Delta \right|^2 - \left| S_{22} \right|^2 $$

Optimal matching

$$\Gamma^{*}_{MS} = S_{11} + \frac{S_{12} \cdot S_{21} \cdot \Gamma_{ML}}{1-\left(\Gamma_{ML} \cdot S_{11} \right)}$$

$$ \Gamma^{*}_{ML} = S_{22} + \frac{S_{12} \cdot S_{21} \cdot \Gamma_{MS}}{1-\left(\Gamma_{MS} \cdot S_{22} \right)}$$

Reflection coefficient -> Impedance

$$ Z_{IN}=Z_0 \left( \frac{1+ \Gamma_{IN}}{1- \Gamma_{IN}} \right) $$

$$ Z_{OUT}=Z_0 \left( \frac{1+ \Gamma_{OUT}}{1- \Gamma_{OUT}} \right) $$

Formula 3
Dynamic Range

$$ OIP3 = P_{1-dB} + 10dB $$

$$ OIP3 = P_{OUT} + \frac {IMD}{2} $$

Stability Factor

$$ \mu_L = \frac {1- \left|S_{11} \right|^2}{\left| S_{22}-S_{11}^\ast \cdot \Delta \right| + \left|S_{21} \cdot S_{12} \right|} $$

$$ \mu_S = \frac {1- \left|S_{22} \right|^2}{\left| S_{11}-S_{22}^\ast \cdot \Delta \right| + \left|S_{21} \cdot S_{12} \right|} $$

Noise Figure

$$ F = F_{min} + \frac {4R_n}{Z_0} \frac {\left| \Gamma_s - \Gamma_{opt} \right|}{\left( 1 - \left| \Gamma_S \right|^2\right) \left| 1 + \Gamma_{opt} \right|^2 } $$