# Design and Analysis of a Continuously Tunable Low Noise Amplifier for Software Defined Radio

^{*}

## Abstract

**:**

## 1. Introduction

_{m}. Common Source (CS) LNA with inductive degeneration increases the real part of input impedance. It further improves the overall gain and noise matching of the circuit. Figure 1 illustrates the concept of input tuning LNA using a conventional source degenerated narrowband LNA. Replacing gate inductor L

_{g}with a variable inductor ${L}_{g}^{\prime}$ provides reconfigurable input impedance matching and therefore variable minimum input return loss (S

_{11}) at different center frequencies. Nevertheless, implementing an LNA with ${L}_{g}^{\prime}$ will consume a large on chip area and hysteresis due to tunable inductor would degrade the overall Figure-of-Merit (FOM) of the LNA.

_{g}. Consequently, L

_{g}can be scaled by a factor that is proportional to the gain of the amplifier. However, adding additional amplifier increases the noise in the circuit and power consumption as well.

## 2. Motivation

_{in}is

_{1}, respectively. The resonant frequency of input matching network depends on ${C}_{gs1}$, ${L}_{g}$ and source inductor ${L}_{s}$. The resonant frequency at which ${Z}_{in}$ is real can be determined as

_{x}is equivalent capacitance of ${C}_{gs1}$ and C

_{1}. It can be concluded from Equations (4) and (5) that Z

_{in}and f

_{0}can be made tunable by either varying L

_{s}and L

_{g}. Since, Re(Z

_{in}) is directly proportional to L

_{s}, replacing L

_{g}with ${L}_{g}^{\prime}$ could be a viable solution. Nevertheless, additional amplification stage is required to make L

_{g}tunable or floating, which increases the die-area, implementation costs, NF and power consumption.

_{g}with a physical RF impedance transformer, whose secondary winding can act as a variable inductor. The secondary inductance can be changed through an additional circuit connected to the primary winding of transformer network. Using switching circuits with primary winding and inductive-capacitive resonant networks would not provide continuous tuning. Moreover, additional switching circuits shall increase power consumption and NF of the circuit. In this paper, we propose a CTLNA with tunable input matching network, comprising of a physical RF impedance transformer network. Input impedance can be varied to achieve minimum S

_{11}at each center frequency by changing the magnitude of current flowing through secondary winding of the transformer network. This can be achieved through magnetic coupling between primary and secondary windings of the transformer. Furthermore, the proposed LNA architecture comprises of an inductive load that provides a wideband response in the tuning range. This approach is expedient to maintain small area, continuous tuning and avoiding noise contributing elements in the signal path.

## 3. Proposed Circuit Topology

_{1}and a physical transformer. The second stage consists of a phase shifter network that comprises of two CG transistors connected in parallel to a CS transistor to get a relative 0° or 180° phase shift between the currents through primary and the secondary windings of the transformer. The third stage consists of tuning transistor whose bias voltage V

_{tune}can be varied to get the desired tunability. Finally, the fourth stage is the amplification stage that achieves a tunable wideband gain when V

_{tune}is varied. For better understanding of the proposed circuit topology, design and synthesis of each stage is described as follows.

#### 3.1. Transformer Network

_{u}is connected to the output of tuning transistor, while the other end is connected to the voltage supply V

_{DD2}= 1.3 V. The secondary winding L

_{d}is connected to the input transistor via a DC bias network. If L

_{d}is considered as a variable inductor as shown in Figure 2, then scaling its value will provide a 50 Ω impedance matching at different center frequencies. The design utilizes a similar concept by implementing an RF impedance transformer in place of a variable inductor. Therefore, frequency reconfigurability can be achieved if current passing through L

_{d}can be changed. The magnetism property of transformer can be utilized [22] to change current through L

_{d}. However, the currents i

_{1}and i

_{2}through L

_{u}and L

_{d}must have a relative phase shift ϕ of either 0° or 180° to allow continuous frequency tunability. This is because the RF impedance transformer circuit, shown in Figure 3a, provides a 50 Ω impedance match at a phase difference of 0° or 180° and the impedance is purely real at ϕ = 0°.This can be substantiated by deriving the relationship between transformer’s input impedance ${Z}_{inT}(\omega )$ and $\varphi $. From the simplified transformer network shown in Figure 3b and ${Z}_{inT}(\omega )$ can be given as

_{c}= 0.91 Ω, β = 1, ω = 2πf, f = 3 GHz, L

_{t1}= 3.37 nH, M = 0.5 nH, C = 995 fF and plotting $\mathrm{Re}({Z}_{in})$ vs. $\varphi $ from 0° to 360°, we can verify that $\left|\mathrm{Re}({Z}_{in})\right|$ = 50 Ω at 0° and 180° as shown in Figure 4a, despite the fact that our transformer model is different to that in [22].

_{1}and i

_{2}; however, the desired relative phase shift between i

_{1}and i

_{2}is 0° for continuous tuning. Moreover, the amplified signal is an inverted version of input signal. A possible solution is a phase shifter circuit that can provide a phase mismatch of 0° to ensure that currents ${i}_{1}$ and ${i}_{2}$ are in phase. The resonant frequency ${f}_{T}$ of transformer can be determined as

#### 3.2. Phase Shifter

_{21}(ω) depends upon inductor L

_{p}and capacitor C

_{p}. The shift in phase of the signal with constant signal amplitude is accomplished by variation in inductance or capacitance of the resonant circuit. The values of L

_{p}and C

_{p}for 2.2 to 2.8 GHz band are 17.5 nH and 10 pF, respectively. Figure 6 shows variation of phase of S

_{21}(ω) of APS with V

_{X}. The circuit provides a more than 90° phase shift in our desired frequency range.

#### 3.3. Tuning Stage

_{u}of transformer network in the input stage. Varying the bias voltage (${V}_{tune}$) of tuning transistor Q

_{6}continuously leads to incessant variation in its drain current ${i}_{d6}$. This further leads to variation in current ${i}_{1}$ flowing through ${L}_{u}$ and resultantly in α and β. Figure 7b shows the variation of ${i}_{d6}$ with ${V}_{tune}$. The resultant change in ${Z}_{inT}$ (depends on β) varies the input impedance of CTLNA, leading to continuous tunability.

## 4. Circuit Analysis

_{t}, L

_{p}and k values in transformer network are then selected to focus the desired operating band that ranges from 2.2 GHz to 2.8 GHz. One end of primary winding of the transformer in input stage is terminated with output from the tuning transistor, while the other end is connected to voltage supply. Input capacitor C

_{1}resonates with L

_{d}to achieve a continuously tunable impedance matching at different center frequencies. Continuous tuning shall only take place when ${i}_{1}$ and ${i}_{2}$ are in phase. The input of APS circuit is connected to the drain of Q

_{1}via L

_{3}–C

_{3}network. It provides a phase mismatch of 0° between the currents ${i}_{1}$ and ${i}_{2}$ through L

_{u}and L

_{d}. The output of APS is fed to gate of Q6 whose drain terminal further connects to L

_{u}to achieve tunable input matching.

_{1}. For simplicity, a fixed inductor ${L}_{2}$ was adopted in the output loading section of LNA to achieve a wideband gain. A large resistance ${R}_{1}$ is added in parallel to ${L}_{2}$ for improving LNA stability at different frequencies and DC voltage gain.

#### 4.1. Input Impedance

_{1}and the transformer network. Secondary inductor L

_{d}can be considered as a tunable inductor ${L}_{g}^{\prime}$ that replaces L

_{g}in Figure 1 to achieve tunable input impedance. As L

_{d}cannot be directly varied, magnetic coupling can be utilised to vary the input impedance of LNA. Since ${Z}_{inT}\left(\omega \right)$ depends on α, the input impedance of CTLNA in Figure 8 is derived as

_{x}is equivalent capacitance of ${C}_{gs1}$ and C

_{1}. Equation (17) shows that ${f}_{op}$ depends on constants L

_{d}, L

_{s}, M, ${C}_{gs1}$ and variable α. The value of α can be varied by changing ${V}_{tune}$ that controls ${i}_{d6}$ and ${i}_{1}$. Note that the real part of input impedance depends on L

_{s}and can be changed by varying L

_{s}only. Its value has been selected to ensure that ${Z}_{in}$ is matched to the source. The quality factor of input matching network $\left({Q}_{in}\right)$ is one of the primary elements used to determine the bandwidth of network. For the designed CTLNA, ${Q}_{in}$ can be expressed as

_{in}becomes smaller.

#### 4.2. Gain

_{g}is replaced with a transformer based variable inductor L

_{d}and its impedance ${Z}_{inT}\left(\omega \right)$ depends on M and α. The output loading network is similar to a conventional load. The low noise voltage gain for CTLNA can be derived from its small signal model of input and amplification stage shown in Figure 9. For cascode LNAs, since all transistors are the same,

_{2}and ${V}_{T}$ is the threshold voltage of implemented Philips MOS transistor. The small signal voltage gain ${A}_{v}$ of an LNA is defined as

_{in}expands to

_{2}. Equation (27) substantiates that ${A}_{v}$ for the designed CTLNA depends on α and eventually on ${V}_{tune}$. Hence the gain can also be tuned continuously in the desired band by sweeping ${V}_{tune}$ from 0.5 V to 1.5 V.

#### 4.3. Noise Figure

_{2}, Q

_{3}and Q

_{4}in parallel and ${V}_{n,s}$ is the noise voltage at source. The short circuit noise current due to thermal drain noise of transistor Q

_{1}, Q

_{2}in amplification stage is

_{1}and Q

_{2}. The transistors Q

_{3}, Q

_{4}and Q

_{5}in the PS circuit also contribute to the overall NF of CTLNA. Therefore, short circuit noise current due to drain noise of Q

_{3}, Q

_{4}and Q

_{5}is

_{6}is

_{3}, Q

_{4}, Q

_{5}and Q

_{6}and ${i}_{n,rl}$ is the noise current of load resistance R

_{L}. Using (28) to (33), F for the proposed LNA can be derived as

## 5. Results and Discussion

_{11}achieves a peak minimum for all different values of ${V}_{tune}$ from 0.5 V to 1.5 V in steps of 0.2 V. It is below −10 dB at each center frequency for the entire tuning range and achieves as low as −40.4 dB at 2.57 GHz at ${V}_{tune}$ = 1.2 V.

_{2}. However, due to its dependency on $\alpha $ it can be tuned to different frequencies from 2.2 to 2.8 GHz. In addition, the CTLNA gain depends upon ${g}_{m1}$, ${g}_{m2}$, ${C}_{gs1}$ source degeneration inductor ${L}_{s}$, and designed transformer parameters. The LNA achieves a maximum gain of 18 dB at 2.36 GHz in the stipulated tuning range. The minimum gain at 2.2 GHz center frequency is approximately 8 dB. Transistors Q

_{7}and Q

_{8}in the buffer stage are capable enough to stabilize the LNA and achieve high output impedance.

_{22}is less than -8dB in the tuning range and achieves a peak minimum at center frequency of 2.35 GHz, which is the resonant frequency of output matching network. The reverse isolation S

_{12}also remains more than 30dB across the tuning range. Figure 11c shows the variation of S

_{12}and S

_{22}with frequencies of selected band.

_{tune}, respectively. It is clear from Figure 12b that minimum NF at each center frequency varies between 1.4 dB to 4.8 dB. NF is a bit higher for 2.2 GHz and 2.3 GHz, which are initial frequencies in the tuning range. However, it is lower than 2 dB at center frequencies ranging from 2.4 GHz to 2.8 GHz.

_{t}> 1 is a single variable criterion to determine the unconditional stability of LNA [24]. Subsequently, the LNA is stable in the entire tuning range. Figure 13 shows variation of K with V

_{tune}at different center frequencies.

_{1dB}and third-order intercept point IP

_{3}. Non-linearities in the system lead to gain-compression that causes the LNA gain to deviate from the normal curve. P

_{1dB}and IIP

_{3}calculations have been performed using 1-tone and 2-tone inputs, respectively. A non-linear model of the amplifier is analyzed with a frequency offset of 10 MHz between two tones. The source and load impedances have been set to 50 Ω, while the harmonic frequency was selected to be 2.4 GHz. IP

_{3}and P

_{1dB}values for the designed CTLNA, range between −15 dBm to −31 dBm and −25 dBm to −42 dBm, respectively. Figure 14 shows the variation of P

_{1dB}with V

_{tune}in steps of 0.1V for the proposed CTLNA.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Bazrafshan, A.; Taherzadeh-Sani, M.; Nabki, F. A 0.8–4-GHz Software-Defined Radio Receiver With Improved Harmonic Rejection Through Non-Overlapped Clocking. IEEE Trans. Circuits Syst. I Regul. Pap.
**2018**, 65, 3186–3195. [Google Scholar] [CrossRef] - Adom-Bamfi, G.; Entesari, K. A multiband low noise amplifier with a switchable Gm active shunt feedback for SDRs. In Proceedings of the IEEE Radio and Wireless Symposium (RWS), Austin, TX, USA, 24–27 January 2016; pp. 179–182. [Google Scholar]
- Aneja, A.; Li, X.J.; Li, B.E. Design of Continuously Tunable Low Noise Amplifier for Multiband Radio. In Proceedings of the 2017 Mediterranean Microwave Symposium (MMS), Marseille, France, 28–30 November 2017; pp. 1–4. [Google Scholar]
- Yu, X.; Neihart, N.M. A 2–11 GHz reconfigurable multi-mode LNA in 0.13 µm CMOS. In Proceedings of the IEEE Radio Frequency Integrated Circuits Symposium (RFIC), Montreal, QC, Canada, 17–19 June 2012; pp. 475–478. [Google Scholar]
- El-Nozahi, M.; Sanchez-Sinencio, E.; Entesari, K. A CMOS low-noise amplifier with reconfigurable input matching network. IEEE Trans. Microw. Theory Tech.
**2009**, 57, 1054–1062. [Google Scholar] [CrossRef] - Wu, C.-R.; Hsieh, H.-H.; Lai, L.-S.; Lu, L.-H. A 3–5 GHz frequency-tunable receiver frontend for multiband applications. IEEE Microw. Wirel. Compon. Lett.
**2008**, 18, 638–640. [Google Scholar] [CrossRef] - Kwon, K.; Kim, S.; Son, K.Y. A Hybrid Transformer-Based CMOS Duplexer With a Single-Ended Notch-Filtered LNA for Highly Integrated Tunable RF Front-Ends. IEEE Microw. Wirel. Compon. Lett.
**2018**, 28, 1032–1034. [Google Scholar] [CrossRef] - Wang, J.-J.; Chen, D.-Y.; Wang, S.-F.; Wei, R.-S. A multi-band low noise amplifier with wide-band interference rejection improvement. AEU-Int. J. Electron. Commun.
**2016**, 70, 320–325. [Google Scholar] [CrossRef] - Zokaei, A.; Amirabadi, A. A dual-band common-gate LNA using active post distortion for mobile WiMAX. Microelectron. J.
**2014**, 45, 921–929. [Google Scholar] [CrossRef] - Neihart, N.M.; Brown, J.; Yu, X. A dual-band 2.45/6 GHz CMOS LNA utilizing a dual-resonant transformer-based matching network. IEEE Trans. Circuits Syst. I Regul. Pap.
**2012**, 59, 1743–1751. [Google Scholar] [CrossRef] - Yu, X.; Neihart, N.M. Analysis and design of a reconfigurable multimode low-noise amplifier utilizing a multitap transformer. IEEE Trans. Microw. Theory Tech.
**2013**, 61, 1236–1246. [Google Scholar] [CrossRef] - Fu, C.-T.; Ko, C.-L.; Kuo, C.-N.; Juang, Y.-Z. A 2.4–5.4-GHz wide tuning-range CMOS reconfigurable low-noise amplifier. IEEE Trans. Microw. Theory Tech.
**2008**, 56, 2754–2763. [Google Scholar] - Kia, H.B.; A’ain, A.K.; Grout, I.; Kamisian, I. A reconfigurable low-noise amplifier using a tunable active inductor for multistandard receivers. CircuitsSyst. Signal Process.
**2013**, 32, 979–992. [Google Scholar] [CrossRef] - Wu, C.-R.; Lu, L.-H. A 2.9-3.5-GHz tunable low-noise amplifier. In Proceedings of the IEEE Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems, San Diego, CA, USA, 18–20 January 2006. [Google Scholar]
- Beare, R.; Plett, C.; Rogers, J. Highly reconfigurable single-ended low noise amplifier for software defined radio applications. In Proceedings of the IEEE 10th International New Circuits and Systems Conference (NEWCAS), Montreal, QC, Canada, 17–20 June 2012; pp. 549–552. [Google Scholar]
- Chen, Z.; Zhang, X.; Song, Z.; Jia, W.; Chi, B. A 1.0–5.0 GHz tunable LNA with automatic frequency calibration in 65 nm CMOS. In Proceedings of the 2016 IEEE International Symposium on Radio-Frequency Integration Technology (RFIT), Taipei, Taiwan, 24–26 August 2016; pp. 1–3. [Google Scholar]
- Emami, N.; Arshed, O.; Bakri-Kassem, M.; Albasha, L. Reconfigurable low noise amplifier using MEMS varactor. In Proceedings of the 2013 8th International Conference on Design & Technology of Integrated Systems in Nanoscale Era (DTIS), Abu Dhabi, UAE, 26–28 March 2013; pp. 145–150. [Google Scholar]
- Akbar, F.; Atarodi, M.; Saeedi, S. Design method for a reconfigurable CMOS LNA with input tuning and active balun. AEU-Int. J. Electron. Commun.
**2015**, 69, 424–431. [Google Scholar] [CrossRef] - Macias-Bobadilla, G.; Rodríguez-Reséndiz, J.; Mota-Valtierra, G.; Soto-Zarazúa, G.; Méndez-Loyola, M.; Garduño-Aparicio, M. Dual-Phase Lock-In Amplifier Based on FPGA for Low-Frequencies Experiments. Sensors
**2016**, 16, 379. [Google Scholar] [CrossRef] - Brown, J. Design of a Magnetically Tunable Low Noise Amplifier in 0.13 um CMOS Technology; Iowa State University: Ames, IA, USA, 2012. [Google Scholar]
- Gómez-Espinosa, A.; Hernández-Guzmán, V.M.; Bandala-Sánchez, M.; Jiménez-Hernández, H.; Rivas-Araiza, E.A.; Rodríguez-Reséndiz, J.; Herrera-Ruíz, G. A New Adaptive Self-Tuning Fourier Coefficients Algorithm for Periodic Torque Ripple Minimization in Permanent Magnet Synchronous Motors (PMSM). Sensors
**2013**, 13, 3831–3847. [Google Scholar] [CrossRef] [PubMed][Green Version] - Brown, J.L.; Neihart, N.M. An analytical study of a magnetically tuned matching network. In Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), Seoul, Korea, 20–23 May 2012; pp. 1979–1982. [Google Scholar]
- Hayashi, H.; Mauraguchi, M. An MMIC active phase shifter using a variable resonant circuit [and MESFETs]. IEEE Trans. Microw. Theory Tech.
**1999**, 47, 2021–2026. [Google Scholar] [CrossRef] - Tan, E.L. A quasi-invariant single-parameter criterion for linear two-port unconditional stability. IEEE Microw. Wirel. Compon. Lett.
**2004**, 14, 487–489. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Conceptual representation of a conventional input tuning LNA with L

_{g}(

**b**) Corresponding varying S

_{11}for different values of L

_{g}. (

**c**) Small signal equivalent of conventional LNA.

**Figure 3.**(

**a**) Physical transformer equivalent circuit for designed CTLNA (

**b**) simplified transformer model for calculations.

**Figure 4.**(

**a**) $\mathrm{Re}\left({Z}_{in}\right)$, (

**b**) $\mathrm{Im}\left({Z}_{in}\right)$ as a function of $\varphi $.

**Figure 11.**Simulated (

**a**) input return loss (S

_{11}) (

**b**) Gain (S

_{21}) (

**c**) Reverse isolation (S

_{12}) and output return loss (S

_{22}).

Parameter | Value |
---|---|

Turns Ratio ‘N’ | 0.69 |

Magnetising Inductance ‘L_{tp}’ | 2.23 nH |

Cross loss resistance ‘R_{c}’ | 1000 $\mathsf{\Omega}$ |

Coefficient of Coupling ‘k’ | 0.11 |

Primary loss resistance ‘R_{t1}’ | 0.91 $\mathsf{\Omega}$ |

Secondary loss resistance ‘R_{t2}’ | 4.47 $\mathsf{\Omega}$ |

Primary capacitance ‘C_{t1}’ | 924 fF |

Secondary capacitance ‘C_{t2}’ | 150 fF |

Interwinding capacitance ‘C_{t}’ | 340 fF |

Ref. | Freq. (GHz) | S_{21} (dB) | S_{11} (dB) | NF (dB) | IP_{3} (dBm) | V_{DD} | Tech. | P_{DC} (mW) |
---|---|---|---|---|---|---|---|---|

This work | 2.2–2.8 | 7–18 | −40–−11 | 1.4–4.8 | −31–15 | 1.8 | MIC | 16.2 |

[16] | 1–5 | 19–27 | −18–−5 | 2.4–3.8 | - | 1.2 | 65 nm CMOS | 12.1 |

[5] | 1.9–2.4 | 10–14 | −25–12 | 3.2–3.7 | −6.7 | 1.2 | 0.13 µm CMOS | 17 |

[12] | 2.4–5.4 | 9.9–22 | −14–−30 | 2.4–4.9 | −20.4–−9.7 | 1 | 0.13 µm CMOS | 3.1–4.6 |

[13] | 0.8–2.5 | 17–20 | −27–−11 | 3.1–3.6 | - | 1.8 | 0.18 µm CMOS |

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**MDPI and ACS Style**

Aneja, A.; Li, X.J.
Design and Analysis of a Continuously Tunable Low Noise Amplifier for Software Defined Radio. *Sensors* **2019**, *19*, 1273.
https://doi.org/10.3390/s19061273

**AMA Style**

Aneja A, Li XJ.
Design and Analysis of a Continuously Tunable Low Noise Amplifier for Software Defined Radio. *Sensors*. 2019; 19(6):1273.
https://doi.org/10.3390/s19061273

**Chicago/Turabian Style**

Aneja, Aayush, and Xue Jun Li.
2019. "Design and Analysis of a Continuously Tunable Low Noise Amplifier for Software Defined Radio" *Sensors* 19, no. 6: 1273.
https://doi.org/10.3390/s19061273