Tunable n-path notch filters for blocker suppression: modeling and verification

N-path switched-RC circuits can realize filters with very high linearity and compression point while they are tunable by a clock frequency. In this paper, both differential and single-ended N-path notch filters are modeled and analyzed. Closed-form equations provide design equations for the main filtering characteristics and nonidealities such as: harmonic mixing, switch resistance, mismatch and phase imbalance, clock rise and fall times, noise, and insertion loss. Both an eight-path single-ended and differential notch filter are implemented in 65-nm CMOS technology. The notch center frequency, which is determined by the switching frequency, is tunable from 0.1 to 1.2 GHz. In a 50- environment, the N-path filters provide power matching in the passband with an insertion loss of 1.4–2.8 dB. The rejection at the notch frequency is 21–24 dB,P1 db> + 2 dBm, and IIP3 > + 17 dBm

Quantization effects in the polyphase N-path IIR structure

Polyphase IIR structures have recently proven themselves very attractive for very high performance filters that can be designed using very few coefficients. This, combined with their low sensitivity to coefficient quantization in comparison to standard FIR and IIR structures, makes them very applicable for very fast filtering when implemented in fixed-point arithmetic. However, although the mathematical description is very simple, there exist a number of ways to implement such filters. In this paper, we take four of these different implementation structures, analyze the rounding noise originating from the limited arithmetic wordlength of the mathematical operators, and check the internal data growth within the structure. These analyses need to be done to ensure that the performance of the implementation matches the performance of the theoretical design. The theoretical approach that we present has been proven by the results of the fixed-point simulation done in Simulink and verified by an equivalent bit-true implementation in VHDL

Two-Site Quantum Random Walk

We study the measure theory of a two-site quantum random walk. The truncated decoherence functional defines a quantum measure $\mu_n$ on the space of $n$-paths, and the $\mu_n$ in turn induce a quantum measure $\mu$ on the cylinder sets within the space $\Omega$ of untruncated paths. Although $\mu$ cannot be extended to a continuous quantum measure on the full $\sigma$-algebra generated by the cylinder sets, an important question is whether it can be extended to sufficiently many physically relevant subsets of $\Omega$ in a systematic way. We begin an investigation of this problem by showing that $\mu$ can be extended to a quantum measure on a "quadratic algebra" of subsets of $\Omega$ that properly contains the cylinder sets. We also present a new characterization of the quantum integral on the $n$-path space.Comment: 28 page

Design Considerations of a Sub-50 {\mu}W Receiver Front-end for Implantable Devices in MedRadio Band

Emerging health-monitor applications, such as information transmission through multi-channel neural implants, image and video communication from inside the body etc., calls for ultra-low active power (<50${\mu}$W) high data-rate, energy-scalable, highly energy-efficient (pJ/bit) radios. Previous literature has strongly focused on low average power duty-cycled radios or low power but low-date radios. In this paper, we investigate power performance trade-off of each front-end component in a conventional radio including active matching, down-conversion and RF/IF amplification and prioritize them based on highest performance/energy metric. The analysis reveals 50${\Omega}$ active matching and RF gain is prohibitive for 50${\mu}$W power-budget. A mixer-first architecture with an N-path mixer and a self-biased inverter based baseband LNA, designed in TSMC 65nm technology show that sub 50${\mu}$W performance can be achieved up to 10Mbps (< 5pJ/b) with OOK modulation.Comment: Accepted to appear on International Conference on VLSI Design 2018 (VLSID

The Total Acquisition Number of the Randomly Weighted Path

There exists a significant body of work on determining the acquisition number $a_t(G)$ of various graphs when the vertices of those graphs are each initially assigned a unit weight. We determine properties of the acquisition number of the path, star, complete, complete bipartite, cycle, and wheel graphs for variations on this initial weighting scheme, with the majority of our work focusing on the expected acquisition number of randomly weighted graphs. In particular, we bound the expected acquisition number $E(a_t(P_n))$ of the $n$-path when $n$ distinguishable "units" of integral weight, or chips, are randomly distributed across its vertices between $0.242n$ and $0.375n$. With computer support, we improve it by showing that $E(a_t(P_n))$ lies between $0.29523n$ and $0.29576n$. We then use subadditivity to show that the limiting ratio $\lim E(a_t(P_n))/n$ exists, and simulations reveal more exactly what the limiting value equals. The Hoeffding-Azuma inequality is used to prove that the acquisition number is tightly concentrated around its expected value. Additionally, in a different context, we offer a non-optimal acquisition protocol algorithm for the randomly weighted path and exactly compute the expected size of the resultant residual set.Comment: 19 page

On the digraph of a unitary matrix

Given a matrix M of size n, a digraph D on n vertices is said to be the digraph of M, when M_{ij} is different from 0 if and only if (v_{i},v_{j}) is an arc of D. We give a necessary condition, called strong quadrangularity, for a digraph to be the digraph of a unitary matrix. With the use of such a condition, we show that a line digraph, LD, is the digraph of a unitary matrix if and only if D is Eulerian. It follows that, if D is strongly connected and LD is the digraph of a unitary matrix then LD is Hamiltonian. We conclude with some elementary observations. Among the motivations of this paper are coined quantum random walks, and, more generally, discrete quantum evolution on digraphs.Comment: 6 page

Duality relation between coherence and path information in the presence of quantum memory

The wave-particle duality demonstrates a competition relation between wave and particle behavior for a particle going through an interferometer. This duality can be formulated as an inequality, which upper bounds the sum of interference visibility and path information. However, if the particle is entangled with a quantum memory, then the bound may decrease. Here, we find the duality relation between coherence and path information for a particle going through a multipath interferometer in the presence of a quantum memory, offering an upper bound on the duality relation which is directly connected with the amount of entanglement between the particle and the quantum memory.Comment: 6 pages, 1 figure, comments are welcom