Hard-switched mixers have attractive linearity and noise properties, but are plagued by spurious responses due to the harmonic content of square-wave local oscillator (LO) signals. Harmonic rejection ...mixers (HRMs) reject (some of) these responses and can be constructed combining polyphase mixing and amplitude weighting. This brief presents a generalized model for the analysis of the harmonic rejection (HR) of such HRMs, based on circular convolution. We show that the effective LO signal can be modeled as a periodic Dirac impulse filtered by a time-discrete filter. For a multi-stage HR system, this filter consists of multiple stages as well, and the coefficients of each stage can be found simply by inspection. The total HR is shown to be the sum (in dB) of the rejection of the individual filtering stages, highly simplifying analysis and design of HRMs.
In this paper, we propose and analyze a pulse-output digital-to-frequency converter (DFC) generating square waves, which uses a digital-to-time converter (DTC) to correct the spurious tones (spurs) ...in the output spectrum. We focus on high-level architectural potential, discuss the design features of a DTC suitable for the proposed system, and explore possibilities and limits of this approach in terms of cleanness of the output spectrum. The behavioral model simulations confirm the theoretical analysis presented. Besides an analytical description of the output spurs, we derive a closed-form estimate of the worst-case spur, which leads to a simple design equation. This is useful to determine the DTC requirements number of bits and integral non-linearity (INL), given a certain spurious-free dynamic range (SFDR) target. We show that the maximum spur strength (in dBc) depends exclusively on the ratio between the output frequency and the clock frequency and the DTC features (number of bits, INL, and other impairments) and increases with the ratio by 6 dB/octave.
This article presents a multi-receiver cross-correlation technique for (B)FSK receivers, targeting wireless sensor network applications. Here, multiple receiver outputs are pair-wise cross-correlated ...and the correlated output samples are averaged to lower the noise floor at the receiver output. Compared to a two-receiver cross-correlation, multi-receiver cross-correlation generates more cross-correlated output samples in a given time. Hence it requires a shorter measurement time for a desired noise floor reduction and facilitates a higher data rate for (B)FSK operation. Compared to a single receiver, it improves the linearity and the harmonic interferer tolerance using passive splitters and different LO frequencies in the receiver paths respectively. These theoretical insights are verified with measurements for the first time using a 2- and 3-receiver cross-correlation in a BFSK receiver. Operating at 1GHz and with a data rate of 200kbps, the demonstrator, using sub-mW mixer-first receiver front-ends for power efficiency, achieves −102dBm sensitivity and >40 dB rejection for both narrow and wideband harmonic interferers without any RF filters.
An integrated spectrum analyzer is useful for built-in self-test purposes, software-defined radios, or dynamic spectrum access in cognitive radio. The analog/RF performance is impaired by a number of ...factors, including thermal noise, phase noise, and nonlinearity. In this paper, we present an integrated circuit with two integrated RF-frontends, of which the outputs are crosscorrelated in digital baseband. We show by theory and measurements that the above-mentioned impairments are mitigated by this technique. The presented 65-nm CMOS prototype operates at 1.2 V, and obtains a noise floor below -169 dBm/Hz, an IIP 3 of +25 dBm, and more than 20 dB of phase-noise reduction. In a special high-impedance mode, an even lower noise floor below -172 dBm/Hz is obtained.
Cross-correlation can be used in energy detection applications, such as spectrum analyzers, but also frequency shift keying (FSK) receivers, to improve noise suppression. To achieve higher ...signal-to-noise ratio (SNR), integration in time may be used, but could make it rather slow for communication purposes. In order to achieve better data-rates in low SNR conditions, we propose to use multiple chains instead of the traditional two chains. In this paper, we show an analysis of the SNR improvement and the power consumption penalty for BFSK modulation when using more chains. It shows that for low noise correlation between the chains, the improvement in sensitivity is proportional to the number of chains. Also, we develop a figure-of-merit to evaluate the optimum number of chains for different parameters of the receiver design. Furthermore, two examples from literature are analyzed. At their optimum number of chains, they both show ~6dB improvement in sensitivity with similar or even better figure-of- merit.
High performance and energy efficiency are very crucial aspects in e.g. the field of edge computing where a tight power budget constrains the device operation. Different logic families were explored ...over the years to design standard cells with higher performance and/or lower power while keeping the noise immunity and the compatibility with design automation tools intact. Hybrid pass transistor logic with static CMOS output (HPSC) seems to be promising and is exploited in this paper to design low energy, high performance and toolchain-compatible standard cells without compromising on noise immunity and chip area. This paper presents a 2/3-input XOR cell, a 2/3-input XNOR cell, two variants of a half adder cell, a full adder cell and two variants of a 1-bit multiply-accumulate combinational cell based on a combination of HPSC and static CMOS logic in a commercial 65nm Low-Power CMOS technology. Post-layout simulations over all the process-voltage-temperature corners show a 4.7% - 35.7% lower energy-delay product with significant improvement in the propagation delay of the proposed cells.
High linearity CMOS radio receivers often exploit linear V-I conversion at RF, followed by passive down-mixing and an OpAmp-based Transimpedance Amplifier at baseband. Due to nonlinearity and finite ...gain in the OpAmp, virtual ground is imperfect, inducing distortion currents. This paper proposes a negative conductance concept to cancel such distortion currents. Through a simple intuitive analysis, the basic operation of the technique is explained. By mathematical analysis the optimum negative conductance value is derived and related to feedback theory. In- and out-of-band linearity, stability and Noise Figure are also analyzed. The technique is applied to linearize an RF receiver, and a prototype is implemented in 65 nm technology. Measurement results show an increase of in-band IIP 3 from 9 dBm to >20 dBm, and IIP2 from 51 to 61 dBm, at the cost of increasing the noise figure from 6 to 7.5 dB and <;10% power penalty. In 1 MHz bandwidth, a Spurious-Free Dynamic Range of 85 dB is achieved at <;27 mA up to 2 GHz for 1.2 V supply voltage.
Spectrum sensing is a key enabler of cognitive radio but generally suffers from what is called a signal-to-noise ratio (SNR) wall, i.e., a minimum SNR below which it is impossible to reliably detect ...a signal. For energy detection, which has the advantage of not requiring knowledge of the signal, the SNR wall is caused by uncertainty in the noise level. Cross-correlation has been suggested as a possible means to obtain higher sensitivity but has received little attention in the context of noise uncertainty. The idea of cross-correlation is to have two receive paths, where each path independently processes the signal before they are combined, such that the noise added to the input signal at the individual paths is largely uncorrelated. In this paper, we mathematically quantify the SNR wall for cross-correlation, showing that it linearly scales with the amount of noise correlation. This lower noise correlation results in higher sensitivity, which is significantly better than that for autocorrelation. Equations that can be used to estimate the benefit over autocorrelation and the measurement time for a required probability of detection and false alarm are derived.
The product, convolution, correlation, Wigner distribution function (WDF) and ambiguity function (AF) of two Hermite functions of arbitrary order n and m are derived and expressed as a bounded, ...weighted sum of n+m Hermite functions. It was already known that these mathematical operations performed on Gaussians (Hermite functions of the zeroth-order) lead to a result which can be expressed as a Gaussian function again. We generalize this reciprocity to Hermite functions of arbitrary order. The product, convolution, correlation, WDF, and AF operations performed on two Hermite functions of arbitrary order lead to remarkably similar closed-form expressions, where the difference between the operations is primarily determined by distinct phase changes of the weights of the Hermite functions in the result. The closed-form expressions are generalized to the class of square-integrable functions. A key insight from the closed-form expressions is applied to the design of orthogonal, time-frequency localized communication signals which are characterized by an AF with rotational symmetry. In addition to this application, the theoretical expressions may prove useful for signal analysis in fields ranging from communications, radar and image processing to quantum mechanics.
Highly linear CMOS radio receivers increasingly exploit linear RF V-I conversion and passive down-mixing, followed by an OpAmp based Transimpedance Amplifier at baseband. Due to the finite OpAmp gain ...in wideband receivers operating with large signals, virtual ground is imperfect, inducing distortion currents. We propose to apply a negative conductance to cancel this distortion. In an RF receiver, this increases In-Band IIP 3 from 9dBm to >20dBm, at the cost of 1.5dB extra NF and <;10% power penalty. In 1MHz bandwidth, a Spurious-Free Dynamic Range of 85dB is achieved at <;27mA up to 2GHz for 1.2V supply voltage.
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