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Analysis and design of power and efficiency in third-order matching networks for switched-capacitor power-amplifiers

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Abstract

This paper presents the design of a matching network (MN) for switched-capacitor PAs (SCPA) optimized for efficiency against required load output power. The presented third-order MN exploits the intrinsic output capacitance of the SCPA, reducing the number of passive components required by the MN. As an example, a MN for a 1.1 V switched capacitor power amplifier has been designed with a bluetooth application in mind. The example MN has been implemented in a 28 nm CMOS RF metal stack and provides 16.7 dBm output power with IL = 1.1 dB at 2.4 GHz in an area of 300 × 300 μm2 when resonated by an SCPA capacitance of 2.3 pF. Further structures have then been implemented and characterized, covering a broader set of applications.

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Notes

  1. \(L_p\), once \(P_o\) and n are given, is in fact implicitly given by (10).

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Authors and Affiliations

  1. Intel Mobile Communications, Villach, Austria

    Antonio Passamani, Davide Ponton & Gerhard Knoblinger

  2. Department of Information Engineering, University of Padova, Padua, Italy

    Andrea Bevilacqua

Authors
  1. Antonio Passamani
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  2. Davide Ponton
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  3. Gerhard Knoblinger
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Corresponding author

Correspondence to Antonio Passamani.

Appendix

Appendix

Primary and secondary currents in the T-model of the transformer have ratio

$$\begin{aligned} \dfrac{I_1}{I_2} = \dfrac{\dfrac{R_2+R+j \omega L_2 }{n ^2}}{j \omega L_m } \end{aligned}$$
(19)

and thus,

$$\begin{aligned} \eta= & {} \dfrac{P_o}{P_o + P_{R_2} + P_{R_1}} \nonumber \\= & {} \dfrac{|I_2|^2 \cdot \dfrac{R}{ n^2}}{|I_2|^2 \cdot \dfrac{ R + R_2}{ n^2} + |I_1 + I_2|^2 \cdot R_1}\nonumber \\= & {} \dfrac{\dfrac{R}{ n^2}}{\dfrac{R + R_2}{n^2} + \left| \dfrac{R + R_2 +j \omega L_2 + j \omega L_m n^2}{j \omega L_m n^2}\right| ^2 \cdot R_1 } \end{aligned}$$
(20)

Furthermore, exploiting the fact that

$$\begin{aligned} \eta&= \dfrac{P_o}{P_i} = \left| \dfrac{I_2}{I_1 + I_2} \right| ^2 \dfrac{ R}{n^2 (Z + 1 / j\omega C)} \end{aligned}$$
(21)

where \((Z + 1 / j\omega C)\) is the impedance of the whole matching network, the output power is found to be,

$$\begin{aligned} P_o&= \eta \dfrac{V^2}{(Z + 1 / j\omega C)} = \dfrac{ \eta ^2 n^2 V ^2}{R} \left| \dfrac{I_1 + I_2}{I_2} \right| ^2 \end{aligned}$$
(22)

Finally point of maximum efficiency can the be found by zeroing the derivative (4) with respect to \(\omega L_p\)

$$\begin{aligned} \frac{\partial \eta }{\partial \omega L_p}&= - (\omega L_p)^2 n ^ 4 \left( \dfrac{k^2 }{Q_2} + \dfrac{1}{Q_1 Q_2^2} + \dfrac{1}{Q_1} \right) + \dfrac{ R^2}{n^2 Q_1} \end{aligned}$$
(23)

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Passamani, A., Ponton, D., Knoblinger, G. et al. Analysis and design of power and efficiency in third-order matching networks for switched-capacitor power-amplifiers. Analog Integr Circ Sig Process 89, 307–315 (2016). https://doi.org/10.1007/s10470-016-0801-6

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  • DOI: https://doi.org/10.1007/s10470-016-0801-6

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