Low Noise Amplifier (LNA) Presented By Mohammad Jameel NDG on FSMFPGA Based System Design1.

Low Noise Amplifier (LNA)

Presented By

Mohammad Jameel

NDG on FSM FPGA Based System Design 1

FPGA Based System Design 2

Mathmatical / Behavorial Model of Mathmatical / Behavorial Model of LNALNA

Mathmatical / Behavorial Model of Mathmatical / Behavorial Model of LNALNA

R

I

a1+ a3│x(t) │2+ a5│x(t) │4 SaturationMag

Ang I

R

.5 Noise Power

.5 Noise Power

Output Signal


Designed Mathmatical Model of LNA , Designed Mathmatical Model of LNA , Cont’d Cont’d

Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)

Designed Mathmatical Model of LNA , Designed Mathmatical Model of LNA , Cont’d Cont’d


•Non-linearity of LNA may be characterized by following equation.

•Let x(t) is input to a nonlinear pass band model. Output y (t) of this system is given by

y(t) = a1x(t) + a2x2(t) + a3x3(t) + a4x4(t) + a5x4(t)

•Baseband equivalent of y(t) is given as follows.

ybb(t) = (a1+ a3│x(t) │2+ a5│x(t) │4)│x (t)│ - - - eq. 1

•Input Signal magnitude and these three coefficients (a3,a5 ,a1) are combined according to the above equation to obtain the AM/AM output as even order harmonics( a2, a4, a6 …) do not produce Inter-Modulation (IM) products therefore they are not taken into account in calculation.

•Intermodulation is one of the major causes of distortion in RF systems.




•In order to quantify intermodulation “third intercept point (IP3)” has been devised.

Definition of IP3 The point where the linear gain (a2A2) and 3rd order non-linearity (20log(3a3A3/4) )intercept with the increase in level of input signal (A) is called 3rd order intercept point (IP3). It is a given value and is used to calculate a3 and P1dB ( 1 dB compression point)




AM/AM Simulink Block

Where |u|= magnitude of input signal

LGAIN/ a1= input linear gain

IP3= 3rd Intercept Point

|u| / Out1= modulated magnitude of input signal

AM/AM

|u|

LGAIN

IP3

|u| / Out 1




a3/ k3 Simulink Block

Where

LGAIN/ a1= input linear gain ( 1 - 1000 )

IP3= 3rd Intercept Point ( Range : 5 – 100 dbm )

a3 = 3rd order coefficient/ 3rd order gain

V1 dB/ P1 dB= 1 dB Gain compression point

a3/ k3

LGAIN

IP3

a3

V1 dB/ P1 dB









Where a3= 3rd order coefficient/ 3rd order gain

LGAIN/a1= input linear gain

V1 dB/ P1 dB= 1 dB Gain compression point

a5= 5th order coefficient/ 5th order gain

a5/ k5

a3

LGAIN

V1 dB/ P1 dB

a5






Addition of Thermal NoiseAddition of Thermal NoiseAddition of Thermal NoiseAddition of Thermal Noise

Addition of thermal noiseAWGN noise is added to the output of AM/AM block. This block calculates white noise for the input signal

Pn = 4kRTfs (10NF/10+1)

Where NF = Noise Factor = 2, R = System Impedance = 1, K = Boltzmann Constant

fs = Sample rate = 0, T = Temperature = 290 K

Low Noise Amplifier (LNA) Presented By Mohammad Jameel NDG on FSMFPGA Based System Design1.

Documents