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Low-voltage and low-power Ku-band CMOS LNA using capacitive feedback

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Abstract

An ultra-wideband (12–18 GHz) low-noise amplifier (LNA) using a 65 nm CMOS technology is proposed, in which a common-source cascode structure with capacitive feedback technique is employed, leading to the excellent gain flatness. In order to provide the unconditional stability at all frequencies, a notch filter is placed in the input matching network. The post-layout simulation results confirm the S21 of 11.33 ± 0.33 dB, the input/output return loss of −7.5 to −32.7 dB and −10 to −17 dB, respectively. Moreover, reverse isolation (S12) better than 27 dB, noise figure (NF) of 4.6–5.47 dB and third-order input intercept point (IIP3) of −5.39 to −12.32 dB are obtained over the 12–18 GHz band of interest. The LNA power consumption, excluding the output buffer stage, is only 2.2 mW from a 0.8 V power supply. The LNA layout area is 0.255 mm2.

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Authors and Affiliations

  1. Microelectronic Circuits Laboratory, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran

    Farhad Soleimani & Hossein Shamsi

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  1. Farhad Soleimani
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  2. Hossein Shamsi
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Correspondence to Hossein Shamsi.

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Appendix

Appendix

In order to Simplify the NF calculation, we assume both the buffer stage and cascode transistor \({M}_{2}\) have negligible noise contribution. Besides, among all parasitic elements, only \({r}_{o1}\), \({R}_{{L}_{d2}}\), \({C}_{out}\) and \({C}_{GS1}\) are taken into account as shown in Fig. 

Fig. 15
figure 15

a The simplified model for calculating NF. b The simplified model for calculating \(\frac{{v}_{out}}{{v}_{n}}\)

Full size image

15(a). According to [30], the NF is given as follows.

$$NF=1+\frac{\overline{{{v }_{n,out}}^{2}}}{4kT{R}_{S}\times {\left|{G}_{V}\right|}^{2}}$$
(13)

where \(\overline{{{v }_{n,out}}^{2}}\) and \(\left|{G}_{V}\right|\) are the voltage noise spectrum at the output node caused by \({M}_{1}\) and the magnitude of voltage gain determined in Eq. 5, respectively. Since \({r}_{o1}\) moderately smaller than the input impedance seen from \({r}_{o1}\), to avoid much complexity in the final equation, we presume that the noise current source in Fig. 15(a) generates the voltage noise spectrum at the drain of \({M}_{1}\) identical to:

$$\overline{{{v }_{n}}^{2}}=4KT{\gamma }_{1}{g}_{m1}{{r}_{O1}}^{2}$$
(14)

and also, we have:

$$\overline{{{v }_{n,out}}^{2}}=\overline{{{v }_{n}}^{2}}\times {\left|\frac{{v}_{out}}{{v}_{n}}\right|}^{2}$$
(15)

where \(\frac{{v}_{out}}{{v}_{n}}\) is the voltage gain from the drain of \({M}_{1}\) to the drain of \({M}_{1}\). By using Fig. 15(b), \({\left|\frac{{v}_{out}}{{v}_{n}}\right|}^{2}\) is derived as:

$${\left|\frac{{v}_{out}}{{v}_{n}}\right|}^{2}=\frac{\left(1+{R}_{S}\left(2{g}_{m1}+{R}_{S}\left({{g}_{m1}}^{2}+{\left({C}_{GS1}\omega \right)}^{2}\right)\right)\right){\left({g}_{m2}{R}_{{L}_{d2}}{L}_{d2}\omega \right)}^{2}}{\left(1+{\left({g}_{m2}{L}_{d1}\omega \right)}^{2}\right)\left({\left({L}_{d2}\omega \right)}^{2}+{{R}_{{L}_{d2}}}^{2}{\left({L}_{d2}{C}_{out}{\omega }^{2}-1\right)}^{2}\right){\left({g}_{m1}{R}_{S}\right)}^{2}}$$
(16)

Considering \({{R}_{{L}_{d2}}}^{2}{\left({L}_{d2}{C}_{out}{\omega }^{2}-1\right)}^{2}\gg {\left({L}_{d2}\omega \right)}^{2}\), we can rewrite Eq. 16 as Eq. 17:

$${\left|\frac{{v}_{out}}{{v}_{n}}\right|}^{2}=\frac{\left(1+{R}_{S}\left(2{g}_{m1}+{R}_{S}\left({{g}_{m1}}^{2}+{\left({C}_{GS1}\omega \right)}^{2}\right)\right)\right){\left({g}_{m2}{L}_{d2}\omega \right)}^{2}}{\left(1+{\left({g}_{m2}{L}_{d1}\omega \right)}^{2}\right){\left({g}_{m1}{R}_{S}\left({L}_{d2}{C}_{out}{\omega }^{2}-1\right)\right)}^{2}}$$
(17)

Finally, by replacing Eq. 17 and Eq. 14 in Eq. 15 and performing a few manipulations, the NF is extracted as follows.

$$NF\approx 1+\frac{{\gamma }_{1}\left(1+{g}_{m1}{R}_{S}\right)\left(\left({{A}_{1}A}_{2}\left({A}_{1}{A}_{3}{{R}_{{L}_{d2}}}^{2}+2{A}_{4}{{L}_{d2}}^{2}{\omega }^{2}\right)+{A}_{4}{{L}_{d2}}^{2}{\omega }^{2}\right)\right)}{{\left({A}_{3}{R}_{{L}_{d2}}\right)}^{2}{\left({g}_{m1}{R}_{S}\right)}^{3}\left(1+{\left({g}_{m2}{L}_{d1}\omega \right)}^{2}\right)}$$
(18)

where \({A}_{1}\), \({A}_{2}\), \({A}_{3}\) and \({A}_{4}\) are identical to gm2rO1, (Ld2CGD1 ω2-1), (Ld2Coutω2-1), and (gm2Ld1(Ld2Coutω2-1)), respectively.

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Soleimani, F., Shamsi, H. Low-voltage and low-power Ku-band CMOS LNA using capacitive feedback. Analog Integr Circ Sig Process 109, 435–447 (2021). https://doi.org/10.1007/s10470-021-01922-y

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