Transfer function Definition and 34 Discussions

In engineering, a transfer function (also known as system function or network function) of an electronic or control system component is a mathematical function which theoretically models the device's output for each possible input. In its simplest form, this function is a two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory.
The dimensions and units of the transfer function model the output response of the device for a range of possible inputs. For example, the transfer function of a two-port electronic circuit like an amplifier might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electrical current applied to the device; the transfer function of a photodetector might be the output voltage as a function of the luminous intensity of incident light of a given wavelength.
The term "transfer function" is also used in the frequency domain analysis of systems using transform methods such as the Laplace transform; here it means the amplitude of the output as a function of the frequency of the input signal. For example, the transfer function of an electronic filter is the voltage amplitude at the output as a function of the frequency of a constant amplitude sine wave applied to the input. For optical imaging devices, the optical transfer function is the Fourier transform of the point spread function (hence a function of spatial frequency).

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  1. M

    Engineering How to implement a transfer function in Simulink with variable coefficients?

    The implementations for the two filters in simulink are as follow: For the first filter: For the second one: The obtained results have values of 10^-12, while the expected results should be between 10^-3 - 10. Since it's the first time when I try t implement a tf with variable coefficients I...
  2. StoneBored

    How to get the transfer function for force transmissibility of a wall?

    Hi, I am trying to get the transfer function from a wall between rooms. From one side I have the force of a hammer as an input ,and in the other side of the wall (next room) I have an accelerometer. Is it possible to get the TF without know the damping, stiffness and mass of the wall partition...
  3. M

    From differential equations to transfer functions

    *** MENTOR NOTE: This thread was moved from another forum to this forum hence no homework template. Summary:: Trying to find transfer functions to design a block diagram on simulink with a PID controller and transfer functions for a water tank system. ----EDIT--- The variables and parameters...
  4. H

    Engineering Decomposition minimal phase & all pass

    Hey everybody! I have put G1 = (1-s)/(2-10s) & G2 = (2-10s)/ (2 +10s) but than I read that all poles and zeroes should be inside the unit circle, and I don't know how to move the Zero S_01 = 1 to the unit circle
  5. Will26040

    Engineering Tuning Rules for Lag Dominated FOPDT (first-order plus deadtime) model

    I am trying to find an alternative tuning rule for use with the transfer function specified. Please could someone help by pointing me in the right direction, thanks. Process transfer function: ## \frac {27e^{-3s}} {30s+1} ## Also, am I right in thinking that this process transfer function is...
  6. Ultisonic

    Transfer Function and Control Systems Question

    ıs there anyone to solve 8th 9th and 10th problems? It is about transfer function and control systems Password= 1234
  7. G

    Modeling a third order system

    Homework Statement Determine the parameters of the PI controller such that two of the closed-loop poles of the transfer function Gclr(s) correspond to the poles of a second order LTI system with the following specifications: i) overshoot S% = 25%; and ii) settling time ts(5%) = 120 s. Homework...
  8. AndresPB

    Response of a System: Transfer Function

    Some time ago I made a modelling project and obtained a plot. Now, I want to remember what the transfer function was, as I want to try changing the parameters. The graph is the following: How can I obtain the transfer function? Thanks a lot
  9. mjtsquared

    I On the stability of an LTI circuit

    An LTI circuit such as one composed of resistors, capacitors, and inductors, in general is a stable LTI system, i.e. its impulse response is one that decays over time. I have no problem with that, as it speaks for itself through laws of energy conservation, but I want to see this from a...
  10. Alex Paul

    Equivalence of torque & angular velocity transfer function

    Hello all, I was doing some behavioural modelling of the torque transfer characteristics of a belt drive system from the driver pulley to the driven pulley. While doing the same, i have tried to see how the angular velocity is getting transferred as well. I would explain my point with the...
  11. P

    Derive analytically the transconductance transfer function

    I am planning to derive analytically the transconductance transfer function (Iout/Vin) of this Gm2.sch circuit block. Is my small-signal model for Gm2.sch correct ? There is one minor mistake (Vgs5 should not be zero). Could anyone spot other mistakes in the small-signal circuit ? I am...
  12. kostoglotov

    Which data set should I trust more?

    Homework Statement Control systems subject. Have a DC motor setup on a difference op-amp, then with gain, and the axel moves a wiper on a pot used for feedback. I understand the concepts reasonably well enough to complete the assignment. I'm using MATLAB scripts to approximate parameters...
  13. S

    Simplifying transfer function block diagram

    Homework Statement Simplify the block diagram. I uploaded a single image as it's the easiest way to do this problem. Homework Equations None at this stage. The Attempt at a Solution Please see the image.
  14. kostoglotov

    Viscous drag parallel to the axis of rotation: Control Systems

    Homework Statement seeking G(s) = \frac{\theta_2(s)}{\tau(s)} Homework Equations The Attempt at a Solution What does it mean when the viscous drag is parallel to the axis of rotation?[/B] It also turns out that this system needs two equations. I can...
  15. O

    Derive The Transfer Function from First Principles

    All, I need help deriving the Transfer Function of this circuit from first principles.
  16. genxium

    Does Wien bridge oscillator have a closed-loop gain?

    Homework Statement By Wien bridge oscillator (abbreviated as WBO below) I refer to this circuit where the op-amp is assumed to be ideal and the output is the voltage drained from the upper end of R3. What confuses me is that I hardly find a reference which explicitly states that a WBO has a...
  17. kostoglotov

    Finding the closed form of a recursive LTI system

    Homework Statement Find the closed form of the impulse response of the system y[n] = 7y[n-1]-12y[n-2]+x[n] using the peel away and guess method. Ie, by using Python code to find the geometric ratios and amplitudes of the outputs as n grows large, then calculate residuals, and find the...
  18. kostoglotov

    How transfer functions become Bode plots

    Homework Statement I have a question related to taking the logs of transfer functions, getting the individual Bode plots of each subsequent factor, and adding those plots graphically. I'm working from Fundamentals of Electric Circuits, 5th edt. Let me start with the following screen capture...
  19. Boudy

    A Linear Systems

    The transfer function of a linear system is known in the sinusoidal frequency domain. It is given in its final form as a complex function of the angular frequency ω (not jω ). How to obtain the step response? Thanks in advance.
  20. J

    Bode Plot Method For a Transfer Function

    Hi , I was hoping you could look at this link and let me know if I have interpreted the method correctly As I understand it the transfer function has had s replaced by jw but also the top and bottom are divided by 10 - This is so that the brackets on the bottom...
  21. G

    Control Transfer functions basics

    Hello, I got the following diagram, shown below, and I have to derive its transfer function. I think I have a general misunderstanding about the transfer functions. What I think it is, is: output/input basically. As input is the whole block of things that affect the output. This is the system...
  22. D

    I How to find Y(s)/X(s)

    y(t) = u(t - a) . x(t) u(t) is a unit step function. I have to find Y(s)/X(s). Do I have to do convolution in frequency domain?
  23. R

    Sketch output response of system

    Homework Statement Sketch output respons of system who have a input is a unit step (Amplitude of the system = 1) Homework Equations · Damping factor = 0,5 · Gain factor = 2 · Natural angular frequency = 4 Rad/s The Attempt at a Solution I have: 1. Draw a step respons in a x-y axis...
  24. W

    Transfer function with non zero initial conditions

    Hello guys, I'd just like to ask how can I formulate transfer function of second order differential system when I don't have zero initial conditions? the equation is = y''(t) + B/m*y'(t) + k/m*y(t) = g y(0)= -L don't care what parameters mean .. it's supposed to be solved in general Thank...
  25. A

    Transfer function from a Z = a - i * b number.

    I have a circuit where after a deduction of the impedance, I have found the output to input voltage relation as Vout/Vin = 2 - 3i Can anyone please let me know how can I can convert it to s functions (such as G(s) = 1/1+s) in Matlab so that I can get a transfer function? I would appreciate...
  26. Maxim Nol

    Unstable 4th order system (control theory)

    Homework Statement Hello everyone! To simplify, I have a system whose transfer function looks like this: G = (s^2-1) / (s^4-s^2-1) It's unstable and I have to find a way to stabilize it using PID controller and/or lead/lag compensators. Homework Equations The Attempt at a Solution So far...
  27. D

    Compute damping as a function of frequency

    Hi everyone, I'm french, so sorry for my bad english. I have a problem to compute the damping as a function of frequency. In fact, I plot the transfer function between the input (which is a force applied bu a hammer) and the output (which is an acceleration). Therefore, I can analyse the mode...
  28. Q

    Base excited stacked mass spring damper systems

    Homework Statement I'm trying to derive the equations of motion and state space as well as the transfer function for a system which has two mass spring damper systems stacked on top of each other. The system is base excited. I attached a pic of the system Homework Equations - Sum of the...
  29. H

    Why s is substitute with jw in transfer function?

    Can anybody explain to me briefly on why in a transfer function like G(s), we substitute s=jw such that it become G(jw) in order to find its gain value? Thanks
  30. S

    Inverse Discrete Laplace Transform

    Hi, I have an idea which when tested looks like its clearly flawed. I am hoping someone can tell me where my procedure is flawed, or point me to some other theory that has already done something similar. The first two are the laplace transform. The third line is the Fourier Transform. The...
  31. I

    Internal combustion engine transfer function (request)

    Hello everyone, i need to find reported transfer functions of internal combustion engines for a project, i would appreciate the model of a four cylinder engine. If anyone knows about a book or some article which i can use, please let me know. thank you very much. the topic is related with...
  32. Captain1024

    Help Finding Transfer Function Vo/Vs

    Homework Statement Find ##a)\ H(s)=\frac{V_o}{V_s}## of the filter in the circuit below. ##b)\ ##The center frequency ##\omega_0## ##c)\ ##The band-width B Correct answers: ##a)\ H(s)=\frac{6s}{12s^2+11s+1}## ##b)\ \omega_0=0.28\frac{rad}{s}## ##c)\ B=0.71\frac{rad}{s}##...
  33. Captain1024

    Help Finding the Transfer Function H(s)=Vi(s)/Ii(s)

    Homework Statement Find the transfer function ##H(s)=\frac{Vi(s)}{Ii(s)}## The circuit consists of a voltage source and a 5H Inductor in series with a 10Ohm Resistor which are in parallel with a 10uF Capacitor in series with a 500Ohm Resistor. ##\rightarrow## Diagram here. Homework Equations...
  34. D

    Is there a problem with this Source Transformation?

    Hey guys, i did this source transformation as an alternate method to find the transfer function of a circuit, however I am getting a different transfer function of 2/(2s+(s+3)(s^2+1)) to the solution in the following image. Any help would be really appreciated :)