# 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. ### Questions about motion control and the moment of inertia referred to a motor shaft

hello take a mechanism driven by a DC motor in automation books you find transfer functions such as : G(s) = k1/s(s+k2) normally it s assumed that the moment of inertia referred to motor shaft is a constant the point is that in general it is not a constant take for example a slider - crank...
2. ### Process Control (transfer function) problem

TL;DR Summary: transfer function Hello, I have a doubt on this exercise from my post graduation course: ____________________________________________________________________________________________________ The transfer funtion of a series RL circuit is given by: Determine the answer y(t) for...
3. ### Difficult Understanding Magnitude and Phase Shift of Transfer Function

Hello, My textbook offers the following transfer function as an example. It then goes on to explain that the following equations represent the magnitude and phase shift of the transfer function. However, I am having some difficulty jumping from the first equation to these equations. From...
4. ### Oven controller block diagram, transfer function and temperature calcs

FIGURE 5 shows an electrically heated oven and its associated control circuitry. The current, I, to the oven's heating element is fed from a voltage-controlled power amplifier such that I = EK1. A voltage, VD, derived from a potentiometer, sets the desired oven temperature, TD. The oven...
5. ### 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...
6. ### Engineering RLC circuit -- Phasor Transfer Function calculation

Good morning, I need some help solving those two question. I've attached my attempted solution below. Could i solve the transfer function any further? Thank you for your help
7. ### Engineering What is wrong in this 2nd order transfer function?

I have attached my attempt at a solution. In the solution image, I have computed 3 things: 1. System transfer function based on my understanding of the problem statement. This is a 2nd order system with steady state dc gain=0.9. So I wrote the transfer function accordingly. However, I strongly...
8. ### 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...
9. ### Engineering Is it possible for a low pass filter to have such a transfer function?

Hello! Consider this filter,and that I have to find the transfer function U2/U1 with the norm Ω= ωRC (also double fractions are not allowed) Now I can see that that the resistor and capacitor left as well as right are parallel to each other. So simplifying that ## Z_1 = \frac{R}{jωRC +1}...
10. ### Engineering How do I draw the Bode diagram of this transfer function?

Hello! I have this filter here a) Calculate the transfer function T(Ω) = Ua/Ue using voltage dividers.For this, use the normalized angular frequency Ω = ωRC and bring the result into the form ##T(Ω) = \frac{A+jB}{C+jD} ## . The result must not contain any double fractions. I was able to that...
11. ### 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...
12. ### 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
13. ### Engineering Motion equation and transfer function of mass on a conveyor

Denote wheel turning angle as theta--> Induced EFM (Em)=Kb*Theta_dot. Voltages on the wheel: R*i= V - Em Moments on engine's axis: Kt*i-C*a + a (m+M)*x_double_dot=0 (As Jm negligible). From here I would find another equation to have x and theta expressing each other, but i think I'm...
14. ### Transfer function with initial conditions (DE)

I have a differential equation of the form y''(t)+y'(t)+y(t)+C = 0. I think this implies that there are non-zero initial conditions. Is it possible to write a transfer function for this system? This post...

16. ### Engineering Magnitude of transfer function

Tried this, but not sure how am I supposed to square the whole equation and then square root it since this will inevitably give me imaginary values. Am I supposed to ignore the imaginary values? Also, how can I find out the phase in this case? Usually, it's taking the exponents but in this case...
17. ### Engineering Control block diagram's transfer function

The ac signal is converted to DC signal which is connected to a capacitor to filter the DC signal. The filter DC signal is step down for 12volt to 5 volt using a voltage regulator. The regulated DC signal is connected to a crystal oscillator that converts the DC signal to a square wave signal...
18. ### PID - Root Locus (Sisotool) for Transfer Function with Zeros and Poles

Hi everyone! I have a 8th order transfer function, you can see it in the first image: % Transfer function num = [2.091,0,203.3,0,-2151,0,-1.072e05]; den = [1,0,-830.4,0,-1.036e05,0,-5.767e05,0,2.412e07]; tf = tf(num, den) I need to use a PID, so I'm trying to use a compensator, adding poles...
19. ### Circuits - Transfer function of this LRC circuit

Got B = 9. My school doesn't provide answers, hence could someone double check if my answers is right? Thanks!
20. ### Engineering Transfer function of AC Transformer

I'm solving this exercise, first I did a force diagram for the transformer nucleus and I got this: ∑Fx = ma P(t) - Fk - Fb = ma P(t) = mx''+ bx' + kx So I got that dynamic equation, my question is, after transform that dynamic equation to Laplace Domain how can I relate it with the Output...
21. ### Engineering Finding the natural frequency of transfer function (2s) / (3s^2+5s+2)

In the context of control systems, if I have a vibratory second-order system, (ω_n)^2 / [s^2 + 2ζ(ω_n) + (ω_n)^2], I know how to get the natural frequency ω_n. So, if I have something like 2 / (3s^2+5s+2), I know how to get the natural frequency ω_n. However, if I instead have something like...
22. ### Engineering Determine the transfer function of the block diagram

Step 1: I first started by reducing the inside of the block diagram of picture "bd" (the portion with G1 and the negative feedback G2) I obtained G1/[1 + G1G2] I'll call this term "F" Step 2: Then I'm left with two terms feeding into a summing point: F - G3 I'll call this term "K" I can...
23. ### Engineering Converting a series connected transfer function to the state space model

Hi, I have a question about a homework problem: I am not sure why I do not seem to get the same answers when using different methods. Question: Given transfer functions G(s) = \frac{s - 1}{s + 4} and C(s) = \frac{1}{s - 1} , find the state space models for those systems. Then find the...
24. ### 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...
25. ### Engineering Write the differential equation that's equivalent to this transfer function

I have the solution to the problem, and I mechanically, but not theoretically (basically, why do the C(s) and R(s) disappear?), understand how we go from ##(s^5 + 3s^4 + 2s^3 + 4s^2 + 5s + 2) C(s) = (s^4 + 2s^3 + 5s^2 + s + 1) R(s)## to ##c^{(5)}(t) + 3c^{(4)}(t) + 2c^{(3)}(t) + 4c^{(2)}(t) +...
26. ### Engineering 2 j-terms in a transfer function?

I have the above transfer function for this filter design The transfer function becomes which then becomes Now when I try to use this transfer function to plot a bode plot, I always end up with negative terms which i can't get the square root of For example, at 1hz, where w = 6.283 R1 = 1705...
27. ### Closed Loop Transfer function

Hi all Physics Forum User, I am again coming to you to ask for help. For the above question I can't make sense of how a larger G will cause Vo/Vi to approach 1. For this I'll call Vo=V and Vi=I As can be seen from the control loop B = A*H and V = B*K hence V = A*H*K Also A = I - C and...
28. ### Engineering Finding the transfer function for this circuit

Transformed circuit: Using KVL, Now, I am unsure about the current to use KVL in this case. As far as equation goes: Vi(s) =(I1*R)+(I3*R)+Vc(s), where Vc(s) = V0(s)/u as shown in the circuit. How am I supposed to find the current I1 and I3 for the two resistors in this case? Thanks
29. ### ODE -> Transfer Function Assistance

Homework Statement:: ODE -> Transfer Function Assistance Relevant Equations:: Newtonian physics, buoyancy, drag [Mentor Note -- thread moved to DE from the schoolwork forums, since it is for work and not schoolwork] Hello all, I'm new here but I'm looking for a bit of guidance with a...
30. ### Engineering Control - Transfer function

The correct solution is different than my answer, I am not sure where I am going wrong?

32. ### Engineering Transfer function to block diagram

I am given the following two equations: and where E_1 is an output with corresponding input e and theta_o is an output with corresponding input E_3. The solutions that I was given are as follows: Unfortunately, I do not understand at all how to work out the block diagrams from the equations...
33. ### How to derive a log-antilog opamp square law transfer function?

Firstly, this is not a homework question. I found a worksheet online with an example of a square law circuit built using log-antilog operational amplifiers. I tried to derive the transfer function but I can't seem to eliminate the reverse saturation current term ##I_S##. I would really...
34. ### Steps from state space to transfer function

I mean the first question has derivative form and the second is linear form so what the difference here in steps of converting both to transfer function... please need some ellaboration to make sure i am solving correctly or not... is it correct to apply the same rule on both: Transfer function=...
35. ### Converting linear state space into a transfer function

My questions are now... Do the steps of converting this space to transfer function include any laplace ? or just we do get [SI-A]-1 and then transfer function is = C* [SI-A]-1 * B As [1 0] * [s-1/det -0.5/det ; 0.5/det s-0.5/det] * [0; 1] = -0.5/s^2+s+0.5 I mean do we need any laplace after that...
36. ### Finding the ODE that describes this circuit + find its transfer function

As you can see, I've tried using KCL at node A to find the 2nd order ODE that describes this circuit in terms of the capacitor voltage. The problem I run into, however, is that I can't find anything to put the node voltage at A in terms of. I've tried (not shown here) doing mesh current as well...
37. ### Parameters of a non-standard second-order transfer function

For a standard second-order system, its transfer function is G(s) = ω2/(s2 + 2ζω + ω2) where ω is the natural frequency and ζ is the damping ratio. But for a non-standard second-order transfer function, G(s) = (2s + 1)/(s2 + 2s + 5), what are its natural frequency and damping ratio? Thank you!
38. ### Determine a transfer function in the s domain and the response to a ramp input

1. A process can be represented by the first order equation ##4\frac{dy(t)}{dt}+y(t)=3u(t)## Assume the initial steady state is steady (y=0 at t=-0) (a) Determine the transfer function of this process in the s domain (b) If the input is a ramp change in u(t)=4t, determine the value of...
39. ### Does the transfer function exist for an unforced system?

Homework Statement c is the coefficient of damping, k is the spring constant, and m is the mass. if the cart is displaced from rest by distance X_0 and released at t=0 with initial velocity v_0=1.Homework EquationsThe Attempt at a Solution Ok this might be a stupid question because I wasn't...
40. ### Transfer Function and Control Systems Question

ıs there anyone to solve 8th 9th and 10th problems? It is about transfer function and control systems http://avesis.yildiz.edu.tr/DokumanYetki.aspx?SSNO=33&USER=2813Password= 1234
41. ### I Transfer Function relating momentum and force

Hey all, I hope this is the correct forum section to post this in. I heard about this problem from a youtube video but I've not been able to simulate it because the video was meant only for an introduction into PID control. Here's the problem: A remote control helicopter is hovering just...
42. ### Transfer Function of a FET Differential Amplifier

Homework Statement [Taken from Razavi's Design of Analog CMOS Integrated Circuits 2nd edition]Homework EquationsThe Attempt at a Solution [/B] I'm not too sure what to do with this question. Here's what I think of the circuit This doesn't look like a differential amplifier to me since...
43. ### 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...
44. ### 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
45. ### Transfer function of a curve

How can i calculate transfer function of curve? for example from time response of a curve. or transfer function of ferquency response .
46. ### 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...
47. ### 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...
48. ### Basic Z-Transform Transfer Function

Homework Statement Hi, I'm asked to find the transfer function for the following digital filter described by a difference equation Homework EquationsThe Attempt at a Solution [/B] Usually if there's no constant term (0.7) here, I can just rearrange in the form of Y(z)/X(z) to give me H(z)...
49. ### Rotational Mast System - Transfer Function, PID Design

Homework Statement Given the system above, were a motor is rotating a mast that is attached to a second second mast by a spring with a spring constant K and a damping coefficient D. The motor has a current I applied to it with coefficient K Below are the provided values. K_s is the...
50. ### 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 planning...