# Design and Performance Analysis of W-Band Low Noise Amplifier for RFIC-5G Mobile Systems

Authors: Abdelaziz Hamdi
Journal: Mobile Information Systems
 (2022)

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## Abstract

This paper presents a new approach of the design of a W-band low noise amplifier (LNA) in a 0.13 µm CMOS technology for narrowband and wideband applications. The proposed LNA utilizes input matching bandwidth extensions based on the source degeneration topology, and it is designed and optimized at a center frequency of 94 GHz and a supply voltage of 1.2 V. The obtained results exhibit a noise figure of 3 dB, a power gain of 32 dB, and a VSWR of 1.1. The design technique of this LNA is based on an agreeable tradeoff between the available gain of 30 dB and the noise figure of 3 dB, which leads to good bilateral stability and high linearity described by an input third-order intercept point of -17 dBm. A detailed performance analysis is presented and discussed along this paper. With the aim of a complete and robust integration, all lumped elements and transmission lines are integrated on a silicon PCB havingɛr = 11.7 and a dielectric loss TanΔ = 0.001 for low manufacturing costs. The prominent results of this LNA indicate that it is suitable for 94 GHz-image-radar and RFIC-5G mobile systems.


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## Body

## 1. Introduction

During the past years, massive efforts have been made to obtain optimally designed radio-frequency integrated circuits (RFIC) operating at millimeter-wave bands, addressed to the wide range of 5G use cases and applications. The obtained results have motivated researchers to develop diverse 5G integrated-circuits with limited supply voltages (1-2 V) and ultra-low power consumption [1, 2]. In this context, the low noise amplifier (LNA) is a very important component in RFIC. This is the first block in a receiver whose primary function is to provide enough gain to overcome noise from subsequent blocks (such as the filter and the mixer), but not too much so as not to overload the mixer. In addition, LNA based on CMOS technologies should provide good linearity as demonstrated in [3, 4]. It should have also a specific impedance, conventionally 50 Ω, at the input source and at the output load. Moreover, LNA should provide low-power consumption especially for portable systems and 5G-enabled IoT devices [5, 6]. As W-band LNA applications, Li et al. [7] and Xue et al. [8] proposed various LNA structures for automotive radars.For CMOS technologies [9], these new RFIC potentialities must be added to a series of useful RFICs on insulating silicon substrates despite the high permittivity of silicon (ɛr ≈ 11.7 @ 94 GHz). Among these advantages, we can cite much lower substrate drain and substrate source diffusion capacities, better integration density, strong reduction in junction surfaces, and possibility of using high-resistive substrates to obtain passive devices (inductors) of high-quality factor. Moreover, the frequency performances and characteristics of CMOS devices have been continuously enhancing, and several RFIC/MMIC results using the CMOS technology operating in E/W-band have been published [10–14]. These prior LNAs have achieved acceptable performances but have been modest in terms of tradeoff between the gain and the noise figure (NF), as presented in [11], where G = 14.2 dB and NF = 6.3 dB. In our work, LNA is proposed with miniaturized RF inductors followed by microstrip-transmission-line input/output matching networks, as shown in the block diagram of Figure 1. The LNA core is composed of a cascode topology with a drain/source DC bias and stability circuits. The put/output matching networks are represented as a bandpass topology.Figure 1
Block diagram of proposed W-band LNA.The studied block is that LNA is the first element of the RF reception chain. In this context, the main aim of our work is to optimize the suggested model for low-power consumption with low-cost RF components for 94 GHz anti-collision radar. The application of the proposed LNA model is not limited only for 94 GHz systems but it is compatible to diverse applications over the W-band such as millimeter-wave radar [15] and radar targeting [16] search used for civilian [17, 18] and military purposes [19, 20], satellite communications [21, 22], and various military and civilian geo-tracking applications [23]. To improve these previous applications, the suggested LNA has advantages in terms of power consumption and gain with the NF cost. Moreover, this work gives a good tradeoff between the gain and NF with relatively high LNA linearity, like the results obtained by Li et al. in [24]. Besides, the input/output matching networks, device parameters, LC components, and biasing points have been designed to get the effective results. Thus, the proposed amplifier is designed with standard microelectronic procedures for low cost, all with the aim of achieving a good performance compared to prior research exposed in [3, 4, 11, 13, 14, 24, 25], as summarized in Subsection 5.4 of this manuscript.This paper is structured as follows: Section2 deals with the suggested LNA modeling and its design parameters. Section 3 gives polarization circuits with a DC/RF stopper and the corresponding LNA matching networks. Section 4 concludes the modeling and design techniques with the performance analysis of the proposed LNA. Section 5 exposes the obtained results and the discussion. Section 6 draws the conclusions presented as opportunities for research. Finally, all results are performed by Cadence and advanced design systems (ADS) simulators.


## 2. Proposed LNA Design

The most important step in designing LNA with the desired performances is the choice of the transistor. Various transistor topologies are available for LNA applications. In this context, the suitable transistor should be designated for a good tradeoff between the high gain (G) and the low NF. In practice, the operation frequency is crucial to limit the number of transistors. Figure 2 shows the electronic circuit of the integrated amplifier. The configuration used is a common source (T1) structure with inductive degeneration.Figure 2
Topology of proposed LNA.Before going to the presented analysis and techniques of the suggested LNA, it will be useful to first investigate the topology of the source degeneration cascode LNA, as explored in detail in [26, 27]. In general, the source degeneration LNA, represented by the series source inductor «Ls» of Figure 2, ensures bilateral stability, good input matching, and a low NF by utilizing Ls degeneration to realize 50-Ω input impedance, but without inducing resistive thermal noise.This configuration presents a good compromise between NF, the gain, and the stability of LNA. The output load is by convention resistive 50 Ω tuned to the working frequency 94 GHz. The addition of a cascode stage (T2) guarantees the isolation between the output and the input of the stage, and it prevents any problem of instability at a high frequency. The input power adaptation is carried out thanks to inductorsL6 and L8 which cancel the capacitive part Cin of the input impedance Zin and adjust the real part of Zin to the value of 50 Ω at the pulse working ω0. At the output, the adaptation on a resistive load of 50 Ω is carried out by the capacitive divider C10–C13. The C8 and C10 capacitors prevent the stopper of the DC signal from dissipating in the RF generator. The role of the L7 inductor is to isolate the RF signal from DC. Inductors Li (i = 1, 2, 3, 4, 5, 10) model, the interconnecting conductors; transmission lines (TLi) (i = 1, 2, 3, 4, 5, 6) model, the package effect; and these lines are made up of distributed RLC elements where, R = 0.880 nΩ, L = 1 nH and C = 1.6 pF. Resistors Ri (i = 3, 4, 5) are used to bias the NMOS transistors T1 and T2 and ensure the stability of the amplifier at the operating frequency. However, it should be noted that the power adaptation is necessary to ensure the maximum transfer of power from the source to the load. The supply voltage is fixed at 1 V.There are several steps to follow the design of the RF amplifier [28]. First, choose the point of polarization without forgetting to isolate the DC signal and the RF signal from each other. Then, study the input/output stability of the transistor and stabilize it. If it is not already unconditionally stable, it must then choose a tradeoff between the available gain (Ga) and NF and find the input and output matching circuits that will achieve the desired performance. These steps lead to obtaining a mask for the final circuit.


## 3. Polarization and DC/RF Signal-Stopper Circuits

### 3.1. DC Bias and the Polarization Point

The problem of polarization is quite simple [28]. It is just to find Vgs which gives the transistor a bias current of 1.374 mA with VDS = 1.2 V. We use the complete electrical model of the transistor illustrated in Figure 3 for this DC simulation. Voltage Vgs is then 0.581 V.Figure 3
RF-signal stopper and DS-signal stopper.


### 3.2. RF/DC Signal Stopper

To avoid any loss of power of the RF signal, it must prevent this signal from going to dissipate in the polarization resistors of the gate and the drain. For this, we useλ/4 microstrip TL terminated by capacitors which must behave like a closed circuit at the operating frequency, as depicted in Figure 3.The end of this TL will be seen as an open circuit at the input ofλ/4 − TL. This TL must have a very large characteristic impedance compared to the impedance of the capacitor. By optimization, the width of this TL is equal to 152.4 µm and the capacitance is equal to 0.1 pF. According to the obtained results of the reflection coefficient S11 listed in Table 1, LNA is properly polarized at 94 GHz without lossless power.Table 1
Reflection coefficientS11 at input of polarization circuits of the gate and the drain.
Frequency (GHz)S11, gateS11, drain940.988/0.00080.993/0.0009


## 3.1. DC Bias and the Polarization Point

The problem of polarization is quite simple [28]. It is just to find Vgs which gives the transistor a bias current of 1.374 mA with VDS = 1.2 V. We use the complete electrical model of the transistor illustrated in Figure 3 for this DC simulation. Voltage Vgs is then 0.581 V.Figure 3
RF-signal stopper and DS-signal stopper.


## 3.2. RF/DC Signal Stopper

To avoid any loss of power of the RF signal, it must prevent this signal from going to dissipate in the polarization resistors of the gate and the drain. For this, we useλ/4 microstrip TL terminated by capacitors which must behave like a closed circuit at the operating frequency, as depicted in Figure 3.The end of this TL will be seen as an open circuit at the input ofλ/4 − TL. This TL must have a very large characteristic impedance compared to the impedance of the capacitor. By optimization, the width of this TL is equal to 152.4 µm and the capacitance is equal to 0.1 pF. According to the obtained results of the reflection coefficient S11 listed in Table 1, LNA is properly polarized at 94 GHz without lossless power.Table 1
Reflection coefficientS11 at input of polarization circuits of the gate and the drain.
Frequency (GHz)S11, gateS11, drain940.988/0.00080.993/0.0009


## 4. Analysis and Design of Proposed LNA

### 4.1. Input Impedance

To facilitate the analysis of the LNA circuit, we take the assembly of Figure4(a). This stage presents a common source amplifier with Ls inductance around of 1 nH, inserted between the source and the ground to control the real part of the input impedance. From Figure 4(b), we can extract all physical parameters related to the input impedance (Zin) as follows:(1)V˙x=I˙xjωCgs+jωLsI˙x+gmV˙gs.Figure 4
(a) A circuit with inductor (LS) at the LNA-Source, (b) an equivalent electronic model.
(a)(b)From equation (1), the input impedance (Zin) can be demonstrated as(2)V˙xI˙x=Zjω=1jωCgs+jωLs+gmLsCgs.This impedance which is a series RLC-network is proportional to the value of the inductance LS. It is important to consider that thisLs inductor does not bring thermal noise back to the amplifier circuit because a pure reactance is noise free. This impedance is then purely resistive at a single frequency (at resonance). However, this method can be used in circuits operating at a narrow band.


### 4.2. Input Matching Network

In order to maximize the performance of the circuit and ensure a maximum power transfer from the input-source to load (ZL), it is necessary to design a matching network to match the output impedance of the source-RF-generator (Zg) to the input impedance (Zin) of LNA, where Zg = Zin∗ and Zg = Rs. To achieve this task: (i) we create an impedance of 50 Ω, and (ii) design a resonant circuit with inductance Ls and capacitance Cgs at the resonant frequency 94 GHz. It is often difficult to obtain resonance with these two elements. For this, we add inductance Lg, as shown in Figure 5.Figure 5
Input matching network.To obtain an impedance of 50 Ω, a fine tuning can be introduced on inductanceLg.Let us now consider the circuit presented by Figure6 with the presence of source V. Therefore, we can write as(3)v=vgs+gmvgsZ.Figure 6
Analytical circuits of the matching network.That gives(4)vgs=v1+gmZ,(5)iout=gmvgs=gm1+gmZv.Using expression equation (2) and Figure 6(b), we can write as(6)Zin=1Cgs⋅jω+jωLs+ωTLs,where ωT=gm/Cgs.Suppose now that the resonance is completed byLg and Ls, then we get(7)1−ω02Lg+LsCgs≈1−LgCgsω02=0,(8)ω0≈1Lg+LsCgs.We can neglect term−LgCgsω02, so we directly obtain the gain of the LNA circuit:(9)Gmjω0=gmjω0CgsRs+ωTLs.


### 4.3. NF Analysis

After ensuring the maximum transfer of power from the source-RF-generator to the load, it is essential to evaluate the NF of the circuit. To calculate this parameter, it must evaluate the current at the output of the circuit, while assuming that there is a short circuit at the output of LNA. To achieve this, it must determine the transfer function (transconductance) from the input to the output of the circuit at the resonant frequency which is set at 94 GHz in the spectral (frequency) domain. From equation (9), we can define the function of the spectral density function (SDF). For the resistance (Rs = Zg) and in terms of voltage, the spectral density is(10)v¯s2Δf=4kTRs.By multiplying this expression (SDF) by the squared transconductance, we obtain the first component of the SDF in terms of output-current such that we get(11)i¯o12Δf=4kTRsωTω0211+ωTLs/Rs2.Gate-current (io1) can be analyzed using Figures6(a)–6(b). Then, gate-current (io1) can be expressed as(12)i¯o12Δf=4kTδgg1−c2.This expression shows us that there is a relation between the output-current component (io2) and the gate-current (ig), which can be written as follows:(13)io21+gmLsjωCcsjωRs+jωLg+Ls=igugmjωCgsRs+jωLg+LsRs+jωLg+Ls+1/jωCgs.From this equality, the spectral density of the current at output (io2) can be expressed as follows:(14)i¯o22Δf=i¯gu2Δf11+ωTLs/Rs2ωTω01+QL2,with QL=Lg+Lsω0/Rs=1/ω0RsCgs and gg=ω02Cgs2/5gd0.Using the circuit illustrated by Figure7, we can determine the noise which accompanies the current of drain (id) with SDF using equation (10):(15)i¯d2Δf=4kTγgd0.Figure 7
Analytical circuits of NF evaluation.
(a)(b)(c)The current at output (io2) of the transistor can be expressed as follows:(16)iot2Δf=4kTηγgdo1+ωTLs/Rs2,where(17)η=κ+ξ=1+2cQLδα25γ+δα25γ1+QL2,κ=δα25γc2+1+cQLδα25γ2,ξ=δα25γ1−c21+QL2,α=gmgdo.Finally, the NF of the proposed LNA circuit can be expressed as(18)NF=1+ηγgdoRsωoωT2.


## 4.1. Input Impedance

To facilitate the analysis of the LNA circuit, we take the assembly of Figure4(a). This stage presents a common source amplifier with Ls inductance around of 1 nH, inserted between the source and the ground to control the real part of the input impedance. From Figure 4(b), we can extract all physical parameters related to the input impedance (Zin) as follows:(1)V˙x=I˙xjωCgs+jωLsI˙x+gmV˙gs.Figure 4
(a) A circuit with inductor (LS) at the LNA-Source, (b) an equivalent electronic model.
(a)(b)From equation (1), the input impedance (Zin) can be demonstrated as(2)V˙xI˙x=Zjω=1jωCgs+jωLs+gmLsCgs.This impedance which is a series RLC-network is proportional to the value of the inductance LS. It is important to consider that thisLs inductor does not bring thermal noise back to the amplifier circuit because a pure reactance is noise free. This impedance is then purely resistive at a single frequency (at resonance). However, this method can be used in circuits operating at a narrow band.


## 4.2. Input Matching Network

In order to maximize the performance of the circuit and ensure a maximum power transfer from the input-source to load (ZL), it is necessary to design a matching network to match the output impedance of the source-RF-generator (Zg) to the input impedance (Zin) of LNA, where Zg = Zin∗ and Zg = Rs. To achieve this task: (i) we create an impedance of 50 Ω, and (ii) design a resonant circuit with inductance Ls and capacitance Cgs at the resonant frequency 94 GHz. It is often difficult to obtain resonance with these two elements. For this, we add inductance Lg, as shown in Figure 5.Figure 5
Input matching network.To obtain an impedance of 50 Ω, a fine tuning can be introduced on inductanceLg.Let us now consider the circuit presented by Figure6 with the presence of source V. Therefore, we can write as(3)v=vgs+gmvgsZ.Figure 6
Analytical circuits of the matching network.That gives(4)vgs=v1+gmZ,(5)iout=gmvgs=gm1+gmZv.Using expression equation (2) and Figure 6(b), we can write as(6)Zin=1Cgs⋅jω+jωLs+ωTLs,where ωT=gm/Cgs.Suppose now that the resonance is completed byLg and Ls, then we get(7)1−ω02Lg+LsCgs≈1−LgCgsω02=0,(8)ω0≈1Lg+LsCgs.We can neglect term−LgCgsω02, so we directly obtain the gain of the LNA circuit:(9)Gmjω0=gmjω0CgsRs+ωTLs.


## 4.3. NF Analysis

After ensuring the maximum transfer of power from the source-RF-generator to the load, it is essential to evaluate the NF of the circuit. To calculate this parameter, it must evaluate the current at the output of the circuit, while assuming that there is a short circuit at the output of LNA. To achieve this, it must determine the transfer function (transconductance) from the input to the output of the circuit at the resonant frequency which is set at 94 GHz in the spectral (frequency) domain. From equation (9), we can define the function of the spectral density function (SDF). For the resistance (Rs = Zg) and in terms of voltage, the spectral density is(10)v¯s2Δf=4kTRs.By multiplying this expression (SDF) by the squared transconductance, we obtain the first component of the SDF in terms of output-current such that we get(11)i¯o12Δf=4kTRsωTω0211+ωTLs/Rs2.Gate-current (io1) can be analyzed using Figures6(a)–6(b). Then, gate-current (io1) can be expressed as(12)i¯o12Δf=4kTδgg1−c2.This expression shows us that there is a relation between the output-current component (io2) and the gate-current (ig), which can be written as follows:(13)io21+gmLsjωCcsjωRs+jωLg+Ls=igugmjωCgsRs+jωLg+LsRs+jωLg+Ls+1/jωCgs.From this equality, the spectral density of the current at output (io2) can be expressed as follows:(14)i¯o22Δf=i¯gu2Δf11+ωTLs/Rs2ωTω01+QL2,with QL=Lg+Lsω0/Rs=1/ω0RsCgs and gg=ω02Cgs2/5gd0.Using the circuit illustrated by Figure7, we can determine the noise which accompanies the current of drain (id) with SDF using equation (10):(15)i¯d2Δf=4kTγgd0.Figure 7
Analytical circuits of NF evaluation.
(a)(b)(c)The current at output (io2) of the transistor can be expressed as follows:(16)iot2Δf=4kTηγgdo1+ωTLs/Rs2,where(17)η=κ+ξ=1+2cQLδα25γ+δα25γ1+QL2,κ=δα25γc2+1+cQLδα25γ2,ξ=δα25γ1−c21+QL2,α=gmgdo.Finally, the NF of the proposed LNA circuit can be expressed as(18)NF=1+ηγgdoRsωoωT2.


## 5. Results and Discussion

### 5.1. S-Parameters and Gains

LNA is characterized by its S-parameters [29, 30], such that S11 and S22 give us the amounts of signals reflected at the input/output port. S21 indicates the signal transmission coefficient from the input to the output of the LNA amplifier. It also represents the gain of the amplifier at the operating frequency, after adaptation. S12 indicates the signal transmission coefficient from the output to the input of the LNA amplifier, and is also considered as inverse gain (S12). Figure 8 shows the simulation results of the S parameters. The reflection at input S11 is −14.75 dB, the reflection at output S22 is −19 dB, and the inverse gain (S12) is −34 dB and the forward gain (S21) is 32 dB at 94 GHz.Figure 8
S-parameters of proposed LNA, (a) input/output reflection coefficients (S11 and S22), (b) forward gain (S21) and inverse gain (S12).
(a)(b)These S-parameter results are rigorous enough to achieve the desired performance of LNA and confirm well that the proposed LNA is bilaterally stable and matched at frequencies between 90 and 100 GHz. However, the value ofS22 can be improved by making a fine tuning to the value of the load (ZL) at the output of LNA.


### 5.2. NF

NF varies as a function of the RF-generator impedances (Rs = Zg) and has a minimum NF min for an admittance called optimal (Yopt or Gopt). Figure 9 illustrates the NF of the suggested LNA and that for a frequency range from 90 GHz to 100 GHz, with an operating frequency of 94 GHz, where NF = 3 dB.Figure 9
NF simulation.


### 5.3. Third-Order Input Intercept Point

The third-order input intercept point (IIP3) is a very important parameter to evaluate the performance of LNA. It also determines the non-linearity of the amplifier. Figure10 shows that the value of IIP3 at a 94-GHz operating frequency is –16.78 dB.Figure 10
Third-order input intercept point (IIP3).


### 5.4. Comparison Results

The performance summary and the comparison results with other state of the art W-band LNA in silicon-based technologies are shown in Table2. It can be seen that our work accomplishes a high gain, a required NF, and a competitive linearity at the same time. The figure of merit (FoM) is calculated and simulated as mentioned by equation (3) [3]. Moreover, the obtained results are very promising for active RF devices over the W-band (from 75 GHz to 300 GHz) where ultra-large bands are needed.Table 2
Performance comparison of proposed LNA with existing LNAs operating in silicon-based technologies (post-simulation results).
Ref.[24] 2021[25] 2021[3] 2020[11] 2019[4] 2018[13] 2017[14] 2016This workF0 (GHz)7877927773.577.57894Gain (dB)21.33218.214.22018.51532NF (dB)5.511.85.86.345.57.43IIP3 (dBm)-14.5-8-27.4-10-22.8-15-30-16.7PDC (mW)5232.41633.510.8277.219FoM--150.1416.111.31.887.3


## 5.1. S-Parameters and Gains

LNA is characterized by its S-parameters [29, 30], such that S11 and S22 give us the amounts of signals reflected at the input/output port. S21 indicates the signal transmission coefficient from the input to the output of the LNA amplifier. It also represents the gain of the amplifier at the operating frequency, after adaptation. S12 indicates the signal transmission coefficient from the output to the input of the LNA amplifier, and is also considered as inverse gain (S12). Figure 8 shows the simulation results of the S parameters. The reflection at input S11 is −14.75 dB, the reflection at output S22 is −19 dB, and the inverse gain (S12) is −34 dB and the forward gain (S21) is 32 dB at 94 GHz.Figure 8
S-parameters of proposed LNA, (a) input/output reflection coefficients (S11 and S22), (b) forward gain (S21) and inverse gain (S12).
(a)(b)These S-parameter results are rigorous enough to achieve the desired performance of LNA and confirm well that the proposed LNA is bilaterally stable and matched at frequencies between 90 and 100 GHz. However, the value ofS22 can be improved by making a fine tuning to the value of the load (ZL) at the output of LNA.


## 5.2. NF

NF varies as a function of the RF-generator impedances (Rs = Zg) and has a minimum NF min for an admittance called optimal (Yopt or Gopt). Figure 9 illustrates the NF of the suggested LNA and that for a frequency range from 90 GHz to 100 GHz, with an operating frequency of 94 GHz, where NF = 3 dB.Figure 9
NF simulation.


## 5.3. Third-Order Input Intercept Point

The third-order input intercept point (IIP3) is a very important parameter to evaluate the performance of LNA. It also determines the non-linearity of the amplifier. Figure10 shows that the value of IIP3 at a 94-GHz operating frequency is –16.78 dB.Figure 10
Third-order input intercept point (IIP3).


## 5.4. Comparison Results

The performance summary and the comparison results with other state of the art W-band LNA in silicon-based technologies are shown in Table2. It can be seen that our work accomplishes a high gain, a required NF, and a competitive linearity at the same time. The figure of merit (FoM) is calculated and simulated as mentioned by equation (3) [3]. Moreover, the obtained results are very promising for active RF devices over the W-band (from 75 GHz to 300 GHz) where ultra-large bands are needed.Table 2
Performance comparison of proposed LNA with existing LNAs operating in silicon-based technologies (post-simulation results).
Ref.[24] 2021[25] 2021[3] 2020[11] 2019[4] 2018[13] 2017[14] 2016This workF0 (GHz)7877927773.577.57894Gain (dB)21.33218.214.22018.51532NF (dB)5.511.85.86.345.57.43IIP3 (dBm)-14.5-8-27.4-10-22.8-15-30-16.7PDC (mW)5232.41633.510.8277.219FoM--150.1416.111.31.887.3


## 6. Conclusion

A new approach of modeling and designing W-band LNA in silicon-based technologies has been presented in this paper. The suggested LNA design provides good performances and results compared with the existing work. Biasing point, stability, and matching network components have been designed to obtain better results at a 94-GHz frequency. A tradeoff between the gain and NF have been improved as 32 dB and 3 dB, respectively. Input/output return losses (S11 and S22) are less than −13 dB. Thus, this LNA exhibits a high linearity of −16.78 dBm at 94 GHz and good stability. In future work, power consumption can be reduced. The proposed model can be a good candidate for 5G-RFIC mobile systems.



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