Low Noise Amplifier (LNA)
Presented By
Mohammad Jameel
NDG on FSM
FPGA Based System Design
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Mathmatical / Behavorial Model of
LNA
.5 Noise Power
R
I
Mag
a1+ a3│x(t) │2+ a5│x(t) │4
Saturation
R
Output Signal
Ang
I
.5 Noise Power
FPGA Based System Design
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Designed Mathmatical Model of LNA ,
Cont’d
Characterization of Non-Linearity
(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
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Characterization of Non-Linearity
(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
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Characterization of Non-Linearity
(AM/AM)
 AM/AM Simulink Block
|u|
LGAIN
AM/AM
|u| / Out 1
IP3
Where
|u|= magnitude of input signal
LGAIN/ a1= input linear gain
IP3= 3rd Intercept Point
|u| / Out1= modulated magnitude of input signal
FPGA Based System Design
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Characterization of Non-Linearity
(AM/AM)
 a3/ k3 Simulink Block
LGAIN
IP3
a3/ k3
a3
V1 dB/ P1 dB
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
FPGA Based System Design
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Characterization of Non-Linearity
(AM/AM)
 a3/ k3 Simulink Block
FPGA Based System Design
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Characterization of Non-Linearity
(AM/AM)
 a5/ k5 Simulink Block
a3
LGAIN
a5/ k5
a5
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
FPGA Based System Design
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Characterization of Non-Linearity
(AM/AM)
 a5/ k5 Simulink Block
FPGA Based System Design
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Addition of Thermal Noise
Addition of thermal noise
AWGN 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
FPGA Based System Design
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