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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
FPGA Based System Design 3
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
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
•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.
FPGA Based System Design 4
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
•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)
FPGA Based System Design 5
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
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
FPGA Based System Design 6
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
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
FPGA Based System Design 7
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
a3/ k3 Simulink Block
FPGA Based System Design 8
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
a5/ k5 Simulink Block
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
FPGA Based System Design 9
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
Characterization of Non-Linearity Characterization of Non-Linearity (AM/AM)(AM/AM)
a5/ k5 Simulink Block
FPGA Based System Design 13
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