What is Transfer function: Definition and 362 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. S

    Transfer function of this simple circuit

    Homework Statement The picture of the circuit is attached; I want to find |V_{A}/V_{J}|. This seems really easy but I haven't done circuit analysis in forever. Homework Equations Complex impedances, Z_{C} = 1/i\omega C, Z_{R} = R. The Attempt at a Solution First R_{A} and C_{A} are in...
  2. A

    How to determine gain and phase margins for a transfer function?

    How would I determine gain and phase margins for the following transfer function: G(s) = (0.38(s^2 + 0.1s +0.55)) / (s(s+1)(s^2 + 0.6s + 0.5)) We are learning about Bode plots but I am really struggling. I know that Bode plots display the relationship between magnitude vs. frequency and...
  3. A

    How to estimate transfer function given a transmissibility plot?

    How would I estimate the transfer function for transmissibility given this plot: I am told that the data does not include phase information, but assume that the phase is 0 deg at low frequency and -180 deg at high frequency. I must provide a brief rationale for each component of the transfer...
  4. D

    MHB What is the transfer function for this system?

    In a long-distance telephone communication, an echo is sometimes encountered due to the transmitted signal being reflected at the receiver, sent back down the line, reflected again at the transmitter, and returned to the receiver. The impulse response for a system that modles this effect is...
  5. G

    Combined Translational & Rotational System Transfer Function

    Homework Statement I'm given the following diagram And asked to find the transfer function G(s) = \frac{X(s)}{T(s)} and seem to be having some difficulty doing so. Homework Equations The Attempt at a Solution Apparently this is free body diagram I seem to be having difficulty...
  6. E

    Engineering Transfer function for RC and RL circuits

    Homework Statement I just want to understand, how to calculate transfer function. Here is simple example: Homework Equations The Attempt at a Solution But in this circuit I don't understand how to do it. I have to find T and k as it is in preview. Which is the element for...
  7. Z

    Calculate phase shift using transfer function

    Homework Statement Given that you have found the following transfer function for a circuit, H(jω), what is the phase at very low frequencies? (jωRC-ω2LC)/((1-ω2LC) + jωRC) a:∏ b:-∏/2 c:+∏/2 d:0 The Attempt at a Solution I understand that the phase angle is ψ=arc tan(img(ω)/real(ω))...
  8. U

    Optical Transfer Function of a microscope

    Hi all, I have a question about the "missing cone" problem in wide-field microscopy. The Fourier equivalent of the PSF is the OTF. The OTF has a toroidal (doughnut) shape. I'm a little confused by how to interpret the OTF support in the Z dimension. In 2D and considering lateral...
  9. G

    Transfer Function to State Space Calculator Program

    Hi, Does anyone know a program that I can put on my TI-84 calculator that will allow me to input any transfer function and get the state space representation of the system or the other way around. For example G(s) = \frac{\sum(K_{i}s^{i})}{\sum(P_{i}s^{i})} The calculator prompts you...
  10. G

    Engineering Transfer Function and State Space Analysis of Op-Amp circuit

    Homework Statement http://imagizer.imageshack.us/v2/800x600q90/690/0tab.png I'm asked to find the transfer function and then find the state space representation and seem to be stuck. Homework Equations The Attempt at a Solution My textbook states that for a noninverting...
  11. D

    MHB Transfer function of a damped hanging mass

    How do I find the transfer function of damped masses hanging? I know that the transfer function is \[ H(s) = \frac{\mathcal{L}\{y(t)\}}{\mathcal{L}\{x(t)\}} \] where \(u\) is the input which is a force and \(x_1\) is the output. Given the following diagram (see below), how do I find the input...
  12. L

    Open Loop Transfer Function from Differential Equations

    Homework Statement Generate an open loop u(t) and simulate. Plot x(t) and y(t) \dot{x} = Vcos(θ) \dot{y} = Vsin(θ) \dot{θ} = u I am given initial values. All are 0 except for \dot{x}(0) = V. Homework Equations Laplace Transform Tables The Attempt at a Solution I think I...
  13. O

    Closed-loop transfer function

    Homework Statement Augment the model to include a proportional position controller and derive the closed-loop transfer function. The model is an hydraulic actuator system pushing against a mass. The Attempt at a Solution I think I have completed the first part correctly with...
  14. T

    Mass Spring Damper Transfer Function

    Homework Statement The translational system in the first attachment represents the rear/front suspension of a car of mass 1262kg. The distance between the axles is 2.41m and the distance between the centre of mass and the front axle is 1.22m. I am told that: m2 = 40 kg c1 = 800 Nm/s k1...
  15. S

    Derive transfer function of control system with disturbance.

    This is a revision question rather than homework as I have the answer and working. I have attached the block diagram and first part of the answer which explains how to derive the transfer function from first principles. I understand the principles behind this and how the RHS of the equation...
  16. T

    Simple transfer function question

    Homework Statement Find the transfer function of an RLC circuilt and the magnitude. (All the impedances are in series) and the Vo is in the R. Vi is the source voltage. Homework Equations The Attempt at a Solution So transfer function of the circuit => Vo/Vi = R/ (sL+1/sC +...
  17. S

    Cascading LP filter transfer function

    Hi All, I'm new to this forum. Its been awhile since university, so I've unfortuntely forgotten most of my teachings on transfer functions it seems! Basically I am trying to design a 3 stage cascading digital low pass filter. I am sampling an AC waveform and need to integrate the signal. I'm...
  18. S

    Cascading filter transfer function

    Hi All, I'm new to this forum. Its been awhile since university, so I've unfortuntely forgotten most of my teachings on transfer functions it seems! Basically I am trying to design a 3 stage cascading digital filter. I am sampling an AC waveform and need to integrate the signal. I'm getting...
  19. O

    MATLAB Mastering Matlab for Bode Plots: Understanding Transfer Functions Easily

    Hello I need to do bode plot.. but i not to sure how to use matlab.. i need this 1 / (a + bs)s num = 1 how to key in the den to get (a + bs)s.. i try different way and i can't get 1/(a+bs)s hope to get help
  20. M

    MATLAB Matlab transfer function problem

    I have a transfer function L(s) = A(s)/B(s) that I call Ls. However, when defining H(s)= L(s)/(1+L(s)) by %% Ls = -70.6s^2 - 2003 s + 3375 -------------------------- s^3 + 119.6 s^2 + 2806 s %% Hs = Ls / (1+Ls) things go wild. The highest...
  21. M

    Solving Transfer Function: Kx * 1/(1+τs) = Cx+Kx

    Please see attached for problem and diagram. Equations R(S) = input C(S) = Output G(S) = transfer function = 1 / (1+τs) R(S) * G(S) = C(S) Attempt R(S) = input = Kx? C(S) = Outputs = Cx +Kx Kx * 1/(1+τs) = Cx+Kx ***This is a new topic to me***
  22. A

    Find transfer function, model and space state of mass spring system

    The problem statement: I have to find the transfer function of a mass spring system. There are two masses in the system and 3 spring. I also have to find the state space representation and the model of the system. I have attached a image of my problem and my work so far. I think I found the...
  23. B

    How can I use an ADC to create a transform function for an incoming signal?

    I have a incoming signal from a analog to digital converter, how do I turn it into a transform function ? so how to turn a graph into a transform function? So want to take the incoming signal and used a fast Fourier transform (FFT). so I will take the incoming signal built a function from...
  24. Z

    Engineering Finding the Transfer Function of an RC Circuit in the Laplace domain

    Hi, Basically I have circuit with an input Vi (s) across a capacitor C which is in parallel with a resistor R1. And these 2 components are in series with another resistor R2 (please see attached drawing). The question states: Show that the transfer function of the circuit is: Vo/Vi...
  25. H

    1st order transfer function from data

    Hello, Im trying to model an RF attenuator for use in a control system. The control voltage is from 0-2.1V and I applied a step function signal from 0-2.1V and measured the output. I was able to model it as a first order system in the form Kdc / Xs + 1. The issue I'm having is...
  26. Femme_physics

    Engineering Transfer function of a circuit with a resistor, capacitor, and coil

    Homework Statement Find the transfer function, Vout(s)/Vin(s) The (s) signifies the laplace plane Homework Equations The Attempt at a Solution I'm keenly aware there is an error here (at least from comparing with the answer sheet). Can you tell me where I went wrong?
  27. S

    Transfer function of Mass-Damber-Spring,connected through linkages

    Transfer function of Mass-Damper-Spring,connected through linkages Hi guys,I have posted a picture of the system I am trying to model in order to obtain its transfer function. My question is: Do the linkages affect the modelling of the system and should I take them into account?Also, is X1 the...
  28. L

    Transfer function on a circuit

    I'm tinkering with a software called LTspice. The user can insert circuits and simulate them. After doing some Bode plots I started to wonder what the transfer function looked like. I usually don't bother about this when I build amplifiers, but this LTspice software got me curious. I looked...
  29. N

    Transfer Function of an unknown device

    Hi everyone, in the last times, I'm really interested in controls engineering, and I wanted toknow how to find transfer functions of devices, or systems in the real world, let me explain better, for example, in my house i have various dc motors, and stepper motors, since i want to make an...
  30. L

    Engineering Circuit From Transfer Function

    I'm given the following transfer function: T(s)=\frac{50000s}{(s+50)(s+1000)} and I need to constuct a circuit from it using opamps, resistors, capacitors, and inductors. Capacitors must be 100nF. I'm not quite sure how to start here. I managed to get a time domain version of the transfer...
  31. L

    Control system Transfer Function ( Time constant form)

    Why is time constant form of transfer function in control system better than pole zero form ? If a closed Loop transfer function is given to me how should i find D.C gain ?
  32. M

    Engineering Transfer Function Of A 2nd Order Circuit

    I'm trying to work out the Transfer function for the 2nd order RC circuit in the attachment below: I can't seem to get the right answer :( circuit: My answer: Please see attachment for my attempt and the relevant information:
  33. S

    Finding the Numerator of a Transfer Function

    I am attempting the question shown in the attachment. It can be seen that the poles are located at -2 ± 3j which expressed in terms of s is (s + 2)2 + 32. This is the denominator, but how is the numerator of the transfer function found? Edit: Looking at the Laplace look-up table I...
  34. S

    Plot frquency resonse from transfer function in complex frequency domain

    I am going through a past paper for an upcoming exam and I want to check that I am approaching this question correctly. H(s) = 1/(s2 + 8485.28s + 36x10-6) Calculate and plot frequency response for 0 rad/s, 500 rad/s, 1000 rad/s and 10000 rad/s. I am under the impression that the 's'...
  35. P

    Transfer function and laplace

    Homework Statement Consider this control system below: R = set point E = remaining error V = interference My question is, if both R and V are unit step \frac{a}{s}, what will the value of U be when time t\rightarrow\infty ? Homework Equations This question is based on the...
  36. A

    Find Transfer Function from Experimental Data

    I would like to find a useful function to predict the output based on the input. I'm trying to figure out how to get the transfer function given actual input and output data. What I've tried is getting a transfer function using Fourier transforms. I'm attemping to do a fft on both the input...
  37. F

    Find Impulse Response of LTI system given transfer function

    Homework Statement Find the impulse response of a system with transfer function H(S) = (s+3)/(s^2+2s+1) or H(S)=(s+3)/[(s+1)^2] Homework Equations Poles are s1=s2=-1 y = Ae^st + Be^st The Attempt at a Solution In my notes I do not have an answer for the case when there is...
  38. Femme_physics

    How Does a Missing Component in the Feedback Loop Affect the Transfer Function?

    I'm confused by the fact there's nothing in the feedback loop here http://img706.imageshack.us/img706/6075/feedbackloop.jpg For instance, if I had "H1" in the feedback loop I'd do C/R = (Gcs x Gps) / (1+H1) But since I don't have H1... is it simply C/R = (Gcs x Gps) / 1 = Gcs...
  39. S

    Transfer function of Instrumentation amplifier with DC suppression filter

    Homework Statement I want to find the overall transfer function of Instrumentation amplifier with a DC-Suppression filter. I know how to calculate the TF of a normal Instrumentation amplifier. But when feedback is given from the Filter to the IA, I couldn't find it. Homework Equations...
  40. M

    Engineering Finding Transfer Function from Circuit

    I need to find the transfer function from the attached circuit schematic. V_DD = 5V; R1 = 200kΩ; R2 = 300kΩ; and C1 = 900nF I used nodal analysis to attempt to get Vout over Vin but alas ended up with an equation like this: \frac{Vout}{Vin} = \frac{-j}{120kΩ*ωC} +...
  41. J

    How to measure the transfer function in Simulink?

    Let's say I simulate a simple filter in simulink and I want to see the transfer function graph (bode plot) of it. What do I do to get Vout/ Vin? I tried using the "PS Divide" Block and divide the output voltage and the input voltage, but that didn't work. Could anyone help me out here? This...
  42. L

    Control system - open loop transfer function and open loop gain

    control system -- open loop transfer function and open loop gain Is there any difference between open loop transfer function and open loop gain ?
  43. J

    Calculating Transfer Function off Bode Plot?

    Hey guys. I was wondering if anyone could give me some hints or help me understand well how to get transfer functions off bode plots. Here is an example I need to solve: http://i1226.photobucket.com/albums/ee410/jean28x/bodeplotcalc.jpg
  44. J

    How Do I Find the Peak Magnitude of H(jω) in a Circuit?

    Hey guys. I'm doing some homework for my circuits class and was wondering if anyone could help me with this question. How do I determine the value of ω will the magnitude of H(jω) be maximum?? In my case, the magnitude of the transfer function is (R/L)/ [sqrt((R+RI)/L)2 + ω2)]
  45. K

    Finding A Transfer function:

    Homework Statement For my particular circuit I have found my transfer function already, which comes out to be: H(jω)= R / [R+(1/jωC)+jωL] I am now supposed to express it in polar form. I am confused on how I express such an expression in polar form. Could anyone give me some information on...
  46. D

    Transfer Function and Steady State Response (Some S-domain)

    Homework Statement Find Vo in steady state. V1 = 5cos(1400t) V R = 100 Ω L = 25 mH C = 20 μF Homework Equations L = Ls C = 1/Cs The Attempt at a Solution I first solved for the transfer function T(s): T(s) = \frac{LCs^2 + 1}{LCs^2 + RCs +1} From here I can plug in...
  47. I

    Understanding Transfer Functions in ODEs

    Hi, I am undertaking an undergrad design project and want to ensure I'm doing this correctly, I have derived the ODE as shown below; A*Y = M*X'' + (B+C)*X' + D*X Where A,M,B,C,D are constants. By taking the Laplace transform, I get; A*Y(s) = M*s^2*X(s) + (B+C)*s*X(s) + D*X(s)...
  48. I

    Assistance in checking transfer function

    Hi, I am undertaking an undergrad design project and want to ensure I'm doing this correctly, I have derived the ODE as shown below; A*Y = M*X'' + (B+C)*X' + D*X Where A,M,B,C,D are constants. By taking the Laplace transform, I get; A*Y(s) = M*s^2*X(s) + (B+C)*s*X(s) + D*X(s)...
  49. K

    Homework help: Transfer Function and Half Power Frequency

    Homework Statement I made a quick drawing of the circuit, and I apologize because I am not good at using the computer to draw circuits! Anyway, in this particular circuit R=200Ω , and L=5mH. For part a I am supposed to find the Transfer Function H(jw) = (Vout/Vin) in terms of ω. For part b...
  50. C

    System transfer function

    Homework Statement x[n] = anu[n] A discrete system y[n] = −1/2y[n − 1] + x[n]; where x[n] and y[n] in- and output of the system, respectively. Find the system transfer function H(z), and sketch its zeros and poles in the z-plane Homework Equations u[n] is the unit step function...
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