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An analytic approach for CDMA output of feedforward power amplifier

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Abstract

In this paper, a novel method is introduced to predict the Code-Division Multiple-Access (CDMA) output spectrum of an RF power amplifier linearized with feedforward technique based on transfer function. In this method, an RF power amplifier is modeled mathematically by nonlinear complex envelope transfer function based on AM-AM and AM-PM distortion diagrams. Using this model, analytic expressions of CDMA output spectrum of power amplifier is calculated. Having mathematical model of RF power amplifier leads to derive analytic expressions for InterModulation (IM) products in feedforward amplifier. Based on these expressions, IM products are related to nonlinear complex envelope transfer function of feedforward amplifier. Then, CDMA output spectrum of feedforward linearization technique is predicted. The loops imbalances in feedforward technique are considered in analysis. Finally, the results of derived expressions in MATLAB software are compared with ADS simulations results and good agreements were achieved. Employing this method gives insight for feedforward analysis and loops imbalances effects in feedforward amplifier for CDMA applications.

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Authors and Affiliations

  1. Department of Electrical Engineering, Tehran Polytechnic, Amirkabir University of Technology, Tehran, Iran

    M. M. Rahmati, A. Abdipour, A. Mohammadi & G. Moradi

Authors
  1. M. M. Rahmati
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  2. A. Abdipour
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  3. A. Mohammadi
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  4. G. Moradi
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Corresponding author

Correspondence to A. Abdipour.

Appendix

Appendix

Expressions for the coefficients indicated in (27) are listed as follows:

$$ \begin{aligned} b_{9,1} & = f_{e,1} b_{7,1} + \frac{15}{4}f_{e,5} b_{7,1} b_{7,3} b_{7,5}^{3} + \frac{5}{4}f_{e,5} b_{7,3}^{4} b_{7,5} + \frac{15}{2}b_{7,1} f_{e,5} b_{7,3}^{2} b_{7,5}^{2} + \frac{5}{8}b_{7,3}^{3} f_{e,5} b_{7,5}^{2} + \frac{3}{2}f_{e,3} b_{7,1} b_{7,3}^{{^{2} }} + \frac{3}{2}f_{e,3} b_{7,1} b_{7,5}^{{^{2} }} + \frac{15}{8}b_{7,1}^{2} f_{e,5} b_{7,3}^{{^{3} }} \, \\ & + \frac{15}{8}f_{e,5} b_{7,1} b_{7,3}^{4} + \frac{3}{4}f_{e,3} b_{7,3}^{2} b_{7,5} + \frac{3}{4}f_{e,3} b_{7,1}^{3} + \frac{3}{4}f_{e,3} b_{7,1}^{{^{2} }} b_{7,3} + \frac{45}{8}b_{7,1}^{{^{2} }} f_{e,5} b_{7,3}^{{^{2} }} b_{7,5} + \frac{15}{4}b_{7,1} f_{e,5} b_{7,3}^{{^{3} }} b_{7,5} + 5f_{e,5} b_{7,1}^{{^{3} }} b_{7,3} b_{7,5} \\ & + \frac{15}{4}f_{e,5} b_{7,1}^{{^{3} }} b_{7,5}^{{^{2} }} + \frac{15}{8}b_{7,3}^{{^{2} }} f_{e,5} b_{7,5}^{{^{3} }} + \frac{25}{16}f_{e,5} b_{7,1}^{{^{4} }} b_{7,3} + \frac{5}{16}f_{e,5} b_{7,1}^{{^{4} }} b_{7,5} + \frac{15}{4}b_{7,1}^{{^{2} }} f_{e,5} b_{7,3} b_{7,5}^{{^{2} }} + \frac{15}{4}f_{e,5} b_{7,1}^{{^{3} }} b_{7,3}^{{^{2} }} + \frac{15}{8}f_{e,5} b_{7,1} b_{7,5}^{{^{4} }} \\ & + \frac{3}{2}f_{e,3} b_{7,1} b_{7,3} b_{7,5} + \frac{5}{8}f_{e,5} b_{7,1}^{{^{5} }} \\ \end{aligned} $$
$$ \begin{aligned} b_{9,3} & = \frac{3}{4}f_{e,3} b_{7,1}^{{^{2} }} b_{7,5} + \frac{15}{2}b_{7,1}^{{^{2} }} f_{e,5} b_{7,3} b_{7,5}^{{^{2} }} + \frac{15}{4}f_{e,5} b_{7,1}^{{^{2} }} b_{7,3}^{{^{3} }} + \frac{15}{8}f_{e,5} b_{7,3} b_{7,5}^{{^{4} }} + \frac{3}{2}f_{e,3} b_{7,1} b_{7,3} b_{7,5} + \frac{15}{8}b_{7,1}^{{^{2} }} f_{e,5} b_{7,5}^{{^{3} }} + \frac{5}{4}f_{e,5} b_{7,1}^{{^{4} }} b_{7,5} \\ &+ \frac{15}{8}f_{e,5} b_{7,1}^{{^{4} }} b_{7,3} + \frac{45}{8}b_{7,1}^{{^{2} }} f_{e,5} b_{7,3}^{{^{2} }} b_{7,5} + \frac{3}{4}f_{e,3} b_{7,3}^{{^{3} }} + \frac{15}{8}b_{7,1} f_{e,5} b_{7,3}^{{^{2} }} b_{7,5}^{{^{2} }} \, + \frac{15}{8}f_{e,5} b_{7,1}^{{^{3} }} b_{7,3}^{{^{2} }} + \frac{15}{4}b_{7,1} f_{e,5} b_{7,3} b_{7,5}^{{^{3} }} + \frac{5}{8}f_{e,5} b_{7,3}^{{^{5} }} \\ &+ \frac{15}{4}f_{e,5} b_{7,1}^{{^{3} }} b_{7,3} b_{7,5} + \frac{1}{4}f_{e,3} b_{7,1}^{{^{3} }} + \frac{3}{2}f_{e,3} b_{7,1}^{{^{2} }} b_{7,3} + 5f_{e,5} b_{7,1} b_{7,3}^{{^{3} }} b_{7,5} + f_{e,1} b_{7,3} + \frac{3}{2}f_{e,3} b_{7,3} b_{7,5}^{{^{2} }} + \frac{5}{4}f_{e,5} b_{7,1}^{{^{3} }} b_{7,5}^{{^{2} }} + \frac{15}{4}f_{e,5} b_{7,3}^{{^{3} }} b_{7,5}^{{^{2} }} \\ &+ \frac{5}{16}f_{e,5} b_{7,1}^{{^{5} }} \\ \end{aligned} $$
$$ \begin{aligned} b_{9,5} &= \frac{5}{4}f_{e,5} b_{7,1}^{{^{4} }} b_{7,3} + \frac{3}{4}f_{e,3} b_{7,1} b_{7,3}^{{^{2} }} + \frac{5}{4}f_{e,5} b_{7,1} b_{7,3}^{{^{4} }} + \frac{15}{2}b_{7,1}^{{^{2} }} f_{e,5} b_{7,3}^{{^{2} }} b_{7,5} + \frac{3}{2}f_{e,3} b_{7,1}^{{^{2} }} b_{7,5} + \frac{15}{4}b_{7,3}^{{^{2} }} f_{e,5} b_{7,5}^{{^{3} }} + f_{e,1} b_{7,5} + \frac{15}{8}f_{e,5} b_{7,1}^{{^{4} }} b_{7,5} \\ &+ \frac{15}{8}f_{e,5} b_{7,3}^{{^{4} }} b_{7,5} + \frac{5}{2}f_{e,5} b_{7,1}^{{^{3} }} b_{7,3} b_{7,5} + \frac{1}{16}f_{e,5} b_{7,1}^{{^{5} }} \, + \frac{45}{8}b_{7,1} f_{e,5} b_{7,3}^{{^{2} }} b_{7,5}^{{^{2} }} + \frac{3}{4}f_{e,3} b_{7,5}^{{^{3} }} + \frac{5}{8}f_{e,5} b_{7,5}^{{^{5} }} + \frac{3}{4}f_{e,3} b_{7,1}^{{^{2} }} b_{7,3} + \frac{15}{8}b_{7,1}^{{^{2} }} f_{e,5} b_{7,3}^{{^{3} }} \\ &+ \frac{45}{8}b_{7,1}^{{^{2} }} f_{e,5} b_{7,3} b_{7,5}^{{^{2} }} + \frac{5}{4}f_{e,5} b_{7,1} b_{7,3}^{{^{3} }} b_{7,5} + \frac{15}{4}b_{7,1}^{{^{2} }} f_{e,5} b_{7,5}^{{^{3} }} + \frac{3}{2}f_{e,3} b_{7,3}^{{^{2} }} b_{7,5} + \frac{15}{8}b_{7,1}^{{^{3} }} f_{e,5} b_{7,3}^{{^{2} }} \\ \end{aligned} $$

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Rahmati, M.M., Abdipour, A., Mohammadi, A. et al. An analytic approach for CDMA output of feedforward power amplifier. Analog Integr Circ Sig Process 66, 349–361 (2011). https://doi.org/10.1007/s10470-010-9541-1

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