Academic literature on the topic 'Frequency response characteristics'

There are characteristics which uniquely determine the dynamic individuality of every dynamical system. The frequency response functions can by considered as such characteristics. They are employed usually within the solution in frequency domain. These characteristics can be obtained by the numerical or experimental way. In the submitted paper the frequency response functions are analyzed for the lorry Tatra by numerical way. They are needed within the numerical analysis of moving load effect on pavement in the frequency domain.

Spectral analysis has been widely applied to the detection of bifurcation and the determination of the extent to which dynamic instability and chaotic responses develop. However, because spectral analysis employs stationary sinusoids in representing time-varying signals of inherent nonlinearity, the use of Fourier domain methodologies would inexorably risk misinterpreting the true characteristics and obscuring the underlying physics of the nonlinear system being investigated. The fact that the amplitude and frequency of all the individual spectral component of a nonlinear, nonstationary dynamic response are modulated and coupled in time necessarily implies that, if the inception and transition of a bifurcated state of unstable motion is to be fully characterized, amplitude modulation and frequency modulation need to be temporally decoupled. The fundamental notion of instantaneous frequency defines frequency as the temporal gradient of phase and thus provides a powerful mechanism through which amplitude modulation and frequency modulation can be disassociated. Results of applying instantaneous frequency to the characterization of bifurcation and evolution of instability for a cracked rotor also indicate that instantaneous frequency interprets nonlinear rotary responses with sound physical bases.

The typical construction of a stator coil includes the use of end corona protection (ECP)coating, which is made of semi-conductive materials like silicon carbide (SiC). Thepurpose of ECP is to smooth the electric stress distribution near the slot exit, limitingthe electric field and partial discharge (PD) activity within the insulation system. Thisthesis investigates how ECP affects the dielectric response of a stator coil in highvoltagemeasurements, both in the time-domain and frequency-domain. It also studieshow well time-domain results transformed to the frequency-domain correspond to directmeasurements. As a further point, the effect of the ECP on PD activity was demonstrated.Measurements of dielectric response and PD were made on new coil-halves producedin the usual way in a production run for a motor. The results show that applying theECP design significantly reduces the PD activity and increases the inception voltage. Inaddition, the dielectric response of the coil with ECP tape has shown to have a nonlinearvoltage dependent characteristic due to the presence of ECP. As the voltage goes higher,this causes a shift of the loss peak toward higher frequency. A distributed-element modelof the end section of a stator coil was used to model the nonlinear effect due to ECP, andits results are compared to the measured results. Lastly, FEM simulation of a stator coilend section is presented, showing the contribution of ECP tape in evenly distributing theelectric stress near the slot exit.
Den typiska konstruktionen av en statorhärva använder ändglimmskydd (ECP), somär tillverkad av halvledande material som kiselkarbid (SiC). Syftet med ECP är attjämna ut det elektriska fältet vidövergången från spåret tilländlindningen, för attundvika högpåkänning och partiell urladdningsaktivitet (PD). Arbetet som presenteras här undersöker hur ECP påverkar den dielektriska responsen hos en statorspole, vid tidsdomänoch frekvensdomänmätningar vid höga spänningar. Den studerar också hur väl tidsdomänresultat som omvandlas till frekvensdomänen motsvarar direkta mätningar. Som en annan punkt visades ECP:s inverkan på PD-aktivitet. Mätningar av dielektrisk respons och PD gjordes på nya statorhärvor som tillverkades för en stor motor. Resultaten visar att tillämpningen av ECP-konstruktionen avsevärt minskar PD-aktiviteten och ökar inceptionsspänningen. Dessutom har spolens dielektriska respons med ECP-tejp visat sig ha en ickelinjär spänningsberoende egenskap på grund av närvaron av ECP. Ö kad spänning orsakar en förskjutning av förlusttoppen mot högre frekvens. En modell för ECP användeseteendet, och dess resultat jämförs med mätningarna.utligen presenteras FEM-simulering som visar hur ECP gör fältet jämnare.

This thesis is theoretically described heating surfaces, radiators and regulation valves. There are also described their features, advantages and disadvantages and division according to design. The aim of the work is determine the dynamics characteristics of heating surfaces and radiators including control valves, which are parts of measurement panel. Based on the measurement are determined appropriate characteristics of which are calculated values for regulating. The result of this study can serve as a guide to the practical measurement method of dynamics characteristics of the real-working heating systems, or serve as a template for the settings according to the measured data.

This thesis is oriented to a specific section of energetics concerned with detection and registration of time responses of fast overvoltages in high-voltage power networks. The first part of this text is information about measuring frequency response characteristics of CR-divider and calculation of typical signal distortion caused by transfer function of this divider. The design of anti-aliasing filter is also included. The second part of this thesis is oriented to selecting key features of a measuring instrument specialized for detecting and recording fast events in electrical power networks. A selection of optimal type of processor and also a choice of communication interfaces is included there as well. The last chapter prepares mathematical procedures for classification of typical fast events in electrical power network using artificial neural networks.

This thesis deals with the dynamic properties of electric pressure transducers. These are properties that are reflected in the measurement of rapid, time-dependent processes. They could be described in two ways. Either by using amplitude and phase frequency response characteristics, or just one particular value. Natural frequency, cutoff frequency or time constant. These parameters indicate the extreme values for the use of measuring devices in the measurement of time-dependent processes. In this work will be described procedures for determining these parameters.

Whole body vibration (WBV) delivers a stimulus to the body via an oscillating platform and remains a relatively new area of research. Several applications of WBV stimuli have been developed as strength training and rehabilitation modalities, but inconsistent results have been published. There is little knowledge underpinning the mechanisms to explain the elicited neuromuscular responses to WBV and a wide range of WBV parameters across the literature. As a result, safe and effective protocols are yet to be established or validated. The aim of this current research was to investigate: the electromyography (EMG) and explosive performance responses to varying WBV frequencies; the effect of WBV data analysis techniques; and the influence of external factors on WBV stimulus and neuromuscular responses. Three main studies were completed: 1. An individualised response of both EMG and jump performance appears to exist dependent on vertical WBV frequency, in trained participants. This is in spite of no overall frequency dependent effect of EMG or performance responses across participants as a group. The influence of the role of expectancy effect appears minimal following this particular WBV protocol. 2. There was a significant effect of filter technique on EMG data recorded during vertical WBV. A tailored, WBV specific notch filter technique may offer an effective balance; excluding WBV noise artifacts without removing significant portions of valuable muscle signal EMG data. 3. The influence of external load on WBV acceleration output also appears minimal. Platform acceleration output was dependent on WBV frequency, as expected. Lower accelerations were recorded in superior body segments, suggesting a dampening mechanism, which was also proportionally dependent on frequency. EMG activity of upper and lower leg segments may differ in response to frequency, likely due to transmission distances involved. This may partially account for a potential dampening mechanism. In addition, a protocol to quantify WBV stimuli delivered by this particular WBV type illustrated significant differences in theoretical and actual parameters. This may explain not only the lack of overall explosive performance effect reported earlier; but also the inconsistent WBV literature. Future research should quantify WBV stimulus before investigating possible neuromuscular responses to individualised protocols, which may be assessed via EMG activity.

Vibration measurement and analysis has been an accepted method since decades to meet a number of objectives - machinery condition monitoring, dynamic qualification of any designed structural components, prediction of faults and structural aging-related problems, and several other structural dynamics studies and diagnosis. However, the requirement of the vibration measurement at number of locations in structures, machines and/or equipments makes the vibration measurement exorbitant if conventional piezoelectric accelerometers are used. Hence, there is a need for cheaper and reliable alternative for the conventional accelerometers. The Micro-Electro-Mechanical Systems (MEMS) accelerometers are one such cheap alternative. However, a significant deviation in the performance of the MEMS accelerometers has been observed in earlier research studies and also confirmed by this presented study when compared with well known conventional accelerometer. Therefore, two methods have been suggested to improve the performance of the existing MEMS accelerometers; one for correction in time domain and other in frequency domain. Both methods are based on the generation of a characteristic function (CF) for the MEMS accelerometer using well known reference accelerometer in laboratory tests. The procedures of both methods have been discussed and validations of these methods have been presented through experimental examples. In addition, a Finite Element (FE) model of a typical MEMS accelerometer has been developed and modal analysis has been carried out to understand the dynamics of capacitive type MEMS accelerometer and to identify the source of errors. It has been observed that the moving fingers behave like a cantilever beam while the fixed fingers showed rigid body motion. This cantilever type of motion seems to be causing non-parallel plates effect in the formed capacitors between moving and fixed fingers which results in errors in the vibration measurement. Hence, design modifications on finger shape have been suggested to remove the cantilever motion and results showed remarkable improvement. Moreover, the effect of using synchronous amplitude modulation and demodulation in the readout circuit has been studied. The experimental study showed that this circuit also introduces errors in amplitude and phase of the output signal compared with the input signal. Thus, in the new design of MEMS accelerometers, improvements in both mechanical design and electronic circuit are required.

Master’s thesis deals with the issue of electronic filtering circuits with arbitrary frequency characteristics. First part of the thesis describes theoretical basis. Second part explores the possibilities of design procedures for filters with arbitrary frequency characteristics. Design procedures are demonstrated on examples accordingly to the presented methods, including their circuit implementation and computer simulation to verify the correctness of theoretical assumptions. Thesis also explores the possibilities of tuning circuit structures and electronic setting for characteristics using controllable active elements.

This master's thesis deals with design and implementation of modular system for two-way loudspeaker system's characteristics. Work focus mainly on the enclosure geometry and speaker placement. The individual modules of the system were designed and then implemented. Furthermore, the characteristics of these modules were measured and laboratory tasks using these modules were elaborated.

abstract: Flow measurement has always been one of the most critical processes in many industrial and clinical applications. The dynamic behavior of flow helps to define the state of a process. An industrial example would be that in an aircraft, where the rate of airflow passing the aircraft is used to determine the speed of the plane. A clinical example would be that the flow of a patient's breath which could help determine the state of the patient's lungs. This project is focused on the flow-meter that are used for airflow measurement in human lungs. In order to do these measurements, resistive-type flow-meters are commonly used in respiratory measurement systems. This method consists of passing the respiratory flow through a fluid resistive component, while measuring the resulting pressure drop, which is linearly related to volumetric flow rate. These types of flow-meters typically have a low frequency response but are adequate for most applications, including spirometry and respiration monitoring. In the case of lung parameter estimation methods, such as the Quick Obstruction Method, it becomes important to have a higher frequency response in the flow-meter so that the high frequency components in the flow are measurable. The following three types of flow-meters were: a. Capillary type b. Screen Pneumotach type c. Square Edge orifice type To measure the frequency response, a sinusoidal flow is generated with a small speaker and passed through the flow-meter that is connected to a large, rigid container. True flow is proportional to the derivative of the pressure inside the container. True flow is then compared with the measured flow, which is proportional to the pressure drop across the flow-meter. In order to do the characterization, two LabVIEW data acquisition programs have been developed, one for transducer calibration, and another one that records flow and pressure data for frequency response testing of the flow-meter. In addition, a model that explains the behavior exhibited by the flow-meter has been proposed and simulated. This model contains a fluid resistor and inductor in series. The final step in this project was to approximate the frequency response data to the developed model expressed as a transfer function.
Dissertation/Thesis
M.S.Tech Electrical Engineering 2013

The success of TENS treatment depends on the use of safe and appropriate TENS technique. Uncertainty about optimal TENS technique is due in part to the variety of possible electrode positions and electrical characteristics that can be chosen for treatment. Conventional TENS uses low-intensity, high-frequency currents to activate low-threshold afferent nerve fibres in the skin. AL-TENS uses high-intensity, low-frequency currents to generate non-painful phasic muscle contractions (twitching). The purpose of this chapter is to discuss the principles that underpin the use of safe and appropriate electrode sites and electrical characteristics during TENS. The chapter covers how to choose between conventional and AL-TENS, the appropriate electrode positioning for conventional TENS and AL-TENS including instances where AL-TENS may be more beneficial than conventional TENS, appropriate choice of electrical characteristics for stimulation, and biological, psychological, and social factors influencing response to TENS

<p>Strong seismic shaking is recognized as the direct cause of structural failures. In many cases, however, the factor that initiates the structural damage is ground failure or ground displacement. This chapter deals with the identification of all geotechnical related structural failures. Surface fault rupture has been a well-acknowledged cause of failures of structures built across or near the fault, which are increasing in frequency as the man-made environment constantly expands to new areas. Seismically induced rockfalls, landslides and slope failures have also been associ-ated with major disasters with an increasing frequency in some cases due to an expanding popu-lation, which encroach on areas with landslide risk or in other cases as result of the destruction of the natural environment (vegetation and water routes), which have protected these slopes in the past. Foundation damage may be a result of failure of shallow foundations or piles. In addition, although liquefaction and ground settlement are technically part of foundation failures, they are usually treated as separate, special cases. Retaining wall structures, usually considered as simple systems, may display a complex behaviour, which can be related to extensive seismic failures. Finally, not taking into account soil–structure interaction (SSI) may have a detrimental effect on the dynamic response of structures. Although SSI may never be the direct cause of a structural failure, it has proven to be, in several cases, the underlying reason for the analysis misconception that led to the failure.</p>

AbstractIt is commonly accepted that the Earth’s climate is changing and will continue to change in the future. Rising temperatures are one of the direct indicators of global climate change. To investigate how the rising global temperature will affect the spatial pattern of rainfall in West Africa, the precipitation and potential evapotranspiration variables from ten Global Climate Models (GCMs) under the RCP8.5 scenario were driven by the Rossby Centre regional atmospheric model (RCA4) from the COordinated Regional Climate Downscaling EXperiment (CORDEX) and analyzed at four specific global warming levels (GWLs) (i.e., 1.5 °C, 2.0 °C, 2.5 °C, and 3.0 °C) above the preindustrial level. This study utilized three indices, the precipitation concentration index (PCI), the precipitation concentration degree (PCD), and the precipitation concentration period (PCP) over West Africa to explore the spatiotemporal variations in the characteristics of precipitation concentrations. Besides, the analysis of the effect of the specified GWLs on the Consecutive Dry Days (CDD), Consecutive Wet Days (CWD), and frequency of the intense rainfall events allowed to a better understanding of the spatial and temporal patterns of extreme precipitation in West Africa. Results reveal that, for the projections simulations and at each GWL, the rainfall onset starts one month earlier in the Gulf of Guinea in response to the control period. To encourage adaptation to the various changes in climate in general, and particularly in respect of rainfall, this study proposes several adaptation methods that can be implemented at the local (country) level, as well as some mitigation and adaptation strategies at the regional (West African) level.

Abstract Clearances in mechanical joints have deteriorating effects on the dynamic behavior of a machine in increasing noise and vibration and reducing the performance. In order to properly characterize these effects and to develop analytical techniques for machine design, it is necessary to investigate the dynamics associated with basic models of impacting systems. In this paper, we develop a method of harmonic balance to study a revolute impact pair. We focus on the characteristics of nonlinear frequency response of the system for a single frequency excitation. These characteristics include multiply-valued steady state response, multiple jump resonances, and existence and stability of these solutions. The effectiveness of the harmonic balance method combined with the Fast Fourier Transform technique is shown through numerical examples.

This paper presents experimental and numerical hydrodynamic load and damping results on a surface piercing pivoted circular cylinder, representing a monopile of a floating Marine Renewable installation (Spar-Buoy concept). The resulting load and damping characteristics are applied to predict the response characteristic of the pile and compared with experimental results. The main consideration is given to the characteristic of the cylinder due to steep wave action in the pitching mode. The experiments were conducted in the wave tank at the University of Glasgow using a cylinder model with a diameter of D = 0.21m that was constructed at the Imperial College London, to provide a structural to wave frequency ratio of 2 and 3. The outcome from the investigation supports the importance of the dynamic response to the successful operation of a deep water wind turbine installation.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.