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Parasitic aware impedance matching techniques for RF amplifiers

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Abstract

This paper analyzes the impact of non-idealities of the lumped passive elements (inductor and capacitor) in the matching networks of RF amplifiers. This work infers that the representation of performance matrices of a matching network like sensitivity and harmonic rejection; in terms of input reflection coefficient (S 11) is more convenient than the transfer functions. Expression of S 11 of widely used L-, π- and T-networks have been derived as a function of inductor quality factor (Q L ), capacitor quality factor (Q C ) and transformation ratio. This formulation shows that the matching performance degrades severely due to component non-idealities. To circumvent this degradation, a modified set of design equations have been proposed for the L-network and the same has been extended for π- and T-network. Simulation results show that network synthesized on the basis of proposed set of equations nullify the effect of non-idealities by 70–80% in L-network and 10–20% in π-network but minor improvement in T-network.

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References

  1. Abrie, P. L. D. (1985). The design of impedance-matching networks for radio-frequency and microwave amplifiers. Norwood, MA: Artech House Inc.

    Google Scholar 

  2. Becciolini, B. (1993). Motorola application note: Impedance matching networks applied to RF power transistors. http://www.rfwireless.rell.compdfsAN_721_D.pdf

  3. Asgaran, S., Deen, M. J., & Chen, C.-H. (1998). Design of the input matching network of RF CMOS LNAs for low power operation. IEEE Journal of Solid-State Circuits, 33(12), 2178–2185.

    Article  Google Scholar 

  4. Lee, H., & Mohammadi, S. (2006). A 3 GHz subthreshold CMOS low noise amplifier, IEEE radio frequency integrated circuits symposium (pp. 494–497). San Francisco, USA.

  5. Sun, Y., & Fidler, J. K. (1994). Design of \(\Uppi\) impedance matching network. In Proceedings of the IEEE international symposium circuits and systems (pp. 5–9). London.

  6. Chung, B. K. (2006). Q-based design method for T network impedance matching. Microelectronics Journal, 37(9), 1007–1011.

    Article  Google Scholar 

  7. Chen, F., & Weber, R. J. (Oct, 2004). A novel process-variation insensitive network for on-chip impedance matching. In IEEE international symposium on communications and information technologies (pp. 43–46, no. 1). Sapporo, Japan

  8. Thompson, M., & Fidler, J. K. (2004). Determination of impedance matching domain of impedance matching networks. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(10), 2098–2106.

    Article  MathSciNet  Google Scholar 

  9. Han, Y., & Perreault, D. J. (2006). Analysis and design of high efficiency matching networks. IEEE Transactions on Power Electronics, 21(5), 1484–1491.

    Article  Google Scholar 

  10. Lee, T. H. (2004). Design of CMOS radio-frequency integrated circuits. Cambridge: Cambridge University Press.

    Google Scholar 

  11. Pozar, D. M. (2004). Microwave engineering. New York: John Wiley and Sons.

    Google Scholar 

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Authors and Affiliations

  1. Department of Electronics & Electrical Communication Engineering, Indian Institute of Technology, Kharagpur, Kharagpur, 721302, India

    K. Dasgupta, A. Dutta & T. K. Bhattacharyya

Authors
  1. K. Dasgupta
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  2. A. Dutta
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  3. T. K. Bhattacharyya
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Corresponding author

Correspondence to T. K. Bhattacharyya.

Appendices

Appendix 1: S-parameter representation of high-pass L-section matching network

The expression for S 11 in terms of Q L and Q C can be derived for the L-match high-pass section as

$$ S_{11}(\omega) = \frac{C}{D} $$
(28)

where,

$$C = \left[\left\{\left(\frac{\omega_0}{\omega}\right)^2 - 1\right\} + \left\{\frac{1}{Q}\left(\frac{\omega_0}{\omega}\right)\left(\frac{1}{Q_C} - \frac{1}{Q_L}\right)\right\}\right] + j\left[ - \left(\frac{\omega_0}{\omega}\right)\frac{1}{QQ_L Q_C} + \left(\frac{\omega_0}{\omega}\right)^2 \frac{1}{Q_C} + \frac{1}{Q_L}\right] D = \left[\left\{1 - \left(\frac{\omega_0}{\omega}\right)^2 \right\} + \left\{\frac{1}{Q}\left(\frac{\omega_0} {\omega}\right)\left(\frac{1}{Q_C} - \frac{1} {Q_L}\right)\right\}+\frac{2}{Q^2} \right] -j\left[\left(\frac{\omega_0}{\omega}\right)\frac{1} {Q}\left(2+\frac{1}{Q_L Q_C}\right) + \left(\frac{\omega_0} {\omega}\right)^2 \frac{1}{Q_C} + \frac{1}{Q_L} + \frac{2} {Q^2 Q_L}\right]$$

Appendix 2: S-parameter representation of π-network

The input reflection coefficient (S 11) of π-section assuming no-loss is expressed as

$$ S_{11} (\omega ) = \frac{M}{N} $$
(29)

where,

$$M = \left(\frac{1}{k} -1\right) - \left(\frac{\omega }{\omega _0 }\right)^2 \frac{Q_0\left(Q_2 - Q_1\right)}{1 + Q_1 ^2 } + j\left(\frac{\omega }{\omega _0 }\right)\left[\frac{Q_0}{1+Q_1^2}-\left(\frac{Q_1}{k}+Q_2 \right) + \left(\frac{\omega }{\omega _0 }\right)^2 \frac{Q_0 Q_1 Q_2 }{1 + Q_1 ^2 }\right] N = \left(\frac{1}{k} +1\right) - \left(\frac{\omega }{\omega _0 }\right)^2 \frac{Q_0\left(Q_2 + Q_1\right)}{1 + Q_1 ^2 } + j\left(\frac{\omega }{\omega _0}\right)\left[\frac{Q_0}{1+Q_1^2}+\left(\frac{Q_1}{k}+Q_2 \right) - \left(\frac{\omega }{\omega _0 }\right)^2 \frac{Q_0 Q_1 Q_2 }{1 + Q_1 ^2 }\right] $$
$$ Q_0=Q_{in},\quad Q_1=Q_{left},\quad Q_2=Q_{right} \quad \hbox{and} \quad k = \frac{R_1}{R_2 } $$

However, in practice components are lossy, then the expression of S 11 in terms of inductor quality factor (Q L ) and capacitor quality factor (Q C ) for π-section network is modified as

$$ S_{11} (\omega ) = \frac{\frac{Z_{in} (\omega )}{R_1 } - 1}{\frac{Z_{in} (\omega )}{R_1} + 1} $$
(30)

where, \(\frac{Z_{in} (\omega )}{R_1} = \frac{P}{Q}\);

$$ P = \frac{1}{k} + \left[ j\left(\frac{\omega }{\omega _0 }\right)\frac{2Q_0}{1 + Q_1 ^2} + \frac{2Q_0} {\left(1 + Q_1 ^2 \right)Q_L }\right] \left[1 +\frac{j\left(\frac{\omega }{\omega _0 }\right)Q_2 }{1 + j\left(\frac{1}{Q_{CR}}\right)\left(\frac{\omega }{\omega_0 } \right)}\right] $$
$$ Q = 1 + j\left(\frac{\omega }{\omega _0}\right)\left[\frac{\frac{Q_1}{k}}{1 + j\left(\frac{1}{Q_{CL}}\right)\left( \frac{\omega }{\omega _0 } \right)} + \frac{Q_2}{1 + j\left(\frac{1}{Q_{CR}}\right)\left( \frac{\omega }{\omega _0 }\right)}\right] + \left[\frac{j\left(\frac{\omega }{\omega _0 }\right)Q_2 }{1 + j\left(\frac{1}{Q_{CR}}\right)\left( \frac{\omega } {\omega _0 } \right)}\right] \left[ j\left(\frac{\omega }{\omega _0 }\right)\frac{2Q_0 }{1 + Q_1 ^2 } + \frac{2Q_0 }{\left(1 + Q_1 ^2 \right)Q_L } \right] \left[ 1 + \frac{j\left(\frac{\omega }{\omega _0}\right)Q_1}{1 + j\left(\frac{1}{Q_{CL}}\right)\left( \frac{\omega }{\omega_0 } \right)} \right] $$

Q CR and Q CL are the right and left side capacitor quality factor.

Appendix 3: S-parameter representation of T-network

The input reflection coefficient (S 11) of T-section assuming no-loss is expressed as

$$ S_{11} (\omega ) = \frac{R}{S} $$
(31)

where

$$ R=\left(k - 1\right) - \left(\frac{\omega }{\omega _0}\right)^2 \frac{Q_0\left(Q_1 - Q_2\right)}{1 + Q_2 ^2 } + j\left(\frac{\omega }{\omega _0}\right)\left[\left(Q_1 + kQ_2 \right) - \frac{2Q_0}{1 + Q_2 ^2 } - \left(\frac{\omega }{\omega _0 }\right)^2 \frac{2Q_0 Q_1 Q_2 }{1 + Q_2 ^2 }\right] S=\left(k + 1\right) - \left(\frac{\omega }{\omega _0 }\right)^2 \frac{Q_0\left(Q_1 + Q_2\right)}{1 + Q_2 ^2 } + j\left(\frac{\omega }{\omega _0}\right)\left[\left(Q_1 + kQ_2 \right) + \frac{2Q_0}{1 + Q_2 ^2 } - \left(\frac{\omega }{\omega _0}\right)^2 \frac{2Q_0 Q_1 Q_2 }{1 + Q_2 ^2 }\right] $$
$$ Q_{0} = Q_{in},\quad Q_1=Q_{left},\quad Q_2=Q_{right} \quad \hbox{and} \quad k = \frac{R_1}{R_2 } $$

The expression of S 11 in terms of inductor quality factor (Q L ) and capacitor quality factor (Q C ) for T-section network can be modified as

$$ S_{11} (\omega ) = \frac{\frac{Z_{in} (\omega )}{{R_1}} -1} {\frac{Z_{in} (\omega )}{R_1} + 1} $$
(32)

where

$$ \frac{Z_{in} (\omega )}{R_1} = \left[\frac{k\left[1 + j\left(\frac{\omega }{\omega_0}\right)Q_2 \left(1 - \frac{j}{Q_{LR} \left(\frac{\omega}{\omega_0}\right)}\right)\right]}{j\left(\frac{\omega} {\omega_0}\right)\frac{2Q_0}{1 + Q_2 ^2}\left(\frac{1}{1 + \frac{j}{Q_C }\left( \frac{\omega }{\omega _0 } \right)}\right)\left[1 + j\left(\frac{\omega }{\omega _0 }\right)Q_2 \left(1 - \frac{j}{Q_{LR} \left( \frac{\omega } {\omega _0 }\right)}\right)\right] + 1}\right] +j\left[\left(\frac{\omega }{\omega _0 }\right)Q_1 \left(1 - \frac{j}{Q_{LL} \left( \frac{\omega }{\omega _0} \right)}\right)\right] $$

Q LR and Q LL are the right and left side inductor quality factor.

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Dasgupta, K., Dutta, A. & Bhattacharyya, T.K. Parasitic aware impedance matching techniques for RF amplifiers. Analog Integr Circ Sig Process 70, 91–102 (2012). https://doi.org/10.1007/s10470-011-9659-9

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