User:Jakub.duchon

Low Noise Amplifier Design

Tutorial - resources :

May - 2009

LNA for CDMA [1]

Circuit Examples LNAa - different frequency ranges : [2]

BFP740F [3]

June - 2009

Modelithics [4]

Infineon Trasistors for LNA [5]

Infineon BFP620 app Note 60 [6]

LNA Design Queen's Wiki [7]

IEEE CMOS LNA Design [8]

A Scalable High-Frequency Noise Model for Bipolar Transistors with Application to Optimal Transistor Sizing for Low-Noise Amplifier Design [9]

A new calculation approach of transistor noise parameters as afunction of gatewidth and bias current [10]

ADS Tutorial Files - ECE Department University of California Santa Barbara [11]

Tutorial [12]

Neste [13]

Thesis [14]

AT 41533 + biasing [15]

Criteria for the Evaluation of Unconditional Stability of Microwave Linear Two-Ports: A Critical Review and New Proof [16]

Modified determinations of stability criteria for accurate designing the linear two-port amplifiers [17]

A New Criterion for Linear 2-Port Stability Using a Single Geometrically Derived Parameter [18]

White Paper - Overview of the 3GPP Long Term Evolution Physical Layer [19]

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.

Specification

Parameter	min	typ	max	unit	Note
Center frequency				Hz
Bandwidth				Hz
Gain				dB
Gain Flatness				dB
RL input				dB
RL output				dB
Noise Figure				dB
OIP3				dBm
Consumption				dBm
Stability				-
Size
Cost				€
Temperature				°C
I/O Impedance				Ω

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
5. ...

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

$\Gamma _{MS}={\frac {B_{1}}{2\cdot C_{1}}}-{\frac {1}{2}}{\sqrt {\left({\frac {B_{1}}{C_{1}}}\right)-4{\frac {C_{1}^{\ast }}{C_{1}}}}}$

$C_{1}=S_{11}-S_{22}^{\ast }\cdot \Delta$

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

Matched load reflection coefficient

$\Gamma _{ML}={\frac {B_{2}}{2\cdot C_{2}}}-{\frac {1}{2}}{\sqrt {\left({\frac {B_{2}}{C_{2}}}\right)-4{\frac {C_{2}^{\ast }}{C_{2}}}}}$

$C_{2}=S_{22}-S_{11}^{\ast }\cdot \Delta$

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

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

$F=F_{min}+{\frac {4R_{n}}{Z_{0}}}{\frac {\left|\Gamma _{s}-\Gamma _{opt}\right|}{\left(1-\left|\Gamma _{S}\right|^{2}\right)\left|1+\Gamma _{opt}\right|^{2}}}$