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. Q

    Integrator Circuit Transfer Function (voltage divide)

    I have attached a picture of the circuit in which I am attempting to build a transfer function for, however, as you can see it is not a normal integrator. Normally it is evident which resistor is the resistor that is part of the series connection to the op amp. When I do the KVL on the...
  2. L

    Calculating the transfer function from Laplace Transforms

    Homework Statement A Control system for a spacecraft platform is governed by the following equations: d²p/dt² + 2 dp/dt + 4p = θ v1 = r - p dθ/dt = .6*v2 v2 = 7*v1 All the variavles v1, v2, r, p, θ are functions in the time domain Determine the system transfer function P(s)/R(s) Homework...
  3. L

    Refreshing stuff - transfer function

    I'm trying to determine the transfer function to a simple circuit, see pdf. Is the simplest way to describe H(jω) by finding Y(jω) and U(jω) in H = Y/U. Further using the impedances for each component. If so, is each function Y(jω) and U(jω) determine by 'walking' through each impedance path...
  4. M

    Transfer Function: Magnitude and Phase of Complex Function

    Homework Statement f(s) = f(\sigma + j\omega) = \frac{1}{(1+s)^2} Find the magnitude and phase angle of f(j\omega) Homework Equations s = j\omega is a substitution you can make, but I'm not sure if you are supposed to apply that here The Attempt at a Solution I tried substituting \sigma +...
  5. C

    Optical modulation transfer function of an image and its cutoff

    I have an image taken with a camera. I know the f/#, focal length, CCD characteristics, and an approximate distance to my scene. I computed the modulation transfer function but I am trying to map the pixel space to cy/m and having trouble. I essentially want to determine the cutoff spatial...
  6. E

    Finding the transfer Function of a Voltage Buffer

    This is the circuit that I'm trying to work with. Essentially, as far as I can see it's a voltage divider connected to a voltage follower. I have the output of the first op amp as: H(s)=S1/In1= 1/10 = 0.1. However I'm not sure if there are how to obtain characteristics of such a simple...
  7. E

    Open loop transfer function

    In many books i saw that open loop transfer function is given by KG(s)H(s) , where G(s) is forward path gain and H(s) is the feedback gain. But according to the definition of open loop it does not contain feedback , then why there is a term of H(s) ? reference url...
  8. O

    Find Transfer Function of Circuit: KVL, KCL Equations Used

    Homework Statement Find the transfer function Vout(s)/Vi(s) of the circuit Homework Equations Zr = R; Zl=Ls; Zc=1/Cs; KVL; KCL The Attempt at a Solution I have to find the transfer function of the complete circuit I send.For this, I divided the all circuit into small pieces.I tried...
  9. P

    Inverter Transfer Function

    Regarding the transfer function of the inverter,why do we take the transition region between the slopes of '-1'.Is there any special significance for this slope in this context of inverter. Thank you all
  10. D

    Gain & Transfer Function - Difference?

    I know the transfer function = Laplace{output}/Laplace{input}, while gain = output/input, but why is that matter? The ratio will still be the same (or is it?). And if there is a distinct different, is the result of the mason's formula using signal-flow graph a gain or a transfer function...
  11. D

    Get transfer function from bode plot

    Homework Statement What is the transfer function described by this bode plot: http://img96.imageshack.us/img96/4775/capturegib.jpg *The answer is 3s, but I don't know where it comes from. Homework Equations None The Attempt at a Solution Correct me if I am wrong. A bode plot is a...
  12. C

    Transfer function and magintude known, unsure how to appoarch

    Homework Statement Vs=7200V 0 degrees ZLine=2Ω+20jΩ ZLoad=138Ω+460jΩ XC=unknown capacitance (omega not given) Find the capacitive reactance when, place in parallel with ZLoad will make the load appear purely resistive Homework Equations conj(Zline) =2Ω-20jΩ (for max power...
  13. H

    Transfer function for a system

    i need a help to obtain transfer function for a tank, where a heater is placed. the liquid temperature should be maintained at 45C . no inlet or out let. how to obtain the transfer function?? for analysisng about the controller?
  14. S

    How Can You Project and Combine Two Topographical Curves onto the XY Plane?

    My question is a lot simpler than the whole process, but I've reached a plateau and need a push. My issue is that I want to take 2 curves, one in the XZ-plane, the other in the YZ-plane, combine them and project them down to the XY plane, but make it topographical (i.e. contain Z values given an...
  15. S

    Simplifying a transfer function to find overshoot

    Hi, I have question where I am asked to find the % overshoot of a system based only on its transfer function. T(s) = 15(s+2.1) (s+2)(s2+4s+29)(s2+2s+50) I'm assuming I need to use second order assumptions and then find the damping...
  16. B

    Building a physical circuit from a transfer function

    I am trying to build a high frequency analog filter. I don't have the specs quite yet, but I do know how to create the transfer function. The trouble is, once I have that, how do I go about making this into a physical circuit? All the online stuff I can find is either digital or low frequency...
  17. J

    Transfer function Of A Highpass Filter

    Please how do i transform this transfer function of a highpass filter H(w) = jwR2 / [ (R1R2/L) + jw(R1 + R2)] to H(w) = [R2/(R1+R2)][jw/(jw+wc)] wc is the corner freq. The circuit consists of a voltage source Vs(t) ,R1 in series with R2||L,Vo collected on R2. Thanks.
  18. M

    Finding Impulse Transfer Function with Impulse Invariant Method

    Homework Statement Transfer functions of the continuous compensation links are given as follows. Find the impulse transfer functions of the digital compensation links using the impulse invariant method. \frac{a}{s+a} I don't know how to solve the problem correctly :cry: Homework...
  19. E

    Finding a Transfer Function using Laplace

    I'm trying to find the Transfer function of the circuit below so that I can draw the Bode plot for it. I chose to use Laplace because I think it made it a little simpler. My equations so far: KVL of Left Loop: EQUATION1 Vs=I1(900+1800)-900I2 KVL of Right Loop: EQUATION2...
  20. H

    Engineering Transfer function for electrical circuit

    Hello! I have a problem to get a transfer function from my circuit(this circuit is marked with question sign "?"). For upper circuit this function is calculated...this can be seen in image. I tought that it would be easier to get transfer function by using matrix, so then W(s) = 1/a11 By doing...
  21. G

    Laplace and transfer function ( input output voltage)

    Homework Statement Given transfer function : H(s)=Vo/V1=(10/s)/(4+0.4s+(10/s)) and the input voltage is given as V1=10(u(t)-u(t-0.1))V. Use the convolution integral to find Vo for t>=0.1 Homework Equations convolution integral..its hard to write and laplace table The Attempt at a...
  22. J

    Op amp transfer function incorporating output impedance

    Hello, I was trying to derive the transfer function of a simple inverting op amp topology, incorporating the output impedance, Ro, of the non-ideal op amp, to see how it, when combined with a load capacitance can induce oscillations (or at least ringing). I haven't been able to get a valid...
  23. M

    Bode plot of transfer function

    Homework Statement I have the transfer function: for the circuit: The component values are know, and are: R1 = 47kΩ R2 = 4K7Ω C = 10nF Homework Equations The Attempt at a Solution I have derivied the transfer function but have become stuck on plotting the bode plot. I understand...
  24. G

    Responses of a transfer function on MATLAB

    I'm given the following system: \frac { 3s+0.5 }{ { s }^{ 3 }+3{ s }^{ 2 }+8s } I'm supposed to find the steady state error of the system by plotting the step and ramp responses, and then find the value when s tends to infinity. Here is the MATLAB code: sys1 = 3 + tf(0.5.*[1], [1...
  25. C

    Is this transfer function unstable?

    Is this transfer function unstabile? Spoiler: This is a feedback control system related issue I am trying to sketch the bode plot of the following transfer function but I can't find a solution. I should use 20log( unknown / 3 * 10) to find where the magnitude starts. G(s) = (s^2+4s+25) /...
  26. V

    Transfer function with laplace transform

    Hi, I am trying to derive one transfer function for a system, but got stuck at a point. I want the solution to the ratio V_o(s)/V_g(s), the transfer function. V_o(s) = [a*L{(V_g)^2} - b*L{V_o * (V_g)^2} - c*V_g(s) - d/s]*z(s) In the following equation, I have: s-> lapace transform...
  27. B

    Determining the transfer function of a humidity chamber

    I have created a mock up of a humidity chamber which i will soon be integrating into a temperature chamber for undergraduate project. I am confused on how i can control the system. I have currently a humidifier with a relay built in, this relay is going to switch on and off from a PWM signal...
  28. D

    Transfer Function of Linear two port system

    So I am suppose to solve for the transfer function of the circuit i have attached. First I would find the V_out at the resistor. This is done by V_in=I(jwL + 1/jwC + R) Then the transfer function is: H(f) = V_out/V_in = R/(jwL + 1/jwC + R) Now I need to find the transfer function by...
  29. M

    Transfer function of a PDE system

    Hi everyone! I want to design a robust controller for a system which is driven by a PDE. I need to acquire its transfer function in 's' parameter which means it should be transferred by Laplace transformation. I know that the result transfer function will be an infinite series of transfer...
  30. Z

    Transfer function of an air levitation system

    I'm building an air levitation system that will levitate a ball in a closed tube with a DC motor fan at one end of it. I'm having a hard time thinking of a way to obtain the transfer function of the system. I know the net vertical force will be the force of gravity the gradients of air pressure...
  31. X

    Transfer function of a circuit in Matlab

    Homework Statement What will be the transfer function in form of I2 / V1 of this circuit http://img813.imageshack.us/img813/198/6… 2. The attempt at a solution here is my coding but it shows incorrect answer, but after doing f=e/d it shows incorrect answer (the answer doesn't match with the...
  32. Z

    Magnitude and Phase of Transfer Function

    Homework Statement I am given the transfer function H(s) = 10/(s(s^2 + 80s +400)) where s = jω [j is the imaginary unit i] and I am trying to get it into its magnitude and phase components. The Attempt at a Solution I rearranged it to 1/(40jω(1+ 4jω/20 + (jω/20)^2)) which is the standard...
  33. S

    Laplace Transform, transfer function

    Homework Statement Given transfer function H(s)=s^2+4 and input x(t)=sin(2t), find the ouput y(t) in time domain, and show whether bounded or unbounded. Okay, so I know L^{-1}[sin(2t)]=2/(s^2+4)=2/[(s+j2)(s-j2)] and that Y(s)=H(s)X(s)=2 Therefore, y(t)=2\delta{(t)} However, I am a...
  34. K

    Current through Voltage in a Transfer Function

    I am trying to solve the transfer function of a circuit. I noticed in the explained notes provided by the teacher, he deduced certain IV characteristics using KCL. The KCL on the node attached to Vout did not consider the output current running to Vout, and instead only incorporated the currents...
  35. V

    Transfer function from Gain Margin and Phase Margin

    Would it be possible to get the Transfer Function of a System if Open Loop Gain Margin and Phase Margin are known.
  36. M

    MATLAB How can I plot a transfer function with linear amplitude in MATLAB?

    hello, please i need ur help. i want to draw this transfer function m = tf ([1,0,1,0],[2,0,1]) in MATLAB and i want the y-axis to be the amplitude and x the frequencies. This is not Bode because i want the amplitude to be linear and not log scale. thank u for your help
  37. Femme_physics

    Is my transfer function right?

    http://img803.imageshack.us/img803/7417/85681304.jpg At least so far...
  38. S

    From a transfer function to a difference equation

    Hello. I have been given a transfer function for a digital system, and I need to find the difference equation for that system. I have attached a pdf with my work. I would be grateful if someone could take a look at it, and see if I am along the right lines. Thanks in advance, and happy...
  39. C

    Transfer function of flow measurement system HELP

    Transfer function of flow measurement system HELP! 1. I have attached the question, which is to derive the transfer function of a volumetric flow measurement system... 2. I know of the following relevant equations: F = Ma = MD^2.x Flow f = area x velocity and f through a...
  40. G

    Why is a transfer function denoted by 'H'?

    During a basic lecture about system design the transfer function H(s) was discussed. The question was raised why the letter 'H' is used for this... Sounds weird, but I did start to think about it... Indeed in many books and publications the letter H (besides sometimes G(ain)) is used to...
  41. T

    Error in asnwer? Finding the transfer function of a system

    Homework Statement Find the transfer function and the impulse response for the system: y'(t) + y(t) = x(t) x = {1 if 0<=t<1,0 1<=t} Homework Equations d/dt y(t) ~ sY(s) -y(0) The Attempt at a Solution I transform into the laplace-domain: sY(s) - y(0) + Y(s) = X(s)...
  42. Femme_physics

    Understanding Transfer Functions: Am I On the Right Track?

    Trying to get the hang of transfer function. Did I get it? http://img24.imageshack.us/img24/5260/ssketch.jpg
  43. P

    MATLAB Steady-State to Transfer Function Using MATLAB

    I am trying to use MATLAB to obtain a transfer function, for my Controls class. I will be honest, I have no experience using MATLAB, but our professor insists on us using it to find the transfer function. MATLAB is not a prerequisite for this class. Before I start attempt to find my transfer...
  44. B

    Transfer function to Pole-Zero Plot to Impulse Response Curve

    Homework Statement The question gives a transfer function. and we are asked to put it into pole zero form and then we are asked to sketch the positions of the poles and zeros of the system on the complex plane and then sketch the impulse response corresponding to each pole. i have...
  45. T

    Transfer Function Help: Find Soln for Attached Image

    Homework Statement I need help finding the transfer function for the attached image. Homework EquationsThe Attempt at a Solution I combined the 1/6F cap and the 1 ohm resistor into a single impedence. I know the AV of the opamp is -0.5/(6s+1). After that I am stumped. Is there a name of...
  46. L

    Engineering Solving a Peculiar Circuit: Find the Transfer Function

    Hi all, New to the forums here, but I've got a question for you guys: I've ran into this rather peculiar circuit. In all the circuits I've seen (as far as transfer functions go), Vout has always referenced ground (e.g. one node of Vout is ground); in this one, however Vout is across an...
  47. T

    Transfer function of an ideal OP amp

    Homework Statement I have to find the transfer function of a linearly and ideally operating OP Amp. http://i.imgur.com/u3f6E.jpg Homework Equations The Attempt at a Solution I know that the current through the capacitor, R1, and R2 is the same, so i=C(dv/dt) = Vin/R1 =...
  48. C

    Engineering Finding the transfer function (H(jw)) of a sinusoidal-input circuit

    1. Find the transfer function of the following circuit. The circuit has been included as an attachment. I have tried using node voltage, which leads me to this equation: (V1 - Vi)/R + V1/C + (V1-Vo)/(R+C) = 0 *V1 is the voltage of the essential node on the top center of the circuit...
  49. A

    Creating a Bode plot by analyzing a transfer function

    Homework Statement I am constructing a Bode plot from a given transfer function. I having trouble because I am unsure how to rewrite the transfer function in the proper form. What makes this transfer function particularly tricky for me, is that there is no "jω" in the numerator, just ω^2...
  50. L

    Engineering Transfer Function Mid-band Gain & Open Circuit/Short Circuit Time Constant Method

    Hey guys, I recently had a quiz on Circuit is attached in photo below. T(s) = (A)(s/s+20)*(s/s+200) **All values of R in the circuit attached are 2000 ohms. and C1>C2 a. find the mid-band gain A. I do not know how to start this question... Can anyone give me an idea of where...
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