Second-order Intermodulation Research Articles

IP2 optimization in frequency mixers using ferroelectric field-effect transistors

Ferroelectric devices have traditionally been utilized in memory circuits due to their ability to retain a polarization charge and potentially act as a nonvolatile storage device. Their usage in applications unrelated to memory has also previously expanded into other digital and analog circuits, and now, it is being investigated in radio frequency circuits. This work explores the implementation of a frequency mixer using ferroelectric field-effect transistors in order to demonstrate stability against voltage offsets in a single-balanced mixer, making use of the polarization in the switching transistors to improve the performance of the second-order intermodulation product.

A High Performance I/Q Zero-IF Mixer with IIP2 Calibration Technique in 45nm SOI CMOS

This paper presents a high performance I/Q zero intermediate frequency (IF) mixer with a second-order input intermodulation point (IIP2) calibration technique in 45nm SOI CMOS process. A behavioral model of the mixer is established to analyze the sources of the second-order intermodulation distortion (IMD2). Based on the analysis, a high accuracy load resistance modulation array is applied to achieve excellent IIP2 performance. The frequency of the local oscillator (LO) signal is 3.5GHz, while the RF input signal frequency range is 3.4GHz∼3.6GHz. Simulation results show that the proposed zero-IF mixer achieves a conversion gain of more than 9.2dB with the input 1dB compression point of -11.28dBm. Noise figure is about 16.9dB at 10kHz and lower than 11.6dB at the frequency above 1MHz. The IIP2 of the circuit is larger than 66dBm after the calibration, which increases more than 40dBm.

Generation Mechanism and Characteristic Analysis of Dual-Frequency Pseudo-Signal Interference of the Swept-Frequency Radar

In order to master the law of the pseudo-signal interference effect of dual-frequency electromagnetic radiation in typical radar equipment, a certain type of Ku-band swept-frequency ranging radar was used as the test object to carry out single-frequency continuous wave and dual-frequency continuous wave pseudo-signal interference effect experiments. Through experiments, it is found that dual-frequency electromagnetic radiation will cause “hill” and “spike” type pseudo-signal interference to the swept-frequency radar. Based on the frequency analysis of the radar receiving circuit, the interference mechanism of the dual-frequency pseudo-signal is revealed, and the morphological characteristics and distance law of the pseudo-signal are explained. The variation law of the pseudo-signal level with interference field strength is obtained. The results show that the in-band dual-frequency nonintermodulation interference is similar to the single-frequency interference, and the only difference is that the number of pseudo-signals increases; when the interference frequency difference is about 400∼600 MHz, the out-of-band dual-frequency second-order intermodulation signal will cause “hill” type pseudo-signal interference, and the pseudo-signal distance is random; when the interference frequency difference is less than 5 MHz, both the dual-frequency second-order intermodulation signal and the third-order intermodulation signal will cause “spike” pseudo-signal interference inside and outside the radar operating frequency band; the pseudo-signal distance is fixed.

Research on Dual-Frequency Electromagnetic False Alarm Interference Effect of a Typical Radar

In order to master the position variation rule of radar false alarm signal under continuous wave (CW) electromagnetic interference and reveal the mechanism of CW on radar, taking a certain type of stepping frequency radar as the research object, theoretical analysis of the imaging mechanism of radar CW electromagnetic interference false alarm signals from the perspective of time-frequency decoupling and receiver signal processing. Secondly, electromagnetic interference injection method is used to test the single-frequency and dual-frequency electromagnetic interference effect of the tested equipment. The results show that under the single frequency CW electromagnetic interference, the sensitive bandwidth of false alarm signal is about ±75 MHz, and the position of false alarm signal irregularity changes. Under the in-band dual-frequency CW electromagnetic interference, the position of non-intermodulation false alarm signal is similar to that of single frequency. However, the distance difference of two non-intermodulation false alarm signals is regular. In addition, the positions of the second-order intermodulation false alarm signals of the tested radar are also regular, and its position changes with the change of the second-order intermodulation frequency difference.

A Model for Predicting Second-Order Intermodulation Low-Frequency Blocking Effects

To identify and improve the electromagnetic compatibility of a global navigation satellite system (GNSS) receiver under a complex electromagnetic environment, the blocking effects of single-frequency and out-of-band dual-frequency electromagnetic radiation (EMR) on a GNSS receiver were experimentally analyzed. This study is the first to investigate second-order intermodulation second-order intermodulation low-frequency blocking (SILB) interference which was newly discovered in our tests. The mechanism of the SILB effect was analyzed, and two key parameters were identified. The SILB interference factor and the relative value of the low-frequency interference level were introduced to establish a model predicting SILB effects. The method of determining the parameters, the modeling process, and the results are discussed in this article on the basis of both theoretical derivations and experimental measurements. A GNSS receiver was used as the equipment under test to verify the model. Notably, the results demonstrated that the threshold for SILB was approximately 30 dB lower than that for out-of-band single-frequency interference. The model proposed in this article accurately evaluated and predicted the SILB interference.

Effect of second harmonic and second‐order intermodulation on third‐order passive intermodulation

Third-order intermodulation (IM3) is considered as a typical metric to evaluate passive intermodulation (PIM) in electrical connectors, which may be affected by the second-order effect in the circuit with cascaded non-linearities. In this study, the effects of second harmonics and second-order intermodulation on the IM3 powers were theoretically modelled and experimentally verified. Combined with mathematical modelling, an equivalent circuit model of a passive non-linear source was presented to investigate the effect of second-order signals on the IM3 powers. A modified non-linear transfer function was developed by considering multiple non-linear superpositions in cascaded non-linearities. Based on the designed two-tone test, a mathematical expression was provided with the determination of correlation model coefficients. Numerical simulations were performed by using the proposed model, demonstrating the effect of signals induced by the second-order non-linearity on the IM3 powers in series passive components. The IM3 powers resulting from cascaded connectors associated with different signal frequencies were predicted. Coaxial connector samples were designed as cascaded PIM sources in circuits, which were experimentally measured in a GSM 900 MHz frequency band. Good agreement was obtained between the predictions and measurements with error of 0.76 dB in average.

A multi-tone high efficient bandwidth system with an eliminated even-order distortions using double dual-parallel Mach-Zehnder modulator

In this paper, a linearization of dual RF channels over a single carrier wavelength is proposed and experimentally demonstrated. Multiple microwave signals with a multi-octave bandwidth are modulated by a double dual-parallel Mach-Zehnder modulator (D-DPMZM) and recovered by a differential balanced detector (BPD). The theoretical and experimental model illustrates the elimination of second-order harmonic distortions (SHD) and second-order intermodulation (IMD2), and significant suppression of the third-order intermodulation (IMD3) by controlling the phase of the input RF signal and DPMZM. The proposed photonic link configuration illustrates the modulation of two microwave signals on a single optical carrier wavelength, and each RF channel is tested for Two-tone signals to illustrate the linearization of the channelized analog photonic link (CAPL). Firstly, a mathematical model is presented to illustrate the elimination of optical carrier and even-order distortions by using only single-tone in each RF channel. Secondly, the purity of the system is mathematically and experimentally investigated by introducing two-tones in each RF channel. We have analyzed both test cases, with single-tone and with a two-tone test, to help us understand and compare the performance of the system. For test case 1 and test case 2 of our proposed configuration, we have achieved a fundamental signal-to-interference ratio (S/I) of 60 dB and 65 dB with a spurious-free dynamic range (SFDR) of 110 dB.Hz2/3 and 116 dB.Hz2/3, respectively.

Fourth‐order nonlinear distortion to the power spectrum of RF amplifiers

Even-order intermodulation distortions are often considered easy to filter in narrowband radio frequency (RF) wireless systems because they are usually located far away from the desired passband and adjacent bands. However, even-order intermodulation distortions have recently attracted more interest with the increasing popularity of wideband RF applications. The authors' previous work was devoted to establishing the power spectrum model of second-order intermodulation distortion. Motivated by the latest efforts on RF power amplifier linearization with second-order and fourth-order intermodulation, our focus now is to establish a power spectrum model of fourth-order intermodulation distortion which can be used to discuss the fourth-order impacts on the passband and adjacent bands. Here, together with the authors' previous work on the odd-order intermodulation, a relatively comprehensive power spectrum model is presented here, including second-, third-, fourth-, and fifth-order intermodulation, which offers a broader view for spectrum planners and RF designers. With qualitative and quantitative reasoning, we further explain that higher-order (i.e., n > 5 ) IM distortions of a weakly nonlinear amplifier are indeed negligible. The experiment measurement at the end of this paper validates the spectrum model.

A CMOS RF Receiver with Improved Resilience to OFDM-Induced Second-Order Intermodulation Distortion for MedRadio Biomedical Devices and Sensors

A MedRadio RF receiver integrated circuit for implanted and wearable biomedical devices must be resilient to the out-of-band (OOB) orthogonal frequency division modulation (OFDM) blocker. As the OFDM is widely adopted for various broadcasting and communication systems in the ultra-high frequency (UHF) band, the selectivity performance of the MedRadio RF receiver can severely deteriorate by the second-order intermodulation (IM2) distortion induced by the OOB OFDM blocker. An analytical investigation shows how the OFDM-induced IM2 distortion power can be translated to an equivalent two-tone-induced IM2 distortion power. It makes the OFDM-induced IM2 analysis and characterization process for a MedRadio RF receiver much simpler and more straightforward. A MedRadio RF receiver integrated circuit with a significantly improved resilience to the OOB IM2 distortion is designed in 65 nm complementary metal-oxide-semiconductor (CMOS). The designed RF receiver is based on low-IF architecture, comprising a low-noise amplifier, single-to-differential transconductance stage, quadrature passive mixer, trans-impedance amplifier (TIA), image-rejecting complex bandpass filter, and fractional phase-locked loop synthesizer. We describe design techniques for the IM2 calibration through the gate bias tuning at the mixer, and the dc offset calibration that overcomes the conflict with the preceding IM2 calibration through the body bias tuning at the TIA. Measured results show that the OOB carrier-to-interference ratio (CIR) performance is significantly improved by 4–11 dB through the proposed IM2 calibration. The measured maximum tolerable CIR is found to be between −40.2 and −71.2 dBc for the two-tone blocker condition and between −70 and −77 dBc for the single-tone blocker condition. The analytical and experimental results of this work will be essential to improve the selectivity performance of a MedRadio RF receiver against the OOB OFDM-blocker-induced IM2 distortion and, thus, improve the robustness of the biomedical devices in harsh wireless environments in the MedRadio and UHF bands.

Spline-Based Adaptive Cancellation of Even-Order Intermodulation Distortions in LTE-A/5G RF Transceivers

Radio frequency transceivers operating in in-band full-duplex or frequency-division duplex mode experience strong transmitter leakage. Combined with receiver nonlinearities, this causes intermodulation products in the baseband, possibly with higher power than the desired receive signal. In order to restore the receiver signal-to-noise ratio in such scenarios, we propose two novel digital self-interference cancellation approaches based on spline interpolation. Both employ a Wiener structure, thereby matching the baseband model of the intermodulation effect. Unlike most state-of-the-art spline-based adaptive learning schemes, the proposed concept allows for complex-valued in- and out-put signals. The optimization of the model parameters is based on the stochastic gradient descent concept, where the convergence is supported by an appropriate step-size normalization. Additionally, we provide a gain control scheme and enable pipelining in order to facilitate a hardware implementation. An optional input transform improves the performance consistency for correlated sequences. In a realistic interference scenario, the proposed algorithms clearly outperform a state-of-the-art least mean squares variant with comparable complexity, which is specifically tailored to second-order intermodulation distortions. The high flexibility of the spline interpolation allows the spline-based Wiener models to match the performance of the kernel recursive least squares algorithm at less than 0.6% of the arithmetic operations.

On IP2 impact to nonlinear distortion of RF amplifiers

The second-order distortion, often using second-order intercept point (IP2) as an indicator, has been considered easy to be filtered in narrowband radio frequency (RF) communications because it is located far away from the passband of transmitted signals. However, with rapidly increased applications in wideband RF communications, the second-order intermodulation (IM) might become important, partially evidenced by the increased appearances of IP2 in the amplifier datasheets in recent years. In this article, a power spectrum model of the second-order IM is derived to quantify the second-order distortion using the IP2. This model could be used to determine under what conditions, in terms of the relation between the carrier frequency and bandwidth, the second-order IM will affect the passband or the adjacent bands or other applications, using three types of frequency scenarios. These discussions are beneficial for RF engineers and spectrum planners to predict interferences from second-order IM. The experimental measurement at the end of the article validates the spectrum model.

무선 중계 시스템에서 2차 수동 상호 변조 왜곡 모델링 비교

PIMD (Passive Intermodulation Distortion)는 무선 통신 시스템의 수동 소자의 비선형성으로 인해 2개 이상의 전송 신호주파수가 서로 간섭하여 원하지 않는 신호가 발생하는 현상입니다. 이러한 상호 변조 왜곡은 무선 통신 시스템의 수신 주파수대역에서 잡음 레벨을 증가시켜 수신기의 성능을 저하시킨다. 본 논문에서는 수정된 Quadratic Volterra 필터와 시간 지연 신경망을 기반으로 한 PIMD 모델링을 조사하여 수동 상호 변조 왜곡 수준을 줄여 업 링크 수신 성능을 향상 시킨다. 모델링 성능은 정규화된 평균 제곱 오차 측면에서 메모리 길이 및 시간 불일치에 따라 LTE 시스템의 중계기에서 샘플링된 데이터에 모델을 적용하여 평가된다.

A 28-GHz High Linearity Up-Conversion Mixer Using Second-Harmonic Injection Technique in 28-nm CMOS Technology

A 28-GHz high linearity active up-conversion mixer using 28-nm CMOS is presented in this letter. To enhance the modulated output power level under high-order modulation with IM3 improvement in the high IF input power region, the second-order intermodulation (IM2) signal injection technique is adopted. The positive third-order intermodulation (IM3) signal is generated by mixing the IM2 signal and IF input signal with transistors in the transconductance stage biasing in triode region. Therefore, by combining these opposite IM3 signal at the output of transconductance stage, the IM3 distortion can be alleviated. Besides, the proposed mixer achieves an IM3 distortion improvement in a wide IF power range. The measurement results demonstrate conversion gain (CG) of −6.4 dB and output 1-dB compression point (OP1 dB) of −2.2 dBm with 19 mW. The two-tone measurement results exhibit 10.2 dBm output third-order intercept point (OIP3). Furthermore, with the modulation measured results using single-carrier 256-QAM signal, the proposed mixer also exhibits a distinguished output power enhancement when the linearizer turns on. To the best of the author’s knowledge, this design is the first demonstration and implemented of an IM2 signal injection technique in millimeter-wave frequency, which also improves the output power level of the high-order modulation measurement.

2.4-GHz CMOS Bluetooth RF Receiver With Improved IM2 Distortion Tolerance

A low-power CMOS sliding-IF RF receiver is presented for Bluetooth Low Energy (BLE) applications. It comprises an LNA, RF mixer, transconductance ( $g_{m}$ ) stage, IF mixer, transimpedance amplifier (TIA), and LO generation block. We present a comprehensive analysis of the second-order intermodulation (IM2) distortion that is induced by an in-band orthogonal frequency-division modulation (OFDM) blocker and its effects on the receiver input sensitivity. Based on the analysis, an in-band two-tone blocker tolerance test procedure is proposed, and an IM2 calibration circuit to enhance the receiver’s IM2 tolerance is presented. Furthermore, a conflict issue in the co-optimization of IM2 calibration at the IF mixer stage and dc offset calibration at the subsequent baseband amplifier stage is alleviated. This is achieved by employing a body bias control method for the dc offset calibration and a gate bias control method for the IM2 calibration. A BLE RF receiver integrated circuit was fabricated in a 65-nm RF CMOS process. Dissipating 3.55 mW from a 1-V supply, it achieves a gain control range from +2 to +62 dB, a minimum noise figure of 3 dB, and an out-of-band (OOB) single-tone blocker tolerance level of −10 dBm. Measurement results demonstrate that the proposed IM2 calibration circuit significantly improves the in-band two-tone blocker tolerance level by 7–12 dB, achieving its range from −41 to −31 dBm.

A Simplified Accuracy Enhancement to the Saleh AM/AM Modeling and Linearization of Solid-State RF Power Amplifiers

The Saleh behavioral model exhibits high prediction accuracy for nonlinearity of traveling-wave tube power amplifiers (TWT-PAs). However, the accuracy of the Saleh model degrades when modeling solid-state power amplifiers (SSPAs) technology. In addition, the polynomial expansion of the Saleh model consists of only odd-order terms as analyzed in this work. This paper proposes a novel model accuracy enhancement for the Saleh amplitude-to-amplitude (AM/AM) model when applied to radio frequency (RF) SSPAs. The proposed model enhancement accounts for the second-order intermodulation distortion, which is an important nonlinearity challenge in wideband wireless communications. The proposed static AM/AM model is a three-parameter rational function, which exhibits low complexity compared to the state-of-the-art behavioral models. A transpose architecture of finite-impulse digital filter is used to quantify the memory effect in SSPAs. A least-squares method is used for extracting all the model parameters. A linearization technique using a three-parameter digital predistortion model is also calculated to compensate for the AM/AM nonlinear distortion in SSPAs. Finally, the identification and evaluation of the enhanced Saleh model is presented based on measurements of RF SSPAs.

Use of Higher-Harmonic and Intermodulation Generation of Ultrasonic Waves to Detecting Cracks due to Steel Corrosion in Reinforced Cement Mortar

The aim of this work was to provide further confirmation of the possible use of non-linear ultrasonic techniques for detecting the cracking due to corrosion of steel reinforcements in concrete. To this end accelerated steel corrosion tests have been conducted on model reinforced cement mortar specimens, while monitoring the appearance and width evolution of visible surface cracks, and performing non-linear ultrasonic measurements based on the phenomena of harmonic distortion and intermodulation. A new parameter, based on the difference between the amplitude of the fundamental frequency and the sum of the amplitudes of all the first-order and second-order intermodulation products, has been proposed in this work. The results confirm that the appearance of visible surface micro-cracks are preceded and accompanied by the observation of strong non-linear features in the received signal. Furthermore, the new parameter proposed in this work is as efficient as the relative non-linearity parameters, classically used in harmonic distortion non-linear ultrasonic studies, for detecting the non-linear features associated with the critical events of the cracking of cement mortar due to embedded steel corrosion. A hypothesis has been developed considering the possible effect of the filling of the void space by liquid containing rust products after the formation of new cracks or the enlargement of its width. This filling process, which might be particularly enhanced by net convective transport of liquid, would explain the evolution of the values of all the parameters used for putting in evidence the non-linear elastic features after the critical events of the cracking process.

Second-order Intermodulation Low Frequency Blocking Effect and Mechanism for Communication Radio under Electromagnetic Radiation

In order to reveal the complex electromagnetic environment effects mechanism of communication radio, the blocking effect of single-frequency and out-of-band dual-frequency electromagnetic radiation for the ultra-short wave digital communication radio is experimentally studied by irradiation method. The rule of single-frequency electromagnetic radiation effect and the susceptible bandwidth are determined. The experimental data show that the tested radio is 9～23 dB more susceptible to out-of-band dual-frequency third-order intermodulation blocking than single-frequency electromagnetic radiation blocking. A sensitive phenomenon of dual-frequency electromagnetic radiation which can neither be explained by the dual-frequency non-intermodulation superposition mechanism nor by the third-order intermodulation mechanism has been found in the experiment.

Spectrally efficient optical orthogonal frequency division multiplexing.

This paper charts the development of spectrally efficient forms of optical orthogonal frequency division multiplexing (OFDM) that are suited for intensity-modulated direct detection systems, such as wireless optical communications. The journey begins with systems using a DC-bias to ensure that no parts of the signal that modulates the optical source are negative in value, as negative optical intensity is unphysical. As the DC-part of the optical signal carries no information, it is wasteful in energy; thus asymmetrically clipped optical OFDM was developed, removing any negative-going peaks below the mean. Unfortunately, the clipping causes second-order distortion and intermodulation, so some subcarriers appear to be unusable, halving spectral efficiency; this is similar for unipolar and flipped optical OFDM. Thus, a considerable effort has been made to regain spectral efficiency, using layered techniques where the clipping distortion is mostly cancelled at the receiver, from a knowledge of one unpolluted layer, enabling one or more extra ‘layers/paths/depths’ to be received on the previously unusable subcarriers. Importantly, for a given optical power and high-order modulation, layered methods offer the best spectral efficiencies and need the lowest signal-to-noise ratios, especially if diversity combining is used. Thus, they could be important for high-bandwidth optical fibre systems. Efficient methods of generating all layers simultaneously, using fast Fourier transforms with their partial calculations extracted, are discussed, as are experimental demonstrations in both wireless and short-haul communications links. A musical analogy is also provided, which may point to how orchestral and rock music is deciphered in the brain.This article is part of the theme issue ‘Optical wireless communication’.

RF pilot tone phase noise cancellation based on DD-MZM SSB modulation for optical heterodyne RoF link

The optical heterodyne radio over fiber (RoF) link using single-sideband (SSB) modulation has advantage in system scalability, tunability, as well as resistance to chromatic dispersion induced frequency selective fading. However, the phase noise which seriously degrades system performance, is a major obstacle to employ low-cost free-running lasers in the aforementioned link. In this paper, the RF pilot tone (RFP) phase noise cancellation (PNC) based on dual drive Mach–Zehnder modulator SSB modulation for optical heterodyne RoF link is investigated and demonstrated. Two kinds of RFP PNC schemes, carrier whole multiplication (CWM) and carrier signal multiplication (CSM), are both derived theoretically and verified experimentally. The impacts of carrier signal power ratio, carrier filter bandwidth and guard band on system performance are studied in detail. The results show that, the RFP-CSM scheme can improve the spectral efficiency by 62.5% and receiver sensitivity of 1.2 dB for 1.25 Gbps quadrature phase shift keying signal at a BER of 3.8 ×10−3, as compared with the RFP-CWM scheme and power detection scheme, mainly attributed to the absence of the second-order nonlinear intermodulation distortion. Furthermore, the RFP-CSM scheme demonstrates good phase noise robustness with different high-order modulation formats under two kinds of linewidth local oscillator lasers.

A Robust Nonlinear RLS Type Adaptive Filter for Second-Order-Intermodulation Distortion Cancellation in FDD LTE and 5G Direct Conversion Transceivers

Transceivers operating in frequency division duplex experience a transmitter leakage (TxL) signal into the receiver due to the limited duplexer stop-band isolation. This TxL signal in combination with the second-order nonlinearity of the receive mixer may lead to a baseband (BB) second-order intermodulation distortion (IMD2) with twice the transmit signal bandwidth. In direct conversion receivers, this nonlinear IMD2 interference may cause a severe signal-to-interference-plus-noise ratio degradation of the wanted receive signal. This contribution presents a nonlinear Wiener model recursive least-squares (RLS) type adaptive filter for the cancellation of the IMD2 interference in the digital BB. The included channel-select-, and DC-notch filter at the output of the proposed adaptive filter ensure that the provided IMD2 replica includes the receiver front-end filtering. A second, robust version of the nonlinear RLS algorithm is derived which provides numerical stability for highly correlated input signals which arise in e.g. LTE-A intra-band multi-cluster transmission scenarios. The performance of the proposed algorithms is evaluated by numerical simulations and by measurement data.