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. A

    Contro Systems - Using Partial Fraction Expansion on Transfer Function

    Homework Statement A system has damping ratio 0.5, natural freq. 100 rad/s, DC gain of 1. Find the response of the system to a unit step input. Homework Equations Im having trouble doing the partial fraction expansion. The Attempt at a Solution I have attached a word document...
  2. H

    How can I find the poles of a transfer function without using a computer?

    Homework Statement This is an example in the book that I am trying to work. I am given L(s) = (10(s+10)) / (s(s+3)(s+5)) The transfer function T(s) = 1 / (1+L(s)) Solving for the transfer function I get T(s) = (10(s+10)) / (s^3 + 8s^2 + 25s + 100) The process of getting the zeros...
  3. K

    Finding the transfer function for a parallel resonant circuit

    Homework Statement Hello, so I'm trying to solve the transfer function for a parallel RLC filter that goes like -------Resistor ------------------- |XXXXXXXXXXXXXXXXX|XXXX| |XXXXXXXXXXXXXXXXX|XXXX| VinXXXXXXXXXXXXXXXXCXXXXL |XXXXXXXXXXXXXXXXX|XXXX| |XXXXXXXXXXXXXXXXX|XXXX|...
  4. U

    Over damped response transfer function (help pls)

    Hi, Not sure on where to post this tread since it involved some fluid mechanics and Maths/ Control theory. I have found the response of a ball flouting in a vertical jet stream of air and the result is a highly non linear system. That is, there is different open loop response as the ball...
  5. M

    Help with deriving transfer function of a second order control system

    Homework Statement Please see attachment for block diagram of the system. Starting with the block diagram given in Figure 2 derive an expression for the overall transfer function of the system, where Gc(s) is in the form given by Eq. (1). Show that the system is a Second Order system...
  6. I

    Characteristic impedance and transfer function

    I have to find the absolute value of the transfer function for the circuit shown in the attachment. However, I have capacitors instead of inductors in my circuit and inductors instead of capacitors. So, the cross circuit will have L in the upper and lower branch and two C in the cross. I...
  7. B

    2nd order filter transfer function normalization

    I'm looking at a guide by Texas Instruments on active filter design. In it are the following equations for a second order lowpass filter, verbatim: The coefficient form of the denominator: s^2 + a_1s + a_0 Normalized: P(s) = (\frac{s}{\sqrt{a_0}*\omega_c})^2 + \frac{a_1s}{a_0*\omega_c} + 1...
  8. S

    Voltage Transfer Function determination from S-Parameters

    Hello everybody I'm trying to obtain the transfer function (Vout/Vin) of some circuits employing an E5062A Vector Network Analyzer. I've been looking for some information on the topic, but I'm quite confused. Somebody told me it can be obtained simply as S21*sqrt(Zo). Additionally, I...
  9. R

    MATLAB MATLAB transfer function question: Fundamentals

    Dear all, This is a query from DSP which I need to implement in MATLAB. I am new to both, DSP and MATLAB. I have gone through the Transfer Function (TF) theory in MATLAB Help but could not really figure out how I use it for my application. Just to give you an idea of my task: I have two...
  10. J

    Engineering Transfer function of RC circuit

    Hello all, I need transfer function of this circuit (it is Bandaxall tone stack). Here is the sheme: Any help would be greatly appreciated.
  11. A

    Append a free integrator to a Transfer Function

    Homework Statement PI Design The transfer functions represent the dynamics of a typical commercial turbofan engine between fuel flow rate \DeltaWF in pps and fan speed increment \DeltaN1 in rpm and between fuel flow rate and high-pressure turbine outlet temperature increment \DeltaT in degrees...
  12. M

    Engineering Write transfer function G(s) of circuit

    Homework Statement The problem ask me to write the transfert function of a electrical circuit witch include an operational amplifier. I've follow some instruction bur I cannot figure out from this problem. Could you suggest me somethings? I'd like to calculate G(S) = U(s) / Y(s) where...
  13. B

    Struggling with Transfer Functions? Here's How to Improve Your Skills!

    Hi everyone - I've been self-studying electronics for the past couple years and I have a confession to make: I'm terrible at deriving transfer functions. I'd really like to improve at it, but every time I see a circuit like the following (to analyze for Z parameters, for example) I start to...
  14. X

    Help trying to derive transfer function

    Homework Statement I am trying to derive the transfer function for the circuit (figure 6). I have what the final transfer function is supposed to be (figure 7) but I can't derive it. Homework Equations ((v2+) - 12)/12k + (v2+)/12k + ((v2+) - v1)/c2= 0 (v2-)/c1 + ((v2-) - Vout)/15k =...
  15. D

    Transfer function of NMOS schematic

    Homework Statement Attachment titled Clapp Schematic is what I am finding the transfer function of. Results are obtained with small signal, low frequency, equivalent circuit for a common-source NMOS. Homework Equations I have derived two different formulas, looking at Vo in 2...
  16. S

    Multiple Input Closed-Loop Transfer Function

    Homework Statement I am given a block diagram (attached below) with 2 inputs (one being disturbance) and I need to find the closed-loop transfer function. I can get the closed-loop transfer function just fine for a normal 1 input system, but I have yet come across one with 2 inputs. I need the...
  17. C

    Obtain transfer function of a system and simulate it with a PID controller

    I want to tune my PID controller. For this I could either do this on-line using the controller on the system, or I could try to obtain the systems' transfer function and then simulate it off-line together with the PID controller to tune it to the desired behavior. I suspect the system is...
  18. M

    Engineering Designing an RLC circuit from a given transfer function.

    Designing a circuit from a given transfer function. I hope you don't mind that I haven't used the default format. It doesn't lend itself well to my problem. The original problem is as follows: We were given a 'black box' that contained a passive circuit and we experimentally determined a...
  19. K

    Incomplete transfer function for phase response

    Hi, I'm currently busy with a 'small' project of translating an analog device (synthesizer, based on schematics) into a digital counterpart. What I do is basically simulate the device using a SPICE model. Then I look at the outputs, and see if can fit some equation on it. Based on the...
  20. S

    Finding the Transfer Function of an RLC Circuit with Parallel Capacitance

    When i tried to find V_o(s)/V_i(s), i got a transfer function in s domain as, degree of denominator was greater than that of numerator. please help me find the transfer function of the attached circuit. i eventually need to find the impulse response.
  21. M

    Trouble Writing Transfer Function for Mass-Spring-Damper System

    (edit: sorry I made a mistake in the thread title. It's the output that isn't a factor of every component in the equation, that is giving me trouble) Hi! I'm new here, and any help would be greatly appreciated. Homework Statement I am modelling a mass-spring-damper system in which the...
  22. R

    Obtain the time constant from a transfer function

    Hey, say I have a transfer function, G(s) = s/(6.25+s) How would I calculate the time constant for this transfer function? Also, if I wanted to sketch a bode plot for this transfer function, would I split it up into s* 1/(6.25+s) ? Thanks in advance.
  23. B

    How do you work out the numerator of a transfer function?

    How do you work out the numerator of a transfer function? -------------------------------------------------------------------------------- G(s)= 60Ka / s(s+2)(s+6) what is the numerator you have to use in MATLAB its givin me a headacheeeee
  24. S

    Frequency response of a transfer function

    If I have a transfer function, and I need the frequency response of it, how do I go about doing it? Is there a easier way than inverse Laplace transforming it, then Fourier transforming that? Thanks
  25. S

    Is a system characterized by it's transfer function?

    This isn't really an electrical engineering question, bit I have other EE-related questions about it. First off, If you are given a system's transfer function, is it unique? Or can other different functions have the same transfer function. Second, does the Transfer function have anything...
  26. 7

    Help with finding a transfer function

    Homework Statement ---Resistor1=47K ohm---------------------------------------------- | | | + | | |...
  27. E

    Quick and easy transfer function question

    This question is more about math than anything, but it comes up in LRC frequency analysis so much that if anyone knows it, its you guys. I am trying to find the values of a resistor, capacitor and inductor. The only knowledge I have is that the three elements are connected in series and the...
  28. K

    How to convert transfer function to state space

    Hi,how can i convert the following transfer function to state space form by hand. H(s)=(s^2+27s+50)/(2s^2+27s+50) Any help will be appreciated!
  29. M

    Root Locus of Unity Feedback Transfer Function: Find K Range for Stability

    I want a MATLAB code to draw the root locus for a characteristic equation of a transfer function of unity feedback, also what is the range of K that keeps the system stable , here is the characteristic equation: s^5+600s^4+50000s^3+ks^2+24ks+80k=0 please help, thanks in previous
  30. B

    Calculating impedance and transfer function of arbitrary length ladder filter?

    Hi everyone - I'm trying to figure out this "tack hammer" method of determining the impedance and transfer function of an arbitrary length RCL ladder filter. This method is briefly explained in the second chapter of Wes Hayward's book "Introduction To Radio Frequency Design," however it is gone...
  31. M

    Transfer function / diff. eq. question

    Hi everyone! I'm stuck with an assignment in control systems and I need some opinions on what I've got so far. Homework Statement The problem relates to an RC circuit as displayed: The task is to form the differential equation and transfer function for the circuit, with V0(t) being the...
  32. G

    How Do You Correctly Plot a Bode Diagram for a High-Pass Filter in MATLAB?

    Hi I have a transfer function< I want to draw a bode diagram in MATLAB, the transfer function is for a simple HPF when I use MATLAB to find the magnitude and phase shift it giving a wrong diagram, the transfer function is: =RCs / (RCs + 1) I want to know how shoud I have to manipulate...
  33. K

    The transfer function of a delayed system x(t-T)

    Hi, I am not looking for the answer, i just want to know how i go about solving it Ive got to find the transfer function of this equation: http://img374.imageshack.us/img374/8149/laplaceeq8.jpg I know that the transfer function G(s) is found by: y(s)=G(s)x(s) As hard as i try i cannot seem...
  34. P

    Band Pass Filter Transfer Function Analysis

    Homework Statement A band Pass filter is given with the following configuration, R-Resistor, C-Capacitor: See Attatchment 1 - Circuit.jpg https://www.physicsforums.com/attachment.php?attachmentid=16241&stc=1&d=1225999965 R1 = R2 = 10 kΩ C1 and C2 are unknown Cut off Frequencies...
  35. I

    What is a composite transfer function?

    Homework Statement Let F(z) = a0 + a1z-1 + a2z-2 denote the composite transfer function of the transmitter, channel and the matched filter in this ultra wide band system. Find a two tap digital equalizer Heq(z) = w0 + w1z-1 that approximates an IIR zero-forcing equalizer for F(z)...
  36. O

    Optical Fiber Transfer Function (attenuation and dispersion)

    I have a few questions regarding the transfer function of a SMF. I'm using the below equation to simulate the effect a single mode fiber (SMF) has on the optical field after some distance \textit{z}. \begin{equation} S_{out}(\omega) = S_{in}(\omega)\exp\left...
  37. M

    Solve ODE: Find Transfer Function G(S)

    Homework Statement M\ddot{X}(t)+c\dot{X}(t)+kx(t) =f(t) Initial Conditions: x(0) = .02 \dot{X}(0)=0 -Use laplace transform to convert the ordinary differential equation in the time domain to an algebraic equation in the frequency domain. -Derive the transfer Function G(S) = \frac{X(S)}{F(S)}...
  38. T

    Engineering Transfer Function for a || RLC Circuit

    Hey all, I'm a new member, so nice to meet you all! Homework Statement I'm currently in the process for deriving the Transfer Function H(s) and H(jw) (w read as omega for angular frequency) for http://www.ebfreedom.com/fwajx/cDiag.jpg" I have taken several approaches but have not been...
  39. R

    Transfer function to state space manually

    Hi, how can i convert a transfer function to state space form by hand: e.g.; G=10/(s+10) ??
  40. B

    Transfer Function & Unity Negative Feedback Control System

    Hi there. I'm wondering if anyone can help. I've got a few past papers I'm working on at the moment and there are a few questions I don't even know where to start with. Here's one: a. Write down the transfer function for a time delay and then evaluate its corresponding frequency response...
  41. R

    Transfer function generation tool

    Dear experts, I'm thinking if there are any free tools available for download which are capable of generating transfer functions based on a drawn amplifier circuit?
  42. Y

    Transfer function to impulse response

    Homework Statement Given the transfer function of a linear, time-invariant system H(z)=\frac{z^2+5z}{z^2+5} compute the impulse response. Homework Equations We are supposed to compute the inverse z-transform with partial fraction decomposition but the problem here is the irreducible...
  43. N

    How Do You Convert Voltage to Current in a Pressure Measurement System?

    Homework Statement A pressure measurement system uses a sensor that converts pressure into voltage according to the transfer function, Vp = (.5)(square root of P). This voltage is then converted into a current. As pressure varies from 0 - 100 psi, the current varies from 4 - 20 mA. A. Find...
  44. U

    Car transfer function (from accelerator to wheels)

    Anyone know what a car's transfer function is, ie the dynamic response written as differential equations and diagrams, so a controller can be designed for it (as in the cruise control feature in some luxury cars)? I mean, many of us are familiar with the torque curve, ie engine torque as a...
  45. D

    RLC Transfer Function for Voltage Across the Capacitor

    Homework Statement We have a series RLC circuit with x(t) as the voltage source. We are to find the frequency response function H(w) from the input x(t) to the output y(t)=Vc(t) - ie the voltage across the capacitor. Homework Equations The Attempt at a Solution My answer...
  46. V

    Engineering Solving a Circuit Transfer Function: Find C2 for R,C1

    Homework Statement http://img252.imageshack.us/img252/410/prelab4problem1tz5.jpg Find transfer function of the circuit above (i.e. - \frac{V_o(s)}{V_i(s)}) \frac{V_o(s)}{V_i(s)}\,=\,\frac{a_1}{s^2\,+\,a_2\,s\,+\,a_3} 1) Find a1, a2, a3 in terms of R, C1 and C2 2) Given that...
  47. P

    MATLAB Entering Transfer Function in MATLAB

    Hi, I'm trying to enter this into matlab: G(s) = -1/((C1+C2)s) How can I enter this into matlab? Thanks!
  48. I

    Engineering Designing a circuit from a transfer function [linear control]

    Homework Statement Linear Control Systems - 2006 past paper If I wanted to design a controller with a transfer function of the form \frac{5(s+0.5)(s+2)}{s(s+10)} How would I go about doing so? Homework Equations A constant gain is given as a constant A differentiator...
  49. N

    Calculating Closed Loop Gain in a Noisy System

    Hi, Is it possible to calculate the gain of a closed loop system with Noise? Here's a diagram describing what i mean: http://img206.imageshack.us/img206/8955/cltfmh8.png I've got the following so far: Vout = \frac{A1A2Vin}{1 + A1A2B} + \frac{AVn}{1 + A1A2B} But the question is...
  50. T

    Simple transfer function - algebra giving me problems

    Homework Statement Find a transfer function: \frac{V_o(s)}{V_i(s)} = \frac{Z_2 (s)}{-Z_1(s)} Homework Equations Z_1(s) = R_1 + \frac{1}{C_1s} Z_2(s) = \frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}final solution should be: G(s) = \frac{V_o(s)}{V_i(s)} = \frac{C_1C_2R_1R_2s^2 + (C_2R_2 +...
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