Nerea Otegi

Study of intermodulation in RF MEMS variable capacitors

This paper provides a rigorous study of the causes and physical origins of intermodulation distortion (IMD) in RF microelectromechanical systems (MEMS) capacitors, its analytical dependence on the MEMS device design parameters, and its effects in RF systems. It is shown that not only third-order products exist, but also fifth order and higher. The high-order terms are mainly originated by the nonlinear membrane displacement versus applied voltage and, in the case considered in this study, with an additional contribution from the nonlinear dependence of the reflection coefficient phase on the displacement. It is also shown that the displacement nonlinear behavior also contributes to the total mean position of the membrane. In order to study these effects in depth, an analytical frequency-dependent IMD model for RF MEMS based on a mobile membrane is proposed and particularized to the case of a MEMS varactor-a device for which IMD can be significant. The model is validated, up to the fifth order, theoretically (using harmonic balance) and empirically (the IMD of a MEMS varactor is measured). To this end, a two-tone IMD reflection measurement system for MEMS is proposed.

Monte-Carlo stability analysis of microwave amplifiers

Pole-zero identification is being increasingly used as a method to analyze the stability of microwave circuits. However, in its current form, the stability analysis through pole-zero identification relies on a quality assessment that is based on visual inspection. This implies a manual approach that limits in practice the handling of a large amount of data as in the case of a yield or sensitivity analysis. Here, an automated methodology based on pole-zero identification is applied to the stability evaluation in the context of a Monte-Carlo analysis. The methodology is based on an algorithm that prevents the adverse effects due to undermodeling and overmodeling on the stability criteria. The approach is illustrated through its application to two in-home built amplifier prototypes: a medium power band L FET amplifier exhibiting a low frequency oscillation and a SiGe HBT reconfigurable amplifier for Wifi/Wimax applications that shows an undesired frequency division for some particular input drive conditions.

Generation of third and higher-order intermodulation products in MEMS capacitors, and their effects

In this work, the intermodulation distortion (IMD) produced by RF MEMS capacitors is studied. It is demonstrated that due to their nonlinear behaviour, parallel-plate MEMS capacitors generate 5th order tones along with 3rd order IMD products. It is shown that MEMS linear models, restricted to small displacements of the MEMS membrane, neglect 5th order distortion while underestimate 3rd order tones, when high voltages are considered. A numerical nonlinear model for simulating intermodulation is presented and validated by means of measurements for the general 2-tone case. Generation of 3rd and 5th IMD products is also demonstrated in MEMS driven by digitally-modulated communication signals. A measurement system is proposed in order to characterize IMD generation in RF MEMS capacitors excited by two RF tones as well as by digitally-modulated signals (QPSK).

Combined control of drain video bandwidth and stability margins in power amplifiers for envelope tracking applications

Envelope tracking amplifiers require significant video bandwidths to accommodate the dynamic variations of the drain bias. However, the increase of drain video bandwidth in a power amplifier can raise the risk of low frequency oscillations when some circuit parameters are changed. In this work, an experimental methodology is presented to monitor the drain video bandwidth and the low frequency stability margin in combination. The methodology is based on adding observation ports to both drain and gate bias paths in order to measure and control the critical and dominant poles that govern the low frequency dynamics of the power amplifier. The complete approach is illustrated in a demonstrator prototype specifically built for that purpose.

Experimental Characterization of Stability Margins in Microwave Amplifiers

This paper proposes a method for the experimental estimation of the stability margins in microwave amplifiers. The approach is based on measuring a closed-loop frequency response representing the linearization of the circuit about a steady-state solution. Critical poles of the amplifier are then obtained by applying conventional pole-zero identification techniques to the measured frequency response. As circuit parameters are modified, the evolution of these critical poles on the complex plane provides a practical way to assess the robustness of the design regarding its stability. Two types of common instabilities in microwave amplifiers are studied: low-frequency bias oscillations and parametric oscillations. For the low-frequency oscillations, the approach proposes the inclusion of an observation RF port into the amplifier bias path to experimentally obtain the critical poles of the circuit from a reflection coefficient measurement. Pole-placement techniques are then applied to increase the stability margin of detected critical resonances. For the parametric oscillations, pole-zero identification is applied to a frequency response obtained from a mixer-like characterization equivalent to the measurement of a “hot” reflection coefficient. The methodology is applied to two amplifier prototypes: an L-band field-effect transistor amplifier and a dual-mode WiFi-WIMAX amplifier that exhibit different kinds of unstable behavior.

Cold-source measurements for noise figure calculation in spectrum analyzers

A detailed analysis of the suitability of cold source based noise figure measurements in a spectrum analyzer is given in this paper. This technique presents some advantages in comparison to classical Y-factor techniques when dealing with problems related to device input match. A fully corrected noise figure calculation procedure, complemented with vector corrections and receiver noise calibration, is analyzed. For that, a noise calibration of the spectrum analyzer receiver, based upon analytical calculation, is given.

A MEMS capacitor with improved RF power handling capability

This paper presents a structure of MEMS capacitor providing independence of its nominal capacity and tuning range from the applied RF signal power. The capacitor includes a third parallel plate acting as an electrode to which an extra DC voltage is applied to compensate for the self-actuation effect. This means that the device can be used in many applications working under different RF power conditions, without changing its performance - nominal capacity and tuning range. Capacitor design concept and simulations are provided. It has been manufactured using a standard surface-micromachining MEMS technology. Experimental results are presented, validating the concept and demonstrating its feasibility and advantages.

Increasing low-frequency stability margins in microwave amplifiers from experimental data

A key aspect in the robust design of microwave amplifiers is to ensure circuit stability beyond the nominal operating conditions. In this work, a method for measuring and controlling the stability margin of low-frequency resonances in microwave amplifiers is proposed. The approach adds an extra RF port in series with an R-C stabilization network that is connected to the amplifier bias path. The extra RF port is used to experimentally obtain the critical poles of the circuit. Then, from the obtained pole-zero map, pole-placement techniques are applied to get the R-C values that increase the stability margin of the critical resonances. In this way, the risk of running into a low frequency oscillation when amplifier conditions are varied can be significantly reduced. The complete approach is experimentally validated in a demonstrator prototype built in printed circuit board technology.

Stability analysis of multistage power amplifiers using Multiple-Input Multiple-Output identification

Determining the origin and nature of the possible instabilities is key for an effective elimination of the unstable dynamics in multistage power amplifier design. In this work, a novel technique is proposed to provide a quantitative metrics that serves to locate and categorize the sensitive sections of the amplifier at which the unstable dynamics can be controlled and eliminated. The technique is based on an automatic Multiple- Input Multiple-Output (MIMO) frequency identification performed at different observation ports, followed by a residue analysis of critical poles. A three-stage amplifier exhibiting two common types of instabilities has been used to illustrate the complete approach.

Characterization techniques for stability and noise in microwave amplifiers under large-signal excitations

In this paper, two characterization approaches for electrical noise and stability in microwave amplifiers operating in large-signal regimes are reviewed. The first technique concerns the experimental determination of amplifier stability margins through pole-zero analysis of measured closed-loop frequency responses. The second technique deals with the measurement of AM and PM amplifier noise in non-linear regime and outlines the main differences with the linear case.