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Resistors
Published in Kevin Robinson, Practical Audio Electronics, 2020
A transfer function is a general description of the behaviour of a device or system, presented in terms of how the output of the system changes as the input to the system is altered. This kind of analysis can take on many specific forms depending on the nature of the system under consideration. In addressing the electrical behaviour of a simple resistor, the input is considered as a voltage applied across the ends of the resistor, and the resulting output is quantified in terms of the current which flows through the resistor as a result of the applied voltage. (This particular relationship, plotting current against voltage is often also referred to as an i-v characteristic.) As discussed in Chapter 2, voltage can be thought of as the electrical push or pressure, and current is the flow of electricity which comes about as a result of that push.
Hydraulic Systems Modeling
Published in Qin Zhang, Basics of Hydraulic Systems, 2019
In mathematical analysis, a transfer function can often be derived from a linear differential equation using the Laplace transform. For a valve-controlled hydraulic cylinder system introduced in the previous section, we may get three transfer functions from the three fundamental equations for its modeling. Applying a Laplace transform to Eqs. (8.15) and (8.25) and rearranging the new equation obtained, we can get the following two Laplace equations: Y=1ms2+cs+K(ALPL−F)PL=1kp+Cil+VL4βs(kxXv−ALsY)
Initial Design Failure Mode and Effects Analysis and Product Risk Assessment
Published in Ali Jamnia, Introduction to Product Design and Development for Engineers, 2018
In a way, these questions may be related to a bigger issue: How well do we know the behavior of the selected sensor and its response to variations from ideal conditions? This leads to the topic of a transfer function, which I will explore in more detail in Chapter 6. In general, a transfer function speaks of the relationship between input variables into a system (and/or subsystem or component) and its response. For instance, to conduct a finite-element analysis of a gasket, the inputs would be applied loads to the gasket, its geometry, and material properties, and the response would be the deflected shape. For the ultrasonic sensor example, the inputs may be frequency and power of modulation of the transmitter as well as the distance between the transmitter and the receiver. The response may then be the frequency and power sensed at the receiver.
Identification of Impulse Responses in Heat Transfer: Parameterization, Doses, Partial Time Moments
Published in Heat Transfer Engineering, 2023
One must remind here that the convolution product in the time domain (1b) becomes a simple product once its Laplace transform is taken. where the upper bar over each quantity designates its Laplace transform, being the Laplace parameter. The initial values of both the impulse response and of the input are zero here. the Laplace transform of the impulse response, is called the transfer function. It is related to the choice of the locations of the excitation and of the response, that is on their mathematical spatial supports. For the transient excitation, this spatial support is the only subset of the domain of study in ℝ3 where it is not equal to zero.
Indoor thermal behaviour of an office equipped with a ventilated slab: a numerical study
Published in Journal of Building Performance Simulation, 2021
Matthieu Labat, Ion Hazyuk, Matthieu Cezard, Sylvie Lorente
A transfer function gives the relationship between an input and one output of the system. When the system has several inputs and outputs, the number of transfer functions is equal to the product of the number of inputs and the number of outputs. The first step consists in defining the inputs of the ventilated slab and proposing relevant outputs. Our objective is to obtain a lumped model that is suitable for computing the heat balance at the room scale, which, at steady state, is: Here, is the total of the heat loads of the room. It can be broken down into several terms to represent the heat flux through the envelope and the ones resulting from the use of appliances for example. However, it has an impact on the indoor temperature, TRoom, rather than on the ventilated slab itself. For this reason, it will not be included in the definition of the transfer functions.
Controller design for the closed loop system with non-interaction condition
Published in Systems Science & Control Engineering, 2020
Wang Jianhong, Ricardo A. Ramirez-Mendoza
In this simple closed loop system, the number of each physical variable is 1, so this system is also called the single-input and single-output closed loop system. Now similar to Figure 1, we start to consider one many-variable closed loop system with many controlled outputs and many control setting, or input , where the number of controlled outputs be and the number of inputs be . Their Laplace transforms are and , respectively. Consider the control designed in Figure 2, the relations between inputs and the outputs are given by the following. In Equation (1), are the closed loop transfer functions. More specifically, for example each is one transfer function on the input , when given a component of the output . Commonly each transfer function is a ratio of the two polynomials of frequency variable . For the sake of simplicity, Equation (1) can be rewritten as