# A Low Power Impedance Transparent Receiver with Linearity Enhancement Technique for IoT Applications

Authors: Sizheng Chen; Tingting Shi; Lei Ma; Cheng Kang; Na Yan; Hao Min
Journal: Wireless Communications and Mobile Computing
 (2018)

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## Abstract

A low power receiver with impedance transparent RF front end is presented. By using the 4-path passive mixer and the active feedback of LNA, the baseband impedance profile is further transferred to receiver input. While a LO-defined input matching is formed by RF front end, the linearity of entire receiver chain is improved. Furthermore, derivative superposition technique is employed to cancel the distortion of the CMOS LNA. A 3rd-order active-RC filter is designed with current-efficient feedforward compensated OTA. And a digital-to-time converter (DTC) assisted fractional-N all-digital phase-locked loop (ADPLL) is codesigned with receiver to meet the IoT requirements. The presented receiver is fabricated in 55 nm CMOS technology with an active area of 2.3 mm2 and power consumption of 20 mW. Measurement results show that the receiver achieves 5.3 dB NF with 78 dB gain from 0.6 to 1 GHz, the RX out-of-band IIP3 is +8 dBm, and in-band IIP3 is −10 dBm, and the ADPLL achieves −94 dBc/Hz in-band PN and −120.5 dBc/Hz at 1 MHz offset.


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## Body

## 1. Introduction

The need for low power and low cost transceivers has been growing with the expansion of portable wireless devices and wireless sensor networks. Because of big market potential and design challenges, narrow-band (NB) receivers have become the focus of industry and academic researches recently. Modern wireless protocols are released, such as the emerging NB-IoT [1] and the IEEE 802.11ah [2], to support IoT applications. Additionally, NB-IoT has been included as an important part of future fifth-generation (5G) mobile communication [3].Different techniques are proposed in recent researches to realize the low power and low cost receiver for IoT protocols. Because of the superior performance (better noise and linearity) of NB LNAs, multiple narrow-band receivers are employed to cover the entire band of the operation. To provide high-Q frequency selectivity, each NB RX uses off-chip components, which increases the entire area and cost [4]. Reconfigurable receiver is able to select signals over a wide operation band. And one of the common challenges of these receivers is out-of-band interference. Academic researches have focused on using passive mixer to suppress the out-band blockers. A mixer-first receiver has an excellent linearity at the cost of large power dissipation and poor LO-to-RF isolation [5]. Others proposed a noise-cancelling receiver to achieve very low noise figure by employing two paths of downconversion which increases the hardware complexity [6], but extra calibration is needed to provide precise gain and phase matching.In this work, an impedance transparent receiver architecture is proposed which only uses one downconversion path. The proposed reconfigurable RF front end employs an active feedback LNA to transfer the baseband filter character to the input of receiver, which can attenuate out-of-band interferers. By using the impedance mapping of passive mixer and the feedback of LNA, a LO-defined input matching is formed. To further improve the linearity of RX, a linearity enhancement technique called “derivative superposition [7]” is employed in the CMOS LNA.This paper proposes a low power impedance transparent receiver with linearity enhancement technique. The description of the system architecture is given in Section2; the design of the building blocks is shown in Section 3; the measured results are described in Section 4 and conclusions are provided in Section 5.


## 2. System Description

### 2.1. System Specifications for the Receiver

Based on the IoT protocols [8], main specifications of the receiver are summarized in Table 1. Low power and low cost are the key features of IoT application. And the system specifications are briefly reviewed as follows.Table 1
Main specifications of receiver for IoT protocols.
Parameters NB-IoT RF frequency 699~915 MHz Channel bandwidth 180 kHz Max. receive level −25 dBm Sensitivity <−109 dBm Noise figure <7 dB P-1dB >−25 dBm OB-IIP3 >+7.75 dBm∗ In-band IIP3 >−15.4 dB ∗Range 2 of NB-IoT protocol.


#### 2.1.1. Noise Figure

Sensitivity level of a receiver is very key requirement in a communication system because most of the other specifications are defined based on it. For the NB-IoT application with 180 kHz transmission bandwidth, the sensitivity level is around −109 dBm. TheSNRmin is 2.5 dB to cover all possible TBS (Transport Block Set) with QPSK modulation and code rate 1/3. Based on the requirements above, the noise figure of the receiver can be expressed as(1)NF=Sensitivity--174dBm+10log⁡BW+SNRmin-IM.I M is implementation and production margin. BW is the transmission bandwidth in Hz. Assuming IM is 3 dB, it can be calculated that NF = 6.94 dB.


#### 2.1.2. Nonlinearity

For RX nonlinearity, there are in-band and out-of-band IIP3 requirements. The in-band IIP3 of the RX is corresponding to the 1-dB compression point (P1dB). Since the maximum input level of the NB-IoT receiver is −25 dBm, the P1dB is −25 dBm. So the in-band IIP3 is −15.4 dB, which is 9.6 dB higher than P1dB. The out-of-band IIP3 is determined by out-of-band blocking parameters. According to [8], the interferer power is −30 dBm in range 2 (60~85 MHz frequency offset from desire signal), while the signal power is 6 dB above the reference sensitivity (about −109 dBm). The IIP3 estimated with 2.5 dB SNR is as follows (where Psignal is the power of signal):(2)OB-IIP3=3Pin-Psignal-SNR2=7.75dBm.For the sensitivity requirement of the protocol, LNA-first architecture should be employed. Compared with mixer-first receiver, the LNA is added for two reasons.(1) LO-to-RF isolation can be improved by adding the LNA, which is one of the most challenging things in mixer-first receiver. The allowable emission level within receiver band is in range of −60 to −80 dBm. For example, according to [9], the LO leakage of mixer-first RX is about −48 dBm without calibration in 28 nm CMOS technology.(2) Providing a gain in first stage is a power efficiency method to realize high sensitivity receiver. Due to lack of LNA, lots of current is burned in baseband transimpedance amplifier (TIA) to make the NF less than 8 dB in mixer-first receiver [5].Because of the narrow-band profile, the 1/f noise and DC offset could degrade the sensitivity. A passive mixer is employed for its superiority on 1/f noise. And a DC offset cancellation circuit is designed.Besides, it is difficult to achieve both high linearity and low power for RF front end, especially without the help of off-chip device (e.g., SAW, BAW). Compared with traditional method of using passive mixer at LNA output only, the proposed receiver is further mapping the impedance of mixer to the RX input with active feedback LNA to realize the input LO-defined impedance matching. The in-band of RX could be a problem due to the incremental gain of LNA. So the derivative superposition technique is utilized to cancel this distortion in LNA.


### 2.2. Receiver Architecture

The proposed receiver architecture is a suitable solution for IoT applications as shown in Figure1, consisting of an impedance transparent receiver front end, a 3rd-order active-RC filter, a fractional-N frequency synthesizer, and SPI interface to configure the system. The local frequency generator consists of a divide-by-two circuit to generate a 25% duty-cycle LO from an on-chip all-digital phase-locked loop. A DTC-assisted fractional-N ADPLL with a TDC is employed in this work. Self-biased CMOS inverters are used to provide rail-to-rail swing to the gate of passive mixer. Compared with the traditional 50% duty-cycle LO, the 25% duty-cycle LO scheme [9] provides isolation timely betweenI- andQ-current-path. Therefore, conversion gain reduction and subsequent NF increase are prevented.Figure 1
Proposed receiver architecture.


### 2.3. Noise Analysis of Receiver RF Front End

The receiver RF front end comprises an LNA, two separate passive mixers for in-phase(I) and quadrature-phase (Q), and a single-pole filter as a TIA which changes the current signal to voltage signal. The passive mixer is implemented with 4 nMOS transistors, which are connected with the output of LNA. According to [10], the output of 4-path passive mixer can be written as(3)SMIXER,current=∑n=-∞+∞anejnωLOt-T/4ian=14e-jnπ/4sin⁡cnπ4.S M I X E R , c u r r e n t is the current gain of 4-path passive mixer and an is the coefficients of the Fourier series. The receiver conversion gain and NF can be calculated as follows:(4)ARX_RF=12·gm,LNA·ZO,LNAωLOZO,LNAωLO+Rsw·a-1·RF(5)NF=1+In,LNA2¯kTRS·gm,LNA2+Rsw·RFRS·ARX_RF∑n=0+∞a-nZO,LNAnωLO+Rsw2+Vn,TIA2¯1+RF/CO,LNA24kTRS·ARX_RF2+RFRS·ARX_RF2.g m , L N A is the transconductance of the LNA. ZO,LNA and In,LNA2¯ are, respectively, the output impedance and output current noise of the LNA. Rsw is the mixer switch on-resistance. And RF is the feedback resistance of TIA. The OTA noise is modeled by Vn,TIA2¯ as shown in Figure 2. Since the thermal noise of passive mixer switches is white noise, all parts of harmonics of the LO will be folded into baseband which is shown in third part of (5). From this equation, we can see that the LNA stage decreases the noise contribution from mixer and TIA.Figure 2
Noise sources inside the RF front end.


### 2.4. Impedance Transparent Profile

Compared with conventional architecture of just employing passive mixer at LNA output, the high-Q filtering profile of passive mixer is further transferred to the input of the receiver in our proposed RF front end. So it can relax the requirement on LNA linearity while achieving a relatively low NF. To figure out how the impedance transparent affects the linearity of the RX, the benefit of a filter is added before or after LNA is analyzed as shown in Figure 3.Figure 3
Two cases to analyze the effect of impedance transparent.To simplify analysis, only the nonlinearity of LNA and mixer are considered. The filter has two rejections as shown in Figure4, Hblocker1 and Hblocker2 for different blockers at Fblocker1 and Fblocker2.A1 andA2 represent the amplitudes of the two blockers. For a memoryless nonlinear system, the input/output characteristic can be modeled as a polynomial [11].Figure 4
The rejection of the filter for two different blockers.Then output IM3 of this cascaded receiver stages (LNA and mixer) is as follows:(6)AIM3,baseband=GLNAGMIXERA12A2AIIP3,LNA2︸OutputIM3  of  LNA+GLNA3GMIXERA12A2AIIP3,MIXER2︸OutputIM3  of  MIXER.G L N A and GMIXER are the gain of the LNA and the mixer stage, respectively. In case one, the filter is added after the LNA. The resulting IM3 is as follows:(7)AIM3,baseband=GLNAGMIXERA12A2AIIP3,LNA2︸OutputIM3  of  LNA+GLNA3GMIXERHblocker12Hblocker2A12A2AIIP3,MIXER2︸OutputIM3  of  MIXER.From (7), we can see that blockers are not attenuated at the input of LNA. But the IM3 levels from the mixer stage are significantly reduced, which helps to improve the IM3 level by a few dB. Therefore, the RX IIP3 is limited by LNA stage in this case. By adding the filter in case two, the IM3 at baseband is calculated as(8)AIM3,baseband=GLNAGMIXERHblocker12Hblocker2A12A2AIIP3,LNA2︸OutputIM3  of  LNA+GLNA3GMIXERHblocker12Hblocker2A12A2AIIP3,MIXER2︸OutputIM3  of  MIXER.In this case, it can be shown that IM3 level from both the LNA stage and mixer stage is attenuated. So the IIP3 of the entire receiver is significantly improved. If the blocker IM3 improvement due to the smaller voltage swing isΔIM3, the entail IIP3 improvement is(9)ΔIIP3dB=Hblocker1dB+12Hblocker2dB+12ΔIM3dB.If the blocker 1 is attenuated by 10 dB and blocker 2 is attenuated by 6 dB, whileΔIM3 is 3 dB, the IIP3 improvement is about 14.5 dB.In our proposed receiver front end, an active feedback LNA is used to further map the bandpass filtering characteristic of 4-path passive mixer to the input of RX, which has the same effects as case 2. So it has a suitable tradeoff between noise and out-of-band attenuation early in the receiver chain.According toN-path filtering theory, the frequency response of the filter is centered at the LO frequency. Because of the reciprocal character of passive mixer, the RF signal is down converted to baseband. After being shaped by baseband load, it is up converted back to RF, which transfers the load response to LO frequency. The input impedance of the mixer can be calculated as follows (where Rsw is the switch on-resistance, Zbaseband is the baseband impedance, and Rsh is equivalent resistance of harmonic mixing) [5]:(10)Zmixerω=Rsw+2π2Zbasebandω-ωLORsh.So the LNA load impedance can be shown to be consisting of the output impedance of LNA and the baseband impedance upconverted by the passive mixer. The input stage of receiver is a CMOS LNA with a shunt-shunt feedback [12]. With the negative feedback, the impedance properties at the baseband can be mapped to the LNA input as(11)Rin=1/gm2+RF,LNA1+gm1·RL,LNAZmixerω.R F , L N A and RL,LNA are feedback resistance and load resistance of LNA, respectively. gm1 and gm2 are the transconductance of main amplifier transistor and feedback transistor, respectively. Zmixer(ω) is the input impedance of passive mixer, which has a bandpass impedance characteristic. Since the input resistance of active feedback LNA is inversely proportional to the LNA gain, making the baseband impedance further transferred to the LNA input. The in-band impedance is matched to 50 Ohms, making the input impedance matched at LO frequency only; thus the power of out-of-band blockers are reflected at RX input. The reduction in the voltage gain out of band causes the impedance to increase instead which means that the shape of the impedance is inverse to the shape of the impedance at the output of the LNA. Simulated s-parameters and input impedance of the front end using steady-state analysis are shown in Figure 5.Figure 5
Simulated Z11 and S11 of receiver RF front end.


## 2.1. System Specifications for the Receiver

Based on the IoT protocols [8], main specifications of the receiver are summarized in Table 1. Low power and low cost are the key features of IoT application. And the system specifications are briefly reviewed as follows.Table 1
Main specifications of receiver for IoT protocols.
Parameters NB-IoT RF frequency 699~915 MHz Channel bandwidth 180 kHz Max. receive level −25 dBm Sensitivity <−109 dBm Noise figure <7 dB P-1dB >−25 dBm OB-IIP3 >+7.75 dBm∗ In-band IIP3 >−15.4 dB ∗Range 2 of NB-IoT protocol.


### 2.1.1. Noise Figure

Sensitivity level of a receiver is very key requirement in a communication system because most of the other specifications are defined based on it. For the NB-IoT application with 180 kHz transmission bandwidth, the sensitivity level is around −109 dBm. TheSNRmin is 2.5 dB to cover all possible TBS (Transport Block Set) with QPSK modulation and code rate 1/3. Based on the requirements above, the noise figure of the receiver can be expressed as(1)NF=Sensitivity--174dBm+10log⁡BW+SNRmin-IM.I M is implementation and production margin. BW is the transmission bandwidth in Hz. Assuming IM is 3 dB, it can be calculated that NF = 6.94 dB.


### 2.1.2. Nonlinearity

For RX nonlinearity, there are in-band and out-of-band IIP3 requirements. The in-band IIP3 of the RX is corresponding to the 1-dB compression point (P1dB). Since the maximum input level of the NB-IoT receiver is −25 dBm, the P1dB is −25 dBm. So the in-band IIP3 is −15.4 dB, which is 9.6 dB higher than P1dB. The out-of-band IIP3 is determined by out-of-band blocking parameters. According to [8], the interferer power is −30 dBm in range 2 (60~85 MHz frequency offset from desire signal), while the signal power is 6 dB above the reference sensitivity (about −109 dBm). The IIP3 estimated with 2.5 dB SNR is as follows (where Psignal is the power of signal):(2)OB-IIP3=3Pin-Psignal-SNR2=7.75dBm.For the sensitivity requirement of the protocol, LNA-first architecture should be employed. Compared with mixer-first receiver, the LNA is added for two reasons.(1) LO-to-RF isolation can be improved by adding the LNA, which is one of the most challenging things in mixer-first receiver. The allowable emission level within receiver band is in range of −60 to −80 dBm. For example, according to [9], the LO leakage of mixer-first RX is about −48 dBm without calibration in 28 nm CMOS technology.(2) Providing a gain in first stage is a power efficiency method to realize high sensitivity receiver. Due to lack of LNA, lots of current is burned in baseband transimpedance amplifier (TIA) to make the NF less than 8 dB in mixer-first receiver [5].Because of the narrow-band profile, the 1/f noise and DC offset could degrade the sensitivity. A passive mixer is employed for its superiority on 1/f noise. And a DC offset cancellation circuit is designed.Besides, it is difficult to achieve both high linearity and low power for RF front end, especially without the help of off-chip device (e.g., SAW, BAW). Compared with traditional method of using passive mixer at LNA output only, the proposed receiver is further mapping the impedance of mixer to the RX input with active feedback LNA to realize the input LO-defined impedance matching. The in-band of RX could be a problem due to the incremental gain of LNA. So the derivative superposition technique is utilized to cancel this distortion in LNA.


## 2.1.1. Noise Figure

Sensitivity level of a receiver is very key requirement in a communication system because most of the other specifications are defined based on it. For the NB-IoT application with 180 kHz transmission bandwidth, the sensitivity level is around −109 dBm. TheSNRmin is 2.5 dB to cover all possible TBS (Transport Block Set) with QPSK modulation and code rate 1/3. Based on the requirements above, the noise figure of the receiver can be expressed as(1)NF=Sensitivity--174dBm+10log⁡BW+SNRmin-IM.I M is implementation and production margin. BW is the transmission bandwidth in Hz. Assuming IM is 3 dB, it can be calculated that NF = 6.94 dB.


## 2.1.2. Nonlinearity

For RX nonlinearity, there are in-band and out-of-band IIP3 requirements. The in-band IIP3 of the RX is corresponding to the 1-dB compression point (P1dB). Since the maximum input level of the NB-IoT receiver is −25 dBm, the P1dB is −25 dBm. So the in-band IIP3 is −15.4 dB, which is 9.6 dB higher than P1dB. The out-of-band IIP3 is determined by out-of-band blocking parameters. According to [8], the interferer power is −30 dBm in range 2 (60~85 MHz frequency offset from desire signal), while the signal power is 6 dB above the reference sensitivity (about −109 dBm). The IIP3 estimated with 2.5 dB SNR is as follows (where Psignal is the power of signal):(2)OB-IIP3=3Pin-Psignal-SNR2=7.75dBm.For the sensitivity requirement of the protocol, LNA-first architecture should be employed. Compared with mixer-first receiver, the LNA is added for two reasons.(1) LO-to-RF isolation can be improved by adding the LNA, which is one of the most challenging things in mixer-first receiver. The allowable emission level within receiver band is in range of −60 to −80 dBm. For example, according to [9], the LO leakage of mixer-first RX is about −48 dBm without calibration in 28 nm CMOS technology.(2) Providing a gain in first stage is a power efficiency method to realize high sensitivity receiver. Due to lack of LNA, lots of current is burned in baseband transimpedance amplifier (TIA) to make the NF less than 8 dB in mixer-first receiver [5].Because of the narrow-band profile, the 1/f noise and DC offset could degrade the sensitivity. A passive mixer is employed for its superiority on 1/f noise. And a DC offset cancellation circuit is designed.Besides, it is difficult to achieve both high linearity and low power for RF front end, especially without the help of off-chip device (e.g., SAW, BAW). Compared with traditional method of using passive mixer at LNA output only, the proposed receiver is further mapping the impedance of mixer to the RX input with active feedback LNA to realize the input LO-defined impedance matching. The in-band of RX could be a problem due to the incremental gain of LNA. So the derivative superposition technique is utilized to cancel this distortion in LNA.


## 2.2. Receiver Architecture

The proposed receiver architecture is a suitable solution for IoT applications as shown in Figure1, consisting of an impedance transparent receiver front end, a 3rd-order active-RC filter, a fractional-N frequency synthesizer, and SPI interface to configure the system. The local frequency generator consists of a divide-by-two circuit to generate a 25% duty-cycle LO from an on-chip all-digital phase-locked loop. A DTC-assisted fractional-N ADPLL with a TDC is employed in this work. Self-biased CMOS inverters are used to provide rail-to-rail swing to the gate of passive mixer. Compared with the traditional 50% duty-cycle LO, the 25% duty-cycle LO scheme [9] provides isolation timely betweenI- andQ-current-path. Therefore, conversion gain reduction and subsequent NF increase are prevented.Figure 1
Proposed receiver architecture.


## 2.3. Noise Analysis of Receiver RF Front End

The receiver RF front end comprises an LNA, two separate passive mixers for in-phase(I) and quadrature-phase (Q), and a single-pole filter as a TIA which changes the current signal to voltage signal. The passive mixer is implemented with 4 nMOS transistors, which are connected with the output of LNA. According to [10], the output of 4-path passive mixer can be written as(3)SMIXER,current=∑n=-∞+∞anejnωLOt-T/4ian=14e-jnπ/4sin⁡cnπ4.S M I X E R , c u r r e n t is the current gain of 4-path passive mixer and an is the coefficients of the Fourier series. The receiver conversion gain and NF can be calculated as follows:(4)ARX_RF=12·gm,LNA·ZO,LNAωLOZO,LNAωLO+Rsw·a-1·RF(5)NF=1+In,LNA2¯kTRS·gm,LNA2+Rsw·RFRS·ARX_RF∑n=0+∞a-nZO,LNAnωLO+Rsw2+Vn,TIA2¯1+RF/CO,LNA24kTRS·ARX_RF2+RFRS·ARX_RF2.g m , L N A is the transconductance of the LNA. ZO,LNA and In,LNA2¯ are, respectively, the output impedance and output current noise of the LNA. Rsw is the mixer switch on-resistance. And RF is the feedback resistance of TIA. The OTA noise is modeled by Vn,TIA2¯ as shown in Figure 2. Since the thermal noise of passive mixer switches is white noise, all parts of harmonics of the LO will be folded into baseband which is shown in third part of (5). From this equation, we can see that the LNA stage decreases the noise contribution from mixer and TIA.Figure 2
Noise sources inside the RF front end.


## 2.4. Impedance Transparent Profile

Compared with conventional architecture of just employing passive mixer at LNA output, the high-Q filtering profile of passive mixer is further transferred to the input of the receiver in our proposed RF front end. So it can relax the requirement on LNA linearity while achieving a relatively low NF. To figure out how the impedance transparent affects the linearity of the RX, the benefit of a filter is added before or after LNA is analyzed as shown in Figure 3.Figure 3
Two cases to analyze the effect of impedance transparent.To simplify analysis, only the nonlinearity of LNA and mixer are considered. The filter has two rejections as shown in Figure4, Hblocker1 and Hblocker2 for different blockers at Fblocker1 and Fblocker2.A1 andA2 represent the amplitudes of the two blockers. For a memoryless nonlinear system, the input/output characteristic can be modeled as a polynomial [11].Figure 4
The rejection of the filter for two different blockers.Then output IM3 of this cascaded receiver stages (LNA and mixer) is as follows:(6)AIM3,baseband=GLNAGMIXERA12A2AIIP3,LNA2︸OutputIM3  of  LNA+GLNA3GMIXERA12A2AIIP3,MIXER2︸OutputIM3  of  MIXER.G L N A and GMIXER are the gain of the LNA and the mixer stage, respectively. In case one, the filter is added after the LNA. The resulting IM3 is as follows:(7)AIM3,baseband=GLNAGMIXERA12A2AIIP3,LNA2︸OutputIM3  of  LNA+GLNA3GMIXERHblocker12Hblocker2A12A2AIIP3,MIXER2︸OutputIM3  of  MIXER.From (7), we can see that blockers are not attenuated at the input of LNA. But the IM3 levels from the mixer stage are significantly reduced, which helps to improve the IM3 level by a few dB. Therefore, the RX IIP3 is limited by LNA stage in this case. By adding the filter in case two, the IM3 at baseband is calculated as(8)AIM3,baseband=GLNAGMIXERHblocker12Hblocker2A12A2AIIP3,LNA2︸OutputIM3  of  LNA+GLNA3GMIXERHblocker12Hblocker2A12A2AIIP3,MIXER2︸OutputIM3  of  MIXER.In this case, it can be shown that IM3 level from both the LNA stage and mixer stage is attenuated. So the IIP3 of the entire receiver is significantly improved. If the blocker IM3 improvement due to the smaller voltage swing isΔIM3, the entail IIP3 improvement is(9)ΔIIP3dB=Hblocker1dB+12Hblocker2dB+12ΔIM3dB.If the blocker 1 is attenuated by 10 dB and blocker 2 is attenuated by 6 dB, whileΔIM3 is 3 dB, the IIP3 improvement is about 14.5 dB.In our proposed receiver front end, an active feedback LNA is used to further map the bandpass filtering characteristic of 4-path passive mixer to the input of RX, which has the same effects as case 2. So it has a suitable tradeoff between noise and out-of-band attenuation early in the receiver chain.According toN-path filtering theory, the frequency response of the filter is centered at the LO frequency. Because of the reciprocal character of passive mixer, the RF signal is down converted to baseband. After being shaped by baseband load, it is up converted back to RF, which transfers the load response to LO frequency. The input impedance of the mixer can be calculated as follows (where Rsw is the switch on-resistance, Zbaseband is the baseband impedance, and Rsh is equivalent resistance of harmonic mixing) [5]:(10)Zmixerω=Rsw+2π2Zbasebandω-ωLORsh.So the LNA load impedance can be shown to be consisting of the output impedance of LNA and the baseband impedance upconverted by the passive mixer. The input stage of receiver is a CMOS LNA with a shunt-shunt feedback [12]. With the negative feedback, the impedance properties at the baseband can be mapped to the LNA input as(11)Rin=1/gm2+RF,LNA1+gm1·RL,LNAZmixerω.R F , L N A and RL,LNA are feedback resistance and load resistance of LNA, respectively. gm1 and gm2 are the transconductance of main amplifier transistor and feedback transistor, respectively. Zmixer(ω) is the input impedance of passive mixer, which has a bandpass impedance characteristic. Since the input resistance of active feedback LNA is inversely proportional to the LNA gain, making the baseband impedance further transferred to the LNA input. The in-band impedance is matched to 50 Ohms, making the input impedance matched at LO frequency only; thus the power of out-of-band blockers are reflected at RX input. The reduction in the voltage gain out of band causes the impedance to increase instead which means that the shape of the impedance is inverse to the shape of the impedance at the output of the LNA. Simulated s-parameters and input impedance of the front end using steady-state analysis are shown in Figure 5.Figure 5
Simulated Z11 and S11 of receiver RF front end.


## 3. Building Block Designs

### 3.1. LNA

Comparing with mixer-first receiver, LNA-first architecture has better noise and LO-to-RF isolation performance. And impedance transparent character is discussed in Section2.2. A feedback buffer is added between the LNA output and input, which is used to further map the bandpass filtering characteristic of 4-path passive mixer to the input of LNA. Since the receiver noise figure is dominated by the LNA, it should be carefully designed. According to [12], the noise figure of LNA can be calculated as(12)F=FRS+FM1+FRF+FM2+FRL+FMB=1+γ1RSgm12+AV1+AV2+RFRS1+AV2+γ21+AV1-RFRS1+AV+1gm1RSAV2+AV1+AV2+γBgmBRS1-RFRS1+AV2.There is a negative item in the equation above, so the noise factor can be optimized with the degree of freedom brought by the active feedback. The layout parasitic is also significantly affecting the NF. The noise of gate resistances is directly amplified to the output; low resistance metal layers should be used for gate connections.As shown in Figure6, main amplifier with CMOS structure is used in LNA, which increases 2x current efficiency. CMOS LNA can also cancel out the second order nonlinearity by properly sizing. A linearization technique called “derivative superposition” [7, 15] is used to improve the linearity of LNA because it determines the linearity of whole RX. The third derivatives (g3) of drain current from the main and auxiliary transistors are added to cancel distortion. Because g3’s sign is different at the moderate and strong inversion region, zero g3 can be created by proper biasing the transistors. The auxiliary inverter only contains weak-inversion transistors, resulting in much smaller power consumption than the common feedforward technique.Figure 6
Schematic of the presented CMOS LNA.


### 3.2. Filter

Figure7 is the proposed 3rd-order Butterworth low-pass filter. The filter consists of two main stages. For higher linearity, the Tow-Thomas biquad filter is arranged after a first-order filter. Programmable resistor and capacitor arrays are designed to adjust gain and compensate for process variations.Figure 7
The proposed architecture of 3rd-order Butterworth low-pass active-RC filter.Feedforward compensated amplifier has less power dissipation than miller-compensated opamps when reaching the same design index [16]. A typical two-stage feedforward compensated amplifier is used in this work, as shown in Figure 8. To further lower power and area, local common-mode feedback circuit is applied. To meet the demand of ripple (<0.2 dB), the GBW of op1, op2, and op3 in Figure 6 are 400 MHz, 200 MHz, and 200 MHz, respectively.Figure 8
Schematic of two-stage feedforward compensated opamp.For high gain filter, it is necessary to eliminate input DC offset. The DC offset cancellation (DCOC) circuit is shown in Figure9. The low-pass feedback circuit will make the filter indicate high-pass feature at relatively low frequency.Figure 9
DCOC circuit of two-stage low-pass filters.


### 3.3. ADPLL

Based on the blocking requirement, the codesign between the RF front end and ADPLL is necessary. The LO phase noise at 1 MHz offset should be less than −116 dBc/Hz with 6 dB margin. Both of the effects of reciprocal mixing of the blocker and the white noise introduced to signal band are considered. A DTC-assisted fractional-N ADPLL is employed with a time-amplified TDC, as shown in Figure 10. The TDC employs time amplifier (TA) realizing fine resolution. DTC is used with phase prediction algorithm to reduce the detection range of TDC. Δ∑-DTC can be cascaded with DTC to suppress the spur induced by DTC quantization. Autocontroller algorithm and gear-shift technique helps to reduce the locking time to less than 20 us.Figure 10
ADPLL architecture.TDC and DCO are the most power-consuming blocks in the traditional ADPLL, so some techniques are used to lower power dissipation of these parts. Firstly, TDC snapshot is utilized to reduce the sampling rate from CKV to CKVS (=FREF), and the DTC can reduce the TDC detection range, which contributes to a prominent power reduction. Secondly, a low-supply structure DCO is designed in this work, which consumes just 900 uW at 1.5–2.05 GHz. A TA-TDC is designed to achieve high quantization to improve in-band phase noise. The DCO is followed by an inductor-less 2x divider to provide a reasonable input frequency for the phase digitization circuits. The divider generates four 90°-spaced phases.


## 3.1. LNA

Comparing with mixer-first receiver, LNA-first architecture has better noise and LO-to-RF isolation performance. And impedance transparent character is discussed in Section2.2. A feedback buffer is added between the LNA output and input, which is used to further map the bandpass filtering characteristic of 4-path passive mixer to the input of LNA. Since the receiver noise figure is dominated by the LNA, it should be carefully designed. According to [12], the noise figure of LNA can be calculated as(12)F=FRS+FM1+FRF+FM2+FRL+FMB=1+γ1RSgm12+AV1+AV2+RFRS1+AV2+γ21+AV1-RFRS1+AV+1gm1RSAV2+AV1+AV2+γBgmBRS1-RFRS1+AV2.There is a negative item in the equation above, so the noise factor can be optimized with the degree of freedom brought by the active feedback. The layout parasitic is also significantly affecting the NF. The noise of gate resistances is directly amplified to the output; low resistance metal layers should be used for gate connections.As shown in Figure6, main amplifier with CMOS structure is used in LNA, which increases 2x current efficiency. CMOS LNA can also cancel out the second order nonlinearity by properly sizing. A linearization technique called “derivative superposition” [7, 15] is used to improve the linearity of LNA because it determines the linearity of whole RX. The third derivatives (g3) of drain current from the main and auxiliary transistors are added to cancel distortion. Because g3’s sign is different at the moderate and strong inversion region, zero g3 can be created by proper biasing the transistors. The auxiliary inverter only contains weak-inversion transistors, resulting in much smaller power consumption than the common feedforward technique.Figure 6
Schematic of the presented CMOS LNA.


## 3.2. Filter

Figure7 is the proposed 3rd-order Butterworth low-pass filter. The filter consists of two main stages. For higher linearity, the Tow-Thomas biquad filter is arranged after a first-order filter. Programmable resistor and capacitor arrays are designed to adjust gain and compensate for process variations.Figure 7
The proposed architecture of 3rd-order Butterworth low-pass active-RC filter.Feedforward compensated amplifier has less power dissipation than miller-compensated opamps when reaching the same design index [16]. A typical two-stage feedforward compensated amplifier is used in this work, as shown in Figure 8. To further lower power and area, local common-mode feedback circuit is applied. To meet the demand of ripple (<0.2 dB), the GBW of op1, op2, and op3 in Figure 6 are 400 MHz, 200 MHz, and 200 MHz, respectively.Figure 8
Schematic of two-stage feedforward compensated opamp.For high gain filter, it is necessary to eliminate input DC offset. The DC offset cancellation (DCOC) circuit is shown in Figure9. The low-pass feedback circuit will make the filter indicate high-pass feature at relatively low frequency.Figure 9
DCOC circuit of two-stage low-pass filters.


## 3.3. ADPLL

Based on the blocking requirement, the codesign between the RF front end and ADPLL is necessary. The LO phase noise at 1 MHz offset should be less than −116 dBc/Hz with 6 dB margin. Both of the effects of reciprocal mixing of the blocker and the white noise introduced to signal band are considered. A DTC-assisted fractional-N ADPLL is employed with a time-amplified TDC, as shown in Figure 10. The TDC employs time amplifier (TA) realizing fine resolution. DTC is used with phase prediction algorithm to reduce the detection range of TDC. Δ∑-DTC can be cascaded with DTC to suppress the spur induced by DTC quantization. Autocontroller algorithm and gear-shift technique helps to reduce the locking time to less than 20 us.Figure 10
ADPLL architecture.TDC and DCO are the most power-consuming blocks in the traditional ADPLL, so some techniques are used to lower power dissipation of these parts. Firstly, TDC snapshot is utilized to reduce the sampling rate from CKV to CKVS (=FREF), and the DTC can reduce the TDC detection range, which contributes to a prominent power reduction. Secondly, a low-supply structure DCO is designed in this work, which consumes just 900 uW at 1.5–2.05 GHz. A TA-TDC is designed to achieve high quantization to improve in-band phase noise. The DCO is followed by an inductor-less 2x divider to provide a reasonable input frequency for the phase digitization circuits. The divider generates four 90°-spaced phases.


## 4. Measured Results

This chip is fabricated in SMIC 55 nm 1P7M CMOS technology. Figure11 shows the die photograph of the receiver. The core area of the chip is 2.3 mm × 1 mm, and the ADPLL occupied 1 mm × 1.2 mm due to the inductor of DCO.Figure 11
Die photograph of the chip in 55 nm CMOS.As shown in Figure12, the in-band phase noise is about −95 dBc/Hz and the out-band phase noise is about −120 dBc/Hz at 1 MHz frequency offset, which can satisfy the requirement of NB-IoT protocol [8]. The rms jitter is about 1.1 ps which is integrated from 1 kHz to 10 MHz. The whole power consumption of ADPLL is about 4 mW.Figure 12
Measured phase noise of the frequency synthesizer.The measured S11 of the receiver with different LO frequency is shown in Figure13. Using the SPI the ADPLL was set up to LO frequency, respectively (1.2 GHz/1.4 GHz/1.6 GHz/1.8 GHz/2 GHz). Then the LO power was expected as 5 dBm. And the received signal is swept fromFLO −100 MHz toFLO +100 MHz. It shows that S11 < −10 dB over a 0.6–0.9 GHz RF range. The matching point is tunable with LO frequency and forms a narrow-band matching character which can improve the linearity of the receiver.Figure 13
Measured S11 of the receiver with different LO frequency.Figure14 shows the measured baseband noise figure of the receiver. We measured a minimum noise figure of 5.3 dB at 1 MHz with the LO frequency of 900 MHz. Both the simulated and measured NF are in good agreement. The simulated result is about 1 dB lower than the measured one. The NF discrepancy is mainly due to layout parasitic which can lower the transconductance of LNA and the inaccuracies of the noise model in simulation.Figure 14
Measured baseband noise figure of the receiver (FLO = 900 MHz).The OB-IIP3 is measured at LO frequency of 900 MHz. Two blockers with −25 dBm input power are injected. IIP3 is measured at different frequency offsets. Figure15 shows the test result of the OB-IIP3. It shows that due to the effect of impedance mapping, with the increase of the offset frequency, IIP3 increases. The highest point of linearity is mainly limited by the on-resistance of mixer and the linearity of LNA. The slope of the change in linearity is mainly limited by the capacitance size before the TIA. The in-band IIP3 is about −10 dBm, and the out-band IIP3 is +8 dBm at 60 MHz offset.Figure 15
Measured IIP3 at 900 MHz for different frequency offsets.The OB-IIP2 is measured at LO frequency of 900 MHz as the IIP3 test method. Two blockers with −25 dBm input power are injected. And two blockers are separated by 1 MHz, with an offset from LO frequency. Figure16 shows the test result of the IIP2. It shows that, due to the effect of impedance mapping, with the increase of the offset frequency, IIP2 increases. The out-band IIP2 is greater than +39 dBm without any calibration. This IIP2 is limited by the mixer mismatch and second nonlinearity of the gain stages. Since a CMOS LNA architecture is used in this work, IIP2 is improved in the proposed receiver. The measured result of this impedance transparent receiver is summarized in Table 2 with comparisons of prior arts. The proposed low power RX architecture has a suitable noise figure and linearity for IoT application and shows a good out-of-band blocker tolerance.Table 2
Comparison with prior arts.
Parameter This work [13] [14] [5] [6] Selective input matching Yes No No Yes Yes Architecture LNA withactive feedback Balun LNA Current mode LNA Mixerfirst Noisecancelling Operation frequency 0.6~1 GHz 0.75~0.96 GHz 1.0–5.2 GHz 0.1–2.4 GHz 0.08–2.7 GHz Gain 78 dB 20~104 dB 23 dB 40–70 dB 72 dB Noise figure 5.3 dB 5.1/4 dB 6.5 dB 7 dB @ 2 GHz 1.9 dB IB-IIP3 −10 dBm −6.2 dBm @ Min Gain - −67 dBm −18 dBm OB-IIP3 +8 dBm - −1.5 dBm +25 dBm +13.5 dB IIP2 39 dBm 45 dBm @ Min Gain - +56 dBm +85 dBm Technology 55 nm CMOS 180 nm CMOS 130 nm CMOS 65 nm CMOS 40 nm CMOS Core power 16 mW RX+4 mW ADPLL 25 mW @1.7V 13 mW RX+22 mW LO 37–70 mW 35.1–78 mWFigure 16
Measured IIP2 at 900 MHz for different frequency offsets.


## 5. Conclusion

A low power impedance transparent receiver for IoT application is proposed in this paper. A reconfigurable receiver with tunable channel filtering and narrow-band input matching at RX input is presented. Passive mixer and active feedback LNA are used in the receiver to further map the baseband impedance to RF input. A 3rd-order active-RC filter is employed in the receiver for meeting the IoT requirements. The filter achieves a relatively low power with the use of current-efficient feedforward compensated OTA. Digital controlled resistor and capacitor arrays are flexible for gain and bandwidth tuning. A DTC-assisted fractional-N ADPLL is employed with a time-amplified TDC. By utilizing blocker filtering and derivative superposition techniques, the proposed RX achieves NF of 5.3 dB with +8 dBm OB-IIP3 while consuming 16 mW. The ADPLL in-band phase noise is about −95 dBc/Hz and the out-band phase noise is about −120 dBc/Hz at 1 MHz frequency offset, while consuming 4 mW. The proposed receiver architecture can be used for low power IoT application, such as IEEE 802.11ah and NB-IoT.



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*Source: 9130910-2018-05-14.xml*