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

2 Mathmatical / Behavorial Model of LNA

FPGA Based System Design3 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. y bb (t) = (a 1 + a 3 │x(t) │ 2 + a 5 │x(t) │ 4 )│x (t)│ eq. 1 Input Signal magnitude and these three coefficients (a 3, a 5,a 1 ) 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 Design4 Characterization of Non-Linearity (AM/AM) 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 (a 2 A 2 ) and 3 rd order non-linearity (20log(3a 3 A 3 /4) )intercept with the increase in level of input signal (A) is called 3 rd order intercept point (IP3). It is a given value and is used to calculate a3 and P1dB ( 1 dB compression point)

FPGA Based System Design5 Characterization of Non-Linearity (AM/AM)  AM/AM Simulink Block Where |u|= magnitude of input signal LGAIN/ a1= input linear gain IP3= 3 rd Intercept Point |u| / Out1= modulated magnitude of input signal AM/AM |u| LGAIN IP3 |u| / Out 1

FPGA Based System Design6 Characterization of Non-Linearity (AM/AM)  a3/ k3 Simulink Block Where LGAIN/ a1= input linear gain ( ) IP3= 3 rd Intercept Point ( Range : 5 – 100 dbm ) a3 = 3 rd order coefficient/ 3 rd order gain V1 dB/ P1 dB= 1 dB Gain compression point a3/ k3 LGAIN IP3 a3 V1 dB/ P1 dB

FPGA Based System Design7 Characterization of Non-Linearity (AM/AM)  a3/ k3 Simulink Block

FPGA Based System Design8 Characterization of Non-Linearity (AM/AM)  a5/ k5 Simulink Block Where a3= 3 rd order coefficient/ 3 rd order gain LGAIN/a1= input linear gain V1 dB/ P1 dB= 1 dB Gain compression point a5= 5 th order coefficient/ 5 th order gain a5/ k5 a3 LGAIN V1 dB/ P1 dB a5

FPGA Based System Design9 Characterization of Non-Linearity (AM/AM)  a5/ k5 Simulink Block

FPGA Based System Design10 AM / AM Simulation in MATLAB  The figures below shows the simulation result ip3 = 10dbm & ip3 = 80 dbm

FPGA Based System Design11 AM / AM Simulation in Verilog

FPGA Based System Design12 AM / AM Simulation in Verilog

FPGA Based System Design13 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 P n = 4kRTf s (10 NF/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 Design14 Inherent Characteristics of LFSR

FPGA Based System Design15 Desired Characteristics of LFSR