# Noise-Cancelling CMOS Active Inductor and Its Application in  RF Band-Pass Filter Design

Authors: Santosh Vema Krishnamurthy; Kamal El-Sankary; Ezz El-Masry
Journal: International Journal of Microwave Science and Technology
 (2010)

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## Abstract

A CMOS active inductor with thermal noise cancelling is proposed. The noise of the transistor in the feed-forward stage of the proposed architecture is cancelled by using a feedback stage with a degeneration resistor to reduce the noise contribution to the input. Simulation results using 90 nm CMOS process show that noise reduction by 80% has been achieved. The maximum resonant frequency and the quality factor obtained are 3.8 GHz and 405, respectively. An RF band-pass filter has been designed based on the proposed noise cancelling active inductor. Tuned at 3.46 GHz, the filter features total power consumption of 1.4 mW, low noise figure of 5 dB, and IIP3 of −10.29 dBm.


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## Body

## 1. Introduction

Inductors, either passive or simulated by active devices are key components in Radio Frequency Integrated Circuits (RFIC) analog building blocks such as filters [1], oscillators [2], phase shifters [3], and low-noise amplifiers (LNA) [4]. As integrated circuit technologies are progressing, the usage of passive inductors is degrading due to their large chip area, low-quality factor, and less tunability. Mainly the inductor is the major chip area consuming building block [5]; the higher the inductance required, the higher the chip area. While tunability can be implemented using passive inductor and low-resistance switches, continuous tuning is not easily achieved. Due to these disadvantages, the concept of active inductors is becoming more attractive.Many proposed active inductor architectures using MOS transistors [1–5] can be found in the literature. Higher noise, nonlinearity and power consumption are the major disadvantages of active inductors due to the fact that these circuits are realized using active devices which have higher noise. Thermal noise cancelling (NC) has been successfully implemented in LNA circuits by cancelling the noise of their input transistors [6, 7]. In this paper, NC is applied to active inductor architecture. First the transistor contributing most of the noise of the active inductor is identified in the forward path of Gyrator-C structure, and its noise contribution is cancelled using the feedback path while the noise contribution of the latter to the input is degenerated by the inclusion of shielding resistor in the feedback. NC allows active inductors to be used in applications such as front-end active RF filter in receivers and also to design low-phase noise oscillators.The paper is organised as follows. In Section2, the NC active inductor is presented, as well as the principle of NC and simulation results. In Section 3, a differential second-order RF band-pass filter based on the proposed NC active inductor and its performance are demonstrated. Finally, the conclusion is given in Section 4.


## 2. NC Active Inductor Design

In the active inductor circuit shown in Figure1(a), M2 is identified as the transistor with the highest noise contribution.(a) Active Inductor Circuit without NC. (b) The ratio of output impedance to the respective gain at nodes 2 and 3.
(a)(b)


### 2.1. Noise Contribution of the TransistorM2

The circuit used to implement NC in active inductor is the Gyrator-C structure proposed in [1] and shown in Figure 1(a). In order to apply NC, we studied the noise contribution of each transistor and identified the transistor that has the highest percentage of noise to the total input referred noise. Usually in LNA, noise cancelling is applied to the input transistor. This is not the case of active inductors, and due to the back-to-back Gm structure a careful study is needed to identify the transistor that contributes the highest noise at the frequency of interest.The noise current ofM2 is modelled as the current source In,M2, between nodes 2 and 3 in Figure 1(a). For better understanding, we have shown the noise of M2 as two current sources, one flowing out of node 3 and other flowing into node 2 [8]. From noise analysis and simulation results, M2 is found to be contributing more than 25% to the input noise at high frequency. The reason behind this high noise contribution is that the noise of M2 will be amplified by the gains from the nodes 2 and 3 when referred to the input. These gains depend on the impedance at nodes 2 and 3 divided by the respective gains calculated from input node 1 to the nodes 2 and 3. As shown in Figure 1(b), the output impedance to the gain ratios go higher as frequency increases. Thus the noise current of M2 multiplied by these two ratios to be referred to the input goes higher as frequency increases.The input referred noise from nodes 2 and 3 can be calculated by breaking the feedback from drain ofM3 to the input. The input referred noise contribution from node 3 is calculated as
(1)In,M2refnode3=In,M2node3Ro3CLAI3CL=In,M2node3Ro3OL/(1+AI3OLβ)AI3OL/(1+AI3OLβ)=In,M2node3Ro3OLAI3OL.
Hence,
(2)In,M2refnode3=In,M2node3C2s+(gm1+gm2+1/ro2)gm1gm2c1s+gm1gm2.
Similarly, we can obtain the input referred noise from node 2 as
(3)In,M2refnode2=In,M2node2(C2s+ro2rob(gm1+gm2+1/ro2))gm1(1+c1s)(1+rob/ro2+robc3s+(gm1+gm2)rob),
where In,M2refnode2,3 are the input referred noise currents of M2 from nodes 2 and 3, respectively. In,M2node2,3 are noise currents of M2 at nodes 2 and 3, Ro3CL is the closed loop resistance at node 3, Ro3OL is the open loop resistance at node 3, AI3CL is the closed loop transimpedance gain from node 1 to node 3 for the shunt-shunt feedback circuit in Figure 1(a), AI3OL is the open loop transimpedance gain from node 1 to node 3, and β=gm3 is the feedback factor.Equations (2) and (3) reveal that the noise contribution of M2 goes higher at high frequencies.  This can be understood from the fact that the Gyrator structure in Figure 1(a) has shunt-shunt feedback structure and the capability of this feedback topology to lower the output impedances at nodes 2 and 3 is reduced at higher frequencies due to the feedback forward gain reduction. That leads to higher contribution of the noise sources In,M2node2,3 when multiplied by these output impedances at nodes 2 and 3 to be referred to the input at node 1.


### 2.2. NC Principle and Simulation Results

Figure2 illustrates the modification introduced for cancelling the noise of M2 (Rf is neglected at this time and nodes 1 and 4 are shorted). The noise current of M2, which is modelled as the current source In,M2, flows into node 2 but out of node 3 as shown in Figure 2. This creates two fully correlated noise voltages at nodes 2 and 3 with opposite phases. These two voltages are converted into current by M3 and M4, respectively. By properly matching the AC currents of M3 and M4 around the resonant frequency, the noise contributed by M2 can be cancelled at the input.Figure 2
Principle of noise cancelling design.Conversely, the signal voltages at nodes 2 and 3 are in phase, resulting in constructive addition at node 1. The condition for complete noise cancelling ofM2 can be derived as
(4)In,input=In,M2ZO3gm3-In,M2ZO2gm4=0(5)⇒gm2ro2+gm1ro2+C2ro2ss2C2c3ro2+sc3ro2(gm2+gm1)+ro2(gm2+gm1)+gm1gm3=ro2robro2robgm1+ro2robgm2+sC2ro2rob+ro2+robgm4,
where ZO2,3 are the total impedance at the nodes 2 and 3, ro3,4,b are the output resistances of transistors M3,4,b, andC1,2,3 are the total capacitances at nodes 1, 2, and 3.For simplicity, we have ignored few terms in the above NC condition in (5). Figure 3 compares the noise contribution of M2 with and without NC to the total output noise after the above NC condition is matched relatively at the frequencies of interest by properly choosing the size and biasing current of M3 and M4. We can see from Figure 3 that the noise contribution from M2 is reduced at all frequencies and it is almost contributing 0% around the resonance frequency.Figure 3
SimulatedIn,M2/In,out versus frequency with and without NC.To further confirm the effect of noise cancelling, the case withM4 being turned OFF is simulated while maintaining the same power consumption by the following steps: (1) connecting the gate of M4 to VDD; (2) Va is adjusted accordingly to increase the bias current of M2; (3) the biasing current of M3 is adjusted to give the same power dissipation as M4 is turned ON.  The simulated total input referred noise current when M4 is turned ON/OFF is shown in Figure 4. It should be noticed from this graph that the noise has been reduced by 80% when M4 is ON (with NC).Figure 4
Simulated input referred noise with and without NC.Even after cancelling the noise ofM2, we can still further suppress the noise of the second stage in Figure 2. We can see that the entire noise of the second stage is directly added to the input noise as is the case in every back-to-back Gyrator active inductor. To further optimize the active inductor for lower noise, the resistor Rf is added to degenerate the noise in,t of the entire 2nd stage as shown in Figure 2. Even though Rf will introduce noise to the input but the benefit of its inclusion on the noise reduction overshadows the effect of its added noise. The noise contributed by the second stage to the input while Rf is included can be calculated as below. Figure 2 can be considered as shunt-shunt feedback structure where M1–4 are considered to be in feed-forward loop and Rf in the feedback loop.The noise contribution of the second stage can be obtained as(6)In,input=In,tZo4CLAI4CL=In,tZo4OL/(1+AI4OLβ)AI4OL/(1+AI4OLβ)=In,tZo4OLAI4OL,(7)In,input=In,tgm2ro2RfA1(gm2gm3ro2+gm4)≈In,tRfA1gm3,
where In,t is the total noise current of the entire 2nd stage, Zo4CL,AI4CL are the closed loop impedance and gain at node 4, Zo4OL,AI4OL are the open loop impedance and gain at node 4 and A1 is the gain contributed from M1 and M2. From (7), it is evident that increasing Rf shields the input node of the active inductor from the noise contribution of the second stage formed by M3, M4, and Ib. Figure 5 shows the simulated noise contribution of the second stage when compared with and without Rf. Figure 5 shows the noise contribution of second stage to the total input referred noise. Here we can see that by adding Rf, the noise contribution of 2nd stage has been reduced to 15% from 45%.Figure 5
Simulated noise contribution with and withoutRf.


### 2.3. Active Inductor Parameters

In this section, the different parameters of the proposed active inductor are derived. The simplified active inductor is shown in Figure6. The Gyrator-C principle on which active inductor is based on is depicted in Figure 7(a) and its equivalent passive model is shown in Figure 7(b). The differential pair M1 and M2 forms the positive transconductance Gm1 with input node at 1 and output nodes at 2 and 3. The transistor pair M3 and M4 forms the negative transconductance -Gm2 with input nodes at 2 and 3 and output node at 1. These two Gm blocks convert the parasitic capacitors at nodes 2 and 3 to an equivalent inductor appearing at node 1. The ideal current sources in the active inductor are implemented using simple current mirror.Figure 6
Simplified active inductor.(a) Gyrator-C realization of active inductor (b) equivalent passive model.
(a)(b)The equivalentZin can be obtained from the small signal analysis circuit in Figure 8. For better intuition, a few parasitic parameters have been ignored. The approximate expression for Zin is as follows:(8)Zin(s)≈s/C1+g3/C1C3s2+s𝔄+𝔅,
where 𝔄 denotes (gm4gm1/GmC1)(g4gf/(g4+gf))+g1/C1+g3/C3+g1g3C2/GmC1C3-ω2(C2/Gm)) and 𝔅 denotes ((gm1gm2gm3+gm1gm4g3)/GmC1C3)(gf/(g4+gf), and gm1–4 are the transconductances of transistors M1–4,C1–3, g1–4 are the total parasitic capacitances and conductances at nodes 1–4, gf is the conductance of feedback resistor, Gm=gm1+gm2+g3, and the cubic term in the denominator is substituted to -ω2s, because the effect of negative real pole arising due to cubic term is of second order [1] when compared to dominant conjugate poles.Figure 8
Small signal model of the simplified active inductor in Figure1.From (8), Zin is equivalent to the input impedance of the RLC passive network shown in Figure 7(b). The passive equivalent elements are obtained as
(9)Rs=Gmg3(gm1gm2gm3+gm1gm4g3)(gf/(g4+gf)),
where Rs is the series resistor with Leq and the parallel parasitic capacitor Cp are given by
(10)Leq=GmC3((gf+g4)/gf)gm1gm2gm3+gm1gm4g3,Cp=C1.
The resonant frequency is given by
(11)ω0=gm1gm2gm3+gm1gm4g3GmC1C3((gf+g4)/gf),f0=12πLeqC1.
The quality factor at the resonant frequency is obtained as
(12)Q0=𝔅𝔄.The simulated frequency response of the active inductor is shown in Figure9. The simulations are carried out in 90 nm STM CMOS process. The transistor sizes (W/L in μm) are M1 (6/0.18), M2 (6/0.18), M3 (11.5/0.18), M4 (2.3/0.18), I1=280μA, Ib=I2=400μA,Va=0.8V, and VDD=1.2V. The active inductor resonates at centre frequency of f0=3.8GHz with a quality factor of Q0=405. The pole-zero analysis performed using Spectre simulator shows that all the poles reside on the left side of the jω axis and consequently the active inductor is stable. Also varying the feedback resistor Rf (from 0 to 30 kΩ) and gm1 and gm2 (by varying the active inductor biasing currents I2 and Ib from 300 μA to 500 μA) was applied to confirm the stability of the active inductor in case of tuning its center frequency and quality factor.  Figure 10 shows the zero-pole plot for the active inductor transfer function while changing Rf from 0 to 15 kΩ. Moreover, transient analysis has been performed to confirm the stability.Figure 9
Simulated frequency response.Figure 10
Pole-zero plot for variation ofRf.Table1 compares the performance of the proposed active inductor with the previously published active inductors [1, 9, 10]. Comparison of performances proves that this inductor has a good quality factor, wide inductive bandwidth, low-power consumption of 1.2 mW, and very less noise when integrated over 500 MHz bandwidth.Table 1
Comparison of active inductor performances.
ParameterReference [1]Reference [9]Reference [10]This workTechnology0.20μm/1.8 V0.13μm/1.2 V0.35μm/1.5 V90 nm/1.2 VInductive bandwidthn.a.300 MHz–7.32 GHz6.8 MHz–2.97 GHz600 MHz–3.8 GHzL (nH)2938–14430.9165–530QLmaxn.a.3900@5.75 GHz434@1 GHz120@3 GHzQR66561n.a.405Pdis (mW)4.410.61.2Noise0.8μV/√Hz69.31μV*91.3μV43.37nV**Calculated.


## 2.1. Noise Contribution of the TransistorM2

The circuit used to implement NC in active inductor is the Gyrator-C structure proposed in [1] and shown in Figure 1(a). In order to apply NC, we studied the noise contribution of each transistor and identified the transistor that has the highest percentage of noise to the total input referred noise. Usually in LNA, noise cancelling is applied to the input transistor. This is not the case of active inductors, and due to the back-to-back Gm structure a careful study is needed to identify the transistor that contributes the highest noise at the frequency of interest.The noise current ofM2 is modelled as the current source In,M2, between nodes 2 and 3 in Figure 1(a). For better understanding, we have shown the noise of M2 as two current sources, one flowing out of node 3 and other flowing into node 2 [8]. From noise analysis and simulation results, M2 is found to be contributing more than 25% to the input noise at high frequency. The reason behind this high noise contribution is that the noise of M2 will be amplified by the gains from the nodes 2 and 3 when referred to the input. These gains depend on the impedance at nodes 2 and 3 divided by the respective gains calculated from input node 1 to the nodes 2 and 3. As shown in Figure 1(b), the output impedance to the gain ratios go higher as frequency increases. Thus the noise current of M2 multiplied by these two ratios to be referred to the input goes higher as frequency increases.The input referred noise from nodes 2 and 3 can be calculated by breaking the feedback from drain ofM3 to the input. The input referred noise contribution from node 3 is calculated as
(1)In,M2refnode3=In,M2node3Ro3CLAI3CL=In,M2node3Ro3OL/(1+AI3OLβ)AI3OL/(1+AI3OLβ)=In,M2node3Ro3OLAI3OL.
Hence,
(2)In,M2refnode3=In,M2node3C2s+(gm1+gm2+1/ro2)gm1gm2c1s+gm1gm2.
Similarly, we can obtain the input referred noise from node 2 as
(3)In,M2refnode2=In,M2node2(C2s+ro2rob(gm1+gm2+1/ro2))gm1(1+c1s)(1+rob/ro2+robc3s+(gm1+gm2)rob),
where In,M2refnode2,3 are the input referred noise currents of M2 from nodes 2 and 3, respectively. In,M2node2,3 are noise currents of M2 at nodes 2 and 3, Ro3CL is the closed loop resistance at node 3, Ro3OL is the open loop resistance at node 3, AI3CL is the closed loop transimpedance gain from node 1 to node 3 for the shunt-shunt feedback circuit in Figure 1(a), AI3OL is the open loop transimpedance gain from node 1 to node 3, and β=gm3 is the feedback factor.Equations (2) and (3) reveal that the noise contribution of M2 goes higher at high frequencies.  This can be understood from the fact that the Gyrator structure in Figure 1(a) has shunt-shunt feedback structure and the capability of this feedback topology to lower the output impedances at nodes 2 and 3 is reduced at higher frequencies due to the feedback forward gain reduction. That leads to higher contribution of the noise sources In,M2node2,3 when multiplied by these output impedances at nodes 2 and 3 to be referred to the input at node 1.


## 2.2. NC Principle and Simulation Results

Figure2 illustrates the modification introduced for cancelling the noise of M2 (Rf is neglected at this time and nodes 1 and 4 are shorted). The noise current of M2, which is modelled as the current source In,M2, flows into node 2 but out of node 3 as shown in Figure 2. This creates two fully correlated noise voltages at nodes 2 and 3 with opposite phases. These two voltages are converted into current by M3 and M4, respectively. By properly matching the AC currents of M3 and M4 around the resonant frequency, the noise contributed by M2 can be cancelled at the input.Figure 2
Principle of noise cancelling design.Conversely, the signal voltages at nodes 2 and 3 are in phase, resulting in constructive addition at node 1. The condition for complete noise cancelling ofM2 can be derived as
(4)In,input=In,M2ZO3gm3-In,M2ZO2gm4=0(5)⇒gm2ro2+gm1ro2+C2ro2ss2C2c3ro2+sc3ro2(gm2+gm1)+ro2(gm2+gm1)+gm1gm3=ro2robro2robgm1+ro2robgm2+sC2ro2rob+ro2+robgm4,
where ZO2,3 are the total impedance at the nodes 2 and 3, ro3,4,b are the output resistances of transistors M3,4,b, andC1,2,3 are the total capacitances at nodes 1, 2, and 3.For simplicity, we have ignored few terms in the above NC condition in (5). Figure 3 compares the noise contribution of M2 with and without NC to the total output noise after the above NC condition is matched relatively at the frequencies of interest by properly choosing the size and biasing current of M3 and M4. We can see from Figure 3 that the noise contribution from M2 is reduced at all frequencies and it is almost contributing 0% around the resonance frequency.Figure 3
SimulatedIn,M2/In,out versus frequency with and without NC.To further confirm the effect of noise cancelling, the case withM4 being turned OFF is simulated while maintaining the same power consumption by the following steps: (1) connecting the gate of M4 to VDD; (2) Va is adjusted accordingly to increase the bias current of M2; (3) the biasing current of M3 is adjusted to give the same power dissipation as M4 is turned ON.  The simulated total input referred noise current when M4 is turned ON/OFF is shown in Figure 4. It should be noticed from this graph that the noise has been reduced by 80% when M4 is ON (with NC).Figure 4
Simulated input referred noise with and without NC.Even after cancelling the noise ofM2, we can still further suppress the noise of the second stage in Figure 2. We can see that the entire noise of the second stage is directly added to the input noise as is the case in every back-to-back Gyrator active inductor. To further optimize the active inductor for lower noise, the resistor Rf is added to degenerate the noise in,t of the entire 2nd stage as shown in Figure 2. Even though Rf will introduce noise to the input but the benefit of its inclusion on the noise reduction overshadows the effect of its added noise. The noise contributed by the second stage to the input while Rf is included can be calculated as below. Figure 2 can be considered as shunt-shunt feedback structure where M1–4 are considered to be in feed-forward loop and Rf in the feedback loop.The noise contribution of the second stage can be obtained as(6)In,input=In,tZo4CLAI4CL=In,tZo4OL/(1+AI4OLβ)AI4OL/(1+AI4OLβ)=In,tZo4OLAI4OL,(7)In,input=In,tgm2ro2RfA1(gm2gm3ro2+gm4)≈In,tRfA1gm3,
where In,t is the total noise current of the entire 2nd stage, Zo4CL,AI4CL are the closed loop impedance and gain at node 4, Zo4OL,AI4OL are the open loop impedance and gain at node 4 and A1 is the gain contributed from M1 and M2. From (7), it is evident that increasing Rf shields the input node of the active inductor from the noise contribution of the second stage formed by M3, M4, and Ib. Figure 5 shows the simulated noise contribution of the second stage when compared with and without Rf. Figure 5 shows the noise contribution of second stage to the total input referred noise. Here we can see that by adding Rf, the noise contribution of 2nd stage has been reduced to 15% from 45%.Figure 5
Simulated noise contribution with and withoutRf.


## 2.3. Active Inductor Parameters

In this section, the different parameters of the proposed active inductor are derived. The simplified active inductor is shown in Figure6. The Gyrator-C principle on which active inductor is based on is depicted in Figure 7(a) and its equivalent passive model is shown in Figure 7(b). The differential pair M1 and M2 forms the positive transconductance Gm1 with input node at 1 and output nodes at 2 and 3. The transistor pair M3 and M4 forms the negative transconductance -Gm2 with input nodes at 2 and 3 and output node at 1. These two Gm blocks convert the parasitic capacitors at nodes 2 and 3 to an equivalent inductor appearing at node 1. The ideal current sources in the active inductor are implemented using simple current mirror.Figure 6
Simplified active inductor.(a) Gyrator-C realization of active inductor (b) equivalent passive model.
(a)(b)The equivalentZin can be obtained from the small signal analysis circuit in Figure 8. For better intuition, a few parasitic parameters have been ignored. The approximate expression for Zin is as follows:(8)Zin(s)≈s/C1+g3/C1C3s2+s𝔄+𝔅,
where 𝔄 denotes (gm4gm1/GmC1)(g4gf/(g4+gf))+g1/C1+g3/C3+g1g3C2/GmC1C3-ω2(C2/Gm)) and 𝔅 denotes ((gm1gm2gm3+gm1gm4g3)/GmC1C3)(gf/(g4+gf), and gm1–4 are the transconductances of transistors M1–4,C1–3, g1–4 are the total parasitic capacitances and conductances at nodes 1–4, gf is the conductance of feedback resistor, Gm=gm1+gm2+g3, and the cubic term in the denominator is substituted to -ω2s, because the effect of negative real pole arising due to cubic term is of second order [1] when compared to dominant conjugate poles.Figure 8
Small signal model of the simplified active inductor in Figure1.From (8), Zin is equivalent to the input impedance of the RLC passive network shown in Figure 7(b). The passive equivalent elements are obtained as
(9)Rs=Gmg3(gm1gm2gm3+gm1gm4g3)(gf/(g4+gf)),
where Rs is the series resistor with Leq and the parallel parasitic capacitor Cp are given by
(10)Leq=GmC3((gf+g4)/gf)gm1gm2gm3+gm1gm4g3,Cp=C1.
The resonant frequency is given by
(11)ω0=gm1gm2gm3+gm1gm4g3GmC1C3((gf+g4)/gf),f0=12πLeqC1.
The quality factor at the resonant frequency is obtained as
(12)Q0=𝔅𝔄.The simulated frequency response of the active inductor is shown in Figure9. The simulations are carried out in 90 nm STM CMOS process. The transistor sizes (W/L in μm) are M1 (6/0.18), M2 (6/0.18), M3 (11.5/0.18), M4 (2.3/0.18), I1=280μA, Ib=I2=400μA,Va=0.8V, and VDD=1.2V. The active inductor resonates at centre frequency of f0=3.8GHz with a quality factor of Q0=405. The pole-zero analysis performed using Spectre simulator shows that all the poles reside on the left side of the jω axis and consequently the active inductor is stable. Also varying the feedback resistor Rf (from 0 to 30 kΩ) and gm1 and gm2 (by varying the active inductor biasing currents I2 and Ib from 300 μA to 500 μA) was applied to confirm the stability of the active inductor in case of tuning its center frequency and quality factor.  Figure 10 shows the zero-pole plot for the active inductor transfer function while changing Rf from 0 to 15 kΩ. Moreover, transient analysis has been performed to confirm the stability.Figure 9
Simulated frequency response.Figure 10
Pole-zero plot for variation ofRf.Table1 compares the performance of the proposed active inductor with the previously published active inductors [1, 9, 10]. Comparison of performances proves that this inductor has a good quality factor, wide inductive bandwidth, low-power consumption of 1.2 mW, and very less noise when integrated over 500 MHz bandwidth.Table 1
Comparison of active inductor performances.
ParameterReference [1]Reference [9]Reference [10]This workTechnology0.20μm/1.8 V0.13μm/1.2 V0.35μm/1.5 V90 nm/1.2 VInductive bandwidthn.a.300 MHz–7.32 GHz6.8 MHz–2.97 GHz600 MHz–3.8 GHzL (nH)2938–14430.9165–530QLmaxn.a.3900@5.75 GHz434@1 GHz120@3 GHzQR66561n.a.405Pdis (mW)4.410.61.2Noise0.8μV/√Hz69.31μV*91.3μV43.37nV**Calculated.


## 3. RF Band-Pass Filter and Simulation Results

Figure11 shows the proposed pseudo-differential RF Band-pass filter implemented using proposed NC active inductor. The input stage is designed by the common-gate transistor Min which is biased by Iin and Rin. A source follower stage is used as an output buffer for output matching and to reduce the loading effect.Figure 11
RF Band-pass filter based on NC Active inductor.The effect of NC is high lightened by comparing the performance of the two band-pass filters. One designed using the active inductor with NC and other using the active inductor without NC (the transistorM4 is turned OFF as mentioned above). In Figure 12, we can see that when the gain and centre frequency of the proposed band-pass filter are same, the NF without and with NC are 17 dB and 5 dB, respectively. And also we can see that when the 2 filters are tuned to have same quality factor and centre frequency, the NF without and with NC are 17 dB and 5.7 dB, respectively.NF and gain comparison for band-pass filter with and without NC active inductor.
(a)(b)(c)(d)Figure13 shows the filter NF and frequency response under extreme cases of combined process and mismatch variations. We can see that the NF has changed by almost 0.75 dB around the centre frequency while the gain of the filter has been changed without much variation in the centre frequency. The gain of the filter can be retrieved by tuning Q using the biasing current I2 in Figure 11.NF and frequency response with process variation.
(a)(b)The linearity of the band-pass filter was examined by plotting the third-order intercept point (IIP3) using periodic steady state simulation as shown in Figure14. The conditions for simulating the linearity are center frequency f0=3.467GHz and the two signals injected were at frequencies of 3.48 GHz and 3.49 GHz, respectively. While noise cancelling reduces the noise floor, the harmonic distortion is not reduced as a result of NC conditions, which leads to almost constant dynamic range for the filter with and without NC. However, the harmonic distortion can be cancelled by selecting different conditions other than the one used for NC, therefore, simultaneous cancellation of noise and distortion is hampered [13]. Despite the fact that this filter presents an acceptable linearity, the latter can be improved by increasing the overdrive voltages of transistors M1–4 at the cost of higher power supply. Moreover, distortion cancelling techniques such as the one presented in [14] can be adapted to cancel the distortion of the proposed active inductor and that to improve the overall linearity of the designed RF filter.Figure 14
IIP3 simulation result.Table2 compares the performance of the band-pass filter using the proposed active inductor with previously published RF band-pass filters. Comparison of performances proves that this filter features lower-power consumption of 1.4 mW and lower noise figure of 5 dB at the filter centre frequency.Table 2
Comparison of band-pass filter performances.
ParameterReference [1]Reference [11]Reference [12]This workTechnology0.20μm0.18μm0.18μm90 nmFilter order2252ω0 (GHz)5.42.443.45~3.63.46Pdis (mW)4.410.8281.4NF (dB)25.618145(at 5.7 GHz)(at 2.45 GHz)(at 3.6 GHz)(at 3.46 GHz)IIP3 (dBm)−13.9—−2.4−10.29


## 4. Conclusion

A 3.8 GHz noise cancelling CMOS active inductor is presented. The proposed active inductor has low noise due to noise cancelling and resistive degeneration. The circuit has wide inductive bandwidth, high-resonant frequencies with high-quality factor. Simulation results are provided in 90 nm 1.2 V STM CMOS process. A second-order band-pass filter has been designed based on this proposed active inductor. The designed filter including the input and output buffer stages has low NF and low-power consumption which makes it suitable for front-end RF filtering applications.



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*Source: 980957-2010-03-21.xml*