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Low Noise Amplifier (LNA)

Low Noise Amplifier (LNA). Presented By Mohammad Jameel. Mathmatical / Behavorial Model of LNA. Designed Mathmatical Model of LNA , Cont’d Characterization of Non-Linearity (AM/AM). Non-linearity of LNA may be characterized by following equation .

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Low Noise Amplifier (LNA)

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  1. Low Noise Amplifier (LNA) Presented By Mohammad Jameel FPGA Based System Design

  2. Mathmatical / Behavorial Model of LNA FPGA Based System Design

  3. 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

  4. 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

  5. Characterization of Non-Linearity (AM/AM) AM/AM |u| LGAIN |u| / Out 1 IP3 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 FPGA Based System Design

  6. Characterization of Non-Linearity (AM/AM) a3/ k3 LGAIN a3 IP3 V1 dB/ P1 dB 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 FPGA Based System Design

  7. Characterization of Non-Linearity (AM/AM) a3/ k3 Simulink Block FPGA Based System Design

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

  9. Characterization of Non-Linearity (AM/AM) a5/ k5 Simulink Block FPGA Based System Design

  10. 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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