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. D

    Sketch and Determine the Transfer Function From Its Poles

    Homework Statement If a transfer function has poles at (-1,2) and (-1,-2) and a zero at (0,0): a) Sketch |H(jω)| on the interval 0≤ω≤10. b) If |H(jω)| = 1, what is the approximate value of |H| at its highest point? Homework Equations The Attempt at a Solution I think I have...
  2. M

    How to find the transfer function (frequency response function) given the EOM

    for a given spring/damper system the equation of motion is: [PLAIN]http://img600.imageshack.us/img600/2140/equation1.png where x is the displacement of a mass from a fixed point d is a damping constant L1 and L2 constant lengths k1 and k2 are 2 spring constants...
  3. K

    First Order Transfer Function

    Homework Statement The dynamic behavior of a pressure sensor/transmitter can be expressed as a first-order transfer function (in deviation variables) that relates the measured value Pm to the actual pressure, P: Pm'(s)/P'(s)=1/(30s+1). Both Pm' and P' have units of psi and the time constant...
  4. B

    Engineering Zeros in a circuit transfer function

    Homework Statement Complete the circuit in the figure in order to get a transfer function as: H(s) = k*[s(s^2+10^10)]/[(s+10^3)(s+10^5)(s^2+1.41*10^5s+10^10)]. The Attempt at a Solution If I split the circuit in four stages: H1(s), H2(s), H3(s) and H4(s), I obtain: H1(s) =...
  5. reddvoid

    Why open loop transfer function ?

    I don't understand why always we use open loop transfer function G(s)H(s) to draw the root locus. can somebody please clarify my doubt. Thanks in advance.
  6. B

    How to calculate transfer function when there is a transformer

    Homework Statement Calculate the transfer function, H(s) = Vo(s)/V1(s), of the given circuit.The Attempt at a Solution I see there is an inverting amplifier with gain A = -10. However, I don't know how to complete the analysis with this ideal transformer. How can I substitute it? Thank you.
  7. B

    Transfer function of transmission line

    Homework Statement Calculate the output vo(t) if the input is the signal vin(t) shown in attached figures. The Attempt at a Solution I've calculated that ransfer function transmission line: H(s) = Vo(s)/Vin(s) = exp(-j*gamma*l), where gamma = -j*omega*sqrt(LC). However, tau = sqrt(LC)*l...
  8. T

    Finding the damping ratio (zeta) of an nth order system from a transfer function

    I am having trouble with some of my homework. I am not quite sure how to find the damping ratio from a third order system when the transfer function (of s) is the only information supplied. Could anyone help me with this? I would like a method that would work with any nth order system...
  9. K

    Control Systems, State space to Transfer Function

    Hi guys, Need a little help with an example my tutor and I are trying to work through. We're converting a dynamics system from a state space representation to a transfer function. This is where we are at so far... [s^2 + (C/Mb)S + (K1/Mb), -((C)S + K1)/Mb; -((C)S + K1)/Mw, S^2 +...
  10. S

    Frequency Response from a Discrete Transfer Function

    Homework Statement Find the DC Gain and the Frequency Response of the above discrete-time system. The Attempt at a Solution This isn't really a homework problem but something I've been struggling with for my exams. I am given a transfer function in terms of z and am asked to find its...
  11. M

    Coefficients of a transfer function

    for a system defined as y(n) + a1y(n-1) + a2y(n-2) = bx(n), for what values of a1, a2, and b is the system realizable? i know that the transfer function is obtained by the following H(z) = Y(z)/X(z) H(z) = b/(1 + a1z-1 + a2z-2) H(z) = bz2/(z2 + a1z + a2) i also know that the poles have...
  12. A

    How to find transfer function for this :

    so here is an LTi system, i/p is given by: (1/k1) exp(-t/K1) ouput being: (1/K2)exp(-t/K2) i could take Fourier transform and then divide the two and find out H(w), then try to take inverse transform of it, to find h(t). but that somehow looks little complicated to me. Is there any...
  13. L

    Estimate and apply transfer function to vibration data

    Hi, I am trying to reduce the error in the controller for a stewart platform. At the moment I am trying to experiment with estimating the transfer function of the error, and applying the inverse of the transfer function to the input data. I have an input file sampled at 50hz of...
  14. R

    Engineering Simple transfer function of circuit

    http://www.flickr.com/photos/61432156@N02/5593767202/ Ok so I'm trying to find the transfer function relating voltage across the 8 ohm resistor (speaker) with the input voltage for the circuit shown above... The two op amps simply provide a gain of 3... and by simple voltage division I am...
  15. P

    Transfer function, Laplace Transform

    Homework Statement [PLAIN]http://img340.imageshack.us/img340/8508/circuit.png Find V2(s)/V1(s) (Laplace transform domain) Homework Equations KCL, capacitor equation. The Attempt at a Solution \frac {-V_2}{R} + \frac {V_1-V_2}{R} + C \frac {d(V_1-V_2)}{dt}=0 But in Laplace domain it follows...
  16. M

    Cut-off frequencies, Quality for a given Transfer Function

    Homework Statement Given the network transfer function H(s)=10s/(s^2+300s+10^6) Find the center frequency, lower and upper half power frequencies and the quality factor Q. Homework Equations Beta=R/L (omega naught)^2=1/(LC) BW=hi-lo=R/L H(s)=(R/L)s/(s^2+(R/L)s+1/(LC))...
  17. M

    Plotting Output of Function Given Transfer Function and Input in MATLAB

    i am trying to plot the output of a function given the transfer function and an input. however, i am having trouble with trying to express the input as a function in MATLAB my transfer function is m = 1; b = 2; k = 1000; num = [ 1000 ]; den = [ m b k ]; transferfunction = tf(num, den) so it's...
  18. M

    Step response and peak response of a transfer function

    Homework Statement The open loop transfer function to a unity negative feedback system is given as: G(s)=50/s(s+10) Homework Equations Unity feedback is used in this problem, and the system input is a step function. Y(s)=50/s(s^2+10s+50) The Attempt at a Solution I have...
  19. C

    Help with proving a transfer function?

    http://img195.imageshack.us/i/89020004.jpg/ I cannot get the Z2Z3 to appear in the bottom. I'm saying Zout = Z2 || Z3 so that gives Z2Z3/Z2+Z3 and Zg = Z1 Then H(s) = Zout/Zg = Z2Z3/Z1Z2+Z1Z3 What am I doing wrong?
  20. C

    Transfer function for a low pass filter

    Homework Statement The input signal of a first-order lowpass filter with a transfer function given by eqn 1 below and a half power frequency of 200 Hz is eqn 2 below. Find an expression for V_outHomework Equations eqn1: H(f) = 1/(1+j*(f/f_B) where f is the frequency and f_B is the half-power...
  21. clope023

    OP AMP Transfer Function Homework: Find Vo(s)/Vi(s) for Circuit

    Homework Statement Find Vo(s)/Vi(s) for the OPAMP circuit in the attachementsHomework Equations V = iR, Kirchoff current law. 1/sC = Laplace transform of capacitor impedance. The Attempt at a Solution Make the voltage at the node = v'. ir1 = (vi - v')/r1 ir2 = v'/r2 iz = (v'-vo)/z z =...
  22. M

    Transfer function of a PLC test rig

    Hi All, I am currently building a test rig for a plc project I am doing, it involves PID control of a pump from the level of a tank. I have built my rig but now I am trying to get the transfer function of it so that I can work out some theory. Any help on how to work out the transfer...
  23. G

    Determining the transfer function

    Homework Statement Determine the transfer function between output x and input F for the following mass-spring system. (see attached image) Homework Equations F=ma Inertia, T = J \alpha Rotational Damper, T=B \omega Rotational Spring, T=K \theta The Attempt at a Solution I'm having...
  24. A

    MATLAB Defining Variables in MATLAB Transfer Function?

    I have the transfer function z+b/z^2-1.5*z+0.7 I want to write this to MATLAB so : syms b h=tf([1 b],[1 -1.5 0.7],1) The problem is that it returns an error of the variable b. How can I define it so that I can get an answer?
  25. R

    Derivation of second order system transfer function

    Hi, I am trying to derive the general transfer function for a second order dynamic system, shown below: \frac{Y(s)}{X(s)}=\frac{K\omega_n^2}{s^2+2\zeta\omega_ns+\omega_n^2} In order to do this I am considering a mass-spring-damper system, with an input force of f(t) that satisfies the...
  26. J

    How Is a Simplified DSP Transfer Function Derived?

    I have taken this example from a Digital Signal Processing book. I have got the simplified transfer function; however do not understand how it was done. I have had a go could someone please look at it and let me know where I am going wrong. I have attached my working out on a Word document...
  27. S

    MDOFs damped system: transfer function estimantion

    I need to calculate the transfer function of a 4 DOFs system, in particular I need to calculate the system natural frequencies. Do you know to figure out these? On books I have found how to get it in the undamped case. Thanks
  28. T

    Argument Of Transfer Function - What does arg(T(w)) mean in real life

    Hi, I have a question something along the lines of Here is a low pass filter, when the resistor = R and the capacitor = C. There is a sinusoidal voltage input source (V1) and a voltage across the capacitor (V2). The transfer function is T(w) = V2/V1. Determine the |T(w)| and arg(T(w)) where...
  29. S

    Transfer function for two-port network with series and parallel components

    I had a little query on transfer functions. My problem is this. I have a two port network with one terminal labeled Vin and one labeled Vout. Now network only has 3 components, one is a resistor in series with an inductor, now this series combination is in parallel with another resistor. My...
  30. O

    How to Derive a Transfer Function for a Fuel Cell Air Flow System?

    Homework Statement Derive a transfer function relating the input(volts) to the out put (pressure) of a fuel celll air fllow system. Homework Equations P(gage)=P(abs)-P(atm) Ideal gas law(PV=mRT) dm/dt=mdot(in)-mdot(out) q=k(P(in)-P(out)) mass flowrate for a linear restriiction The Attempt...
  31. B

    Matlab Bode Plots: 1st Order High Pass & 2nd Order Band Reject

    Homework Statement In Matlab create bode plots for a first-order high-pass filter (with G at infinity = 2 and fc= 1 kHz) in series with a second order band-reject filter (with f0= 5000 Hz, B = 500 Hz, and GDC= G at infinity = 1 ). Homework Equations High pass TF = -jwCiRf/1+jwCiRi...
  32. C

    MATLAB Help plotting transfer function in matlab

    Hello, I need a help here, cause I only have basic matlab.. I want to superimpose two transfer function, Gp(s)=(Kp/sT+1)*e^(-sL) in frequency domain, in time domain y(t)=Kp*(1-exp(t-T)/L)*1(t-L) where, the value of Kp, T and L are known.. and t is matric time from 0-24.5 [0, 0.5, 1...24.5]...
  33. D

    Exploring the Dynamics of Forced Undamped Harmonic Oscillators

    Undamped Harmoni Oscillator differential equation: mx''=-kx (solution (to IC: x(0)=A, x'(0)=0) : x=Acos(wt) with w2=k/m) I need to find out the solution to the forced case with (Initial Condition zero): mx''+kx=F (with F=AFcos(wFt) ) evaluating with the transfer function. But I m not sure...
  34. E

    Find Transfer Function for 2-Input System

    I have a system with two inputs one is reference (constant and known) and another is measured its value and i need to know the transfer function for all the system. Please anyone help me to find the transfer function because I needed it so necessary. thanks a lot.
  35. K

    Transfer Function: U(s) to Y(s): 2 Plants, D(s) Disturbance

    U(s) is my input, Y(s) is the output. I have two plants, G1(s) and G2(s). Between these two plants, i have a disturbance input, D(s). Am i right to say Y(s) = U(s)G1(s)G2(s) + G2(s)D(s)? If that is the case, how can i get the overall transfer function Y(s)/U(s)? Please advise. Thank you.
  36. B

    Doubt in defining transfer function

    why in a transfer function it is written by considering the initial condition to zero.. because if we individual write the integro-differential equation and apply Laplace transform to them and obtain a output/input relation,it definitely contains the initial condition terms in it also.. so...
  37. D

    Convert a discrete time transfer function to a continous time transfer funtion

    Homework Statement I would like to know on how to convert a digital filter transfer function which is in defined in discrete time to continuous time transfer function. Homework Equations The relevant equation is attached...
  38. S

    Laplace Transform vs. Transfer Function

    Hi, I am confused between the difference between the Laplace transform and the Transfer function. I used to think that the Transfer Function was the Laplace transform of the Differential equation representation of a system, but in my readings it seems like that is incorrect - because...
  39. S

    MATLAB Matlab: transfer function determination

    I have a 2 dof vibration system, I have determined the differential equation of the model, can I determine the trasfer function readily with matlab, without using manual algebra operation? In other word, I have that differential equation system: [m]x''+[c]x'+[k]x=[f] where: [m] mass matrix...
  40. R

    Control problem. Transfer function of an electrical system

    http://img28.mediafire.com/bacfa47633147eefb0c3433511d3f1415g.jpg 1. Electrical system given. Find a transfer function. Correct answer UR(s)/U(s)=1/(s+2) 2. My attempt Use Kirchhoff's voltage law u(t)-i(t)*R1-UR(t)=0; u(t)=i(t)R1+uR(t); apply Laplace Transform (L.T.) U(s)=I(s)R1+UR(s)...
  41. R

    Control problem. Transfer function given. Sketch Bode plot

    1. For the control system described by the transfer function H(s)=Y(s)/U(s)=10/(s^2+11s+10) Sketch the bode plot: amplitude and phase diagram. What is the bandwidth of the system? 2. General form of a second order system H(s)=wn^2/(s^2+2*zeta*wn*s+wn^2) Magnitude characteristic in...
  42. M

    Pole and zero of a transfer function

    A transfer function H(S) in s-domain has been obtained as H(s) = 5.0625/(0.0008s^2 + 0.0882s + 5.0625). I’m interested in finding its poles and zeros. I found that denominator polynomial 0.0008s^2 + 0.0882s + 5.0625 has complex conjugate roots. Roots are -55.13 + i 57.35 and -55.13 - i...
  43. S

    Damping ratio from transfer function

    I have a transfer function for system. 23.23*s + 1.421 ------------------------------------- = tf s^2 + 25.88*s + 1.421 Since the numerator has a non-zero coefficient for "s" I am wary about equating 25.88 = 2 * zeta * omega [the stuff we usually do for calculating the damping...
  44. S

    Damping ratio from a transfer function

    I have a transfer function for system. 23.23*s + 1.421 ------------------------------------- = tf s^2 + 25.88*s + 1.421Since the numerator has a non-zero coefficient for "s" I am wary about equating 25.88 = 2 * zeta * omega [the stuff we usually do for...
  45. J

    Block Diagram of Transfer function

    Homework Statement Simplify the block diagram in figure and obtain the closed-loop transfer function. The first attachment is the question and the second attachment is the first step to the simplification of the block diagram.Homework Equations What i don't understand is how do you get rid...
  46. J

    Transfer function problem

    Homework Statement a closed loop control system has a forward path having two series elements of transfer fuctions 2 and 1/s+1.If the feedback has a transfer function of s,what is the overall transfer function of the system? Homework Equations The Attempt at a Solution
  47. G

    Finding Open Loop Transfer Functions and Critical Stability in Root Loci

    Hi, I ve got two problems. 1) The problem i have is how to find an open loop transfer function that gives poles at -3, -6, -7+_ j5 and zero at -5. So i think that the numerator is (s+5), and denominator has (s+3),(s+6). and now I don't know how to carry on. Is it ( s+7+j5) and (s+7-j5)?. Am I...
  48. S

    What is the Transfer Function H(s) for the Given Circuit?

    Homework Statement find the transfer function H(s) [PLAIN]http://img192.imageshack.us/img192/4204/asdwoe.jpg Homework Equations H(s) = Vout/Vin done in the frequency domain so: C1 and C2 turns into 1/sC where C1 = C2 = .1F and R1 = R2 = 20 The Attempt at a Solution to find the...
  49. P

    MATLAB Matlab low-pass filter implementation and transfer function

    Hey guys, Basically, I have been doing some testing with regards to tactile vibrations (I know that isn't very electrical) and using a HET have developed several amplitude plots in the time domain. I've been sampling at 5000Hz and I want to remove the noise from my signals to leave me with a...
  50. C

    Transfer function from amplitude response?

    Hi, in the paper I've attached, they give a method for generating a polynomial g for the amplitude response of a filter that gives arbitrary flatness and roll-off characteristics. \frac{1}{\sqrt{1+g}} And then they say the transfer function can be easily determined from this, but they...
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