Optimized design of harmonic-injection dividers

A new formulation is presented for the efficient harmonic-balance analysis of the division bandwidth of frequency dividers by a high order. The procedure is based on some mathematical properties of the solution curve under low-amplitude of the input generator. Through a simple fitting technique, it is possible to determine the variation of the synchronization bandwidth versus any design parameter, while keeping constant the central frequency of the division band. The procedure also enables a prediction of the frequency-division interval for any value of the input-generator amplitude within the region of linear behavior with respect to the input source. It has been applied to the optimization of the input matching network in a frequency divider by 10, which uses a nonlinear transmission line (NLTL) as a feedback network.Spanish project TEC2011-29264-C03-01 for financial support

Harmonic-injection divider based on feedback through a nonlinear transmission line

An application of nonlinear transmission lines (NLTLs) to the design of harmonic-injection frequency dividers by high division order is presented. The NLTL, composed by inductance-varactor cells, is used as a feedback block of an active-device circuit, which gives rise to a free-running oscillation. Due to its highly nonlinear behavior, the NLTL can be optimized to enhance the harmonic components required for high order division through mixing with the input signal. The frequency bandwidth is further increased through a combination of phase-locking and frequency-locking effects. This is done extracting an error baseband signal from the active-device output, which, after suitable amplification, is applied to the varactor diodes of the NLTL. A design procedure is also presented to enable the switching of the division order between N and N-1 through control of the bias voltage. The novel configuration can have the advantage of a low complexity, low dc power consumption, and scalability. The new concept has been applied for the design a dual-order frequency divider by 10 and 9 with about 2% bandwidth

Two-level stability analysis of complex circuits

A new methodology is proposed for the small- and large-signal stability analysis of complex microwave systems, containing multiple active blocks. It is based on a calculation of the system characteristic determinant that ensures that this determinant does not exhibit any poles on the right-hand side (RHS) of the complex plane. This is achieved by partitioning the structure into simpler blocks that must be stable under either open-circuit (OC) or short-circuit (SC) terminations. Thus, the system stability is evaluated using a two-level procedure. The first level is the use of pole-zero identification to define the OC- or SC-stable blocks, which, due to the limited block size, can be applied reliably. In large-signal operation, the OC- or SC-stable blocks are described in terms of their outer-tier conversion matrices. The second level is the calculation and analysis of the characteristic determinant of the complete system at the ports defined in the partition. The roots of the characteristic determinant define the stability properties. The Nyquist criterion can be applied since, by construction, the determinant cannot exhibit any poles in the RHS. In addition, one can use pole-zero identification to obtain the values of the determinant zeroes. Because the determinant is calculated at a limited number of ports, the analysis complexity is greatly reduced.This work was supported in part by the Spanish Ministry of Science and Innovation and the European Regional Development Fund / Fondo Europeo de Desarrollo Regional (ERDF/FEDER) under research project TEC2017-88242-C3-1-R

Prediction of odd-mode instabilities under output mismatch effects

A methodology is presented to predict odd-mode instability in power amplifiers under output mismatch effects, as in the case of amplifiers connected to an antenna. This kind of instability is often observed in power-combining configurations, due to their symmetry properties. Unlike the single-ended situation, there is a cancellation of odd multiples of the oscillation frequency at the circuit output, so there is no impact of the load impedance values at the sideband frequencies. The odd-mode instability depends on the terminations at the fundamental frequency and its harmonic terms, and can only be detected within the circuit unstable loop, instead of the output plane. Here a methodology for the prediction and suppression of odd-mode instabilities is presented. Low-pass filtering effects and the use of a shorted stub allow the stability analysis to be limited to the fundamental-frequency termination. Then, the stability boundaries are efficiently determined through bifurcation detection inside the unstable loop, using the magnitude and phase of the reflection coefficient as the analysis parameters. Results have been validated through pole-zero identification and experimental measurements.This work has been funded by the Spanish Government under contract TEC2014-60283-C3-1-R, the European Regional Development Fund (ERDF/FEDER) and the Parliament of Cantabria (12.JP02.64069)

Analysis and synthesis of hysteresis loops in an oscillator frequency characteristic

A methodology for the analysis and synthesis of multiple hysteresis loops in the frequency characteristic of a voltage-controlled oscillator (VCO) is presented. This is achieved through the coupling of an oscillator inductance to multiple external (passive) resonators with resonant frequencies in the tuning range of the VCO. A possible application to the implementation of a compact chipless radio frequency identification (RFID) system is explored, using the oscillator as a reader and placing the external resonators in the tag. The system takes advantage of the high sensitivity to the tag resonances in the presence of hysteresis, which leads to vertical jumps in frequency versus the tuning voltage. A desired bit pattern would be encoded in the tag by enabling or disabling passive resonances at a sequence of frequencies. In the practical realization, the inductors in the oscillator and the external board are implemented through spiral inductors so that the resonators in the VCO and the tag have strong broadside coupling. The coupling effect is modeled through electromagnetic simulations, from which a linear admittance, representing the coupled subnetwork, is extracted. The multihysteresis oscillator characteristic can also be obtained experimentally through a new methodology able to stabilize the physically unstable sections without altering their steady-state values. Different demodulation methods for reading the tag are discussed.This work was supported in part by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under research project TEC2017-88242-C3-1-R

Facile fabrication of Fe-TiO2 thin film and its photocatalytic activity

Fe3+-TiO2 (Fe-TiO2) thin films were successfully prepared using a "sandwich" approach. TiO2 NPs were doped with different Fe3+ content (0.05%, 0.1%, 0.2% molar ratio), and the modified TiO2 NPs were deposited on glass flat support by dip coating. Structural, morphological, optical, and photocatalytic properties of Fe-TiO2 thin films were studied. XPS spectra confirm the presence of Ti, Fe, O, and defective -OH groups at the material surface. The Fe 2p spectrum demonstrates the existence of Fe3+. SEM images indicate that the incorporation of Fe3+ deforms in some degree the homogeneity of the TiO2 system. Additionally, incorporation of Fe3+ ions to the network creates an impurity band near the VB due to the oxygen vacancies, resulting in the reduction of the effective optical band gap. Photocatalytic activity of fabricated thin films in the elimination of sulfamethoxazole (SMT) follows pseudo first-order kinetics. The highest SMT removal yields were achieved using the sample with 0.05%Fe. Additionally, the use of greater thicknesses improves the removal performance. However, material detachment limits the maximum usable value around 6 mu m. Finally, stability and reusability of catalysts were confirmed studying the photocatalytic activity over three cycles and evaluating that no Fe3+ leaching occurred.This research was supported by Ministerio de Economia y Competitividad (Project AGL2016-80507-R) and University of Cadiz (Project PR2018-048)

Generalized stability criteria for power amplifiers under mismatch effects

Potential instability of power amplifiers (PAs) under mismatch effects is analyzed, with emphasis on the ease and generality of application of the stability criteria. The methodology is based on the evaluation of a large-signal version of the μ factor, considering mismatch effects in the fundamental frequency and three relevant sidebands: the baseband, the lower sideband and the upper sideband. This requires an outer-tier scattering-type conversion matrix of order 3 × 3 to be obtained, with the rest of sideband equations acting as an inner tier. It is taken into account that the circuit behaves nonlinearly with respect to the termination at the fundamental frequency. The consideration of three sidebands will enable the prediction of the two major forms of large-signal instability: incommensurable oscillations and frequency divisions by two. The analysis is preceded by an evaluation of the circuit own stability properties (proviso) under open and short circuit terminations at the sidebands, for all possible values of the termination at the fundamental frequency. Three different μ factors can be defined between any two ports of the scattering matrix. The analysis of the relationships between these factors and their continuity properties will allow the derivation of a single number able to characterize the PA potential instability for each fundamental-frequency termination. Results have been exhaustively validated with independent circuit-level simulations based on pole-zero identification and with measurements, using a variable output load and loading the PA with an antenna.This work has been supported by the Spanish Government under contract TEC2014-60283-C3-1-R and the Parliament of Cantabria (12.JP02.64069

Oscillation modes in multiresonant oscillator circuits

An in-depth analysis of the oscillation modes in free-running oscillators loaded with multiresonance networks is presented. The analysis illustrates the mechanisms for the generation and stabilization of the various periodic modes and establishes the conditions for existence of a single stable periodic mode in distinct regions of the parameter plane. The mechanisms for the generation and stabilization of quasi-periodic regimes, with two concurrent oscillations, are also analyzed, considering different situations in terms of two relevant poles. The stability analysis of quasi-periodic solutions, derived in terms of admittance functions, can be applied to circuits simulated with harmonic balance, under the assumption of high quality factor resonators. The impact of the transistor biasing on the stability properties of the quasi-periodic regimes has been analyzed, demonstrating that it can be used to isolate the quasi-periodic solution from the periodic ones. The analysis procedures have been applied to a practical oscillator based on two cross-coupled transistors at the two frequencies 900 MHz and 2.5 GHz. The case of two independent oscillations operating in a synchronized regime is also analyzed, as well as its impact on the phase-noise behavior.This work has been funded by the Spanish Government under contract TEC2014-60283-C3-1-R, the European Regional Development Fund (ERDF/FEDER) and the Parliament of Cantabria (12.JP02.64069)