# Why and how to use the transfer function?

Status
Not open for further replies.

#### zhi_yi

##### Full Member level 4 why transfer function?

in control engineering, we learn about transfer function, what is the "function" of the transfer function?

thanks..

#### jayc

##### Member level 3 Re: why transfer function?

The transfer function describes the behavior of the output as a function of the input frequency. This is useful particularly in a linear time-invariant system, where given some input X(f), we can find the output Y(f) directly by using the relation Y(f) = X(f) H(f), where H(f) is the transfer function.

#### zhi_yi

##### Full Member level 4 Re: why transfer function?

okay, thank you, after we get the transfer function by compare the input and output equation in laplace's form, we can know the behavior of the system, therefore it's easy for us to control the system to achieve the output we wanted, is it right?

can you give me example of linear time-invariant system and linear time-variant system please?

thank you..

#### v_c Re: why transfer function?

By the way, the terms "input" and "output" can be confusing. Take for example the impedance of a network at a port. Impedance is the ratio of voltage/current. So current is the "input" and voltage is the "output". But these are measured at the same port -- so you have to be a little more careful. I tend to use excitation (instead of input) and response (instead of output), with the transfer function given by response/excitation.

Take an LRC circuit for example ... if we assume that all of the components are linear, that system can be represented by using ordinary differential equations with constant coefficients. That is a linear time invariant system. Linear means that we can use superposition. Time-invariant means that given a system excitation and its corresponding response, shifting the excitation results in shifting the response by the same interval while the system shape is retained.

#### razor_guy_mania

##### Junior Member level 1 Re: why transfer function?

Transfer function helps us to analyse a system and yes to take control of it.
Transfer function tells us various properties of the system like freq response, stability of system.

Also I would like to contribute that Transfer Function is nothing but Laplace transform of the impulse response of the system in time domain. Hope you know know what is impulse response and impulse function.

An Linear Time Invarient (popularly known LTI) system is a sys which obeys superposition thm i.e. for eg
excitation is x(t1) output is y[x(t1)]
excitation is x(t2) output is y[x(t2)]
then for linear sys when excitation is [x(t1)+x(t2)] output is {y[x(t1)]+y[x(t2)]}
this is not true for non-linear systems.

close eg to non-linear sys is:
suppose
i/p a o/p a²
i/p b o/p b²
but i/p (a+b) o/p is (a+b)² AND NOT a²+b²

Time invarience means delay in excitation causes similar delay in o/p but form of o/p remains same.
In time varient systems delay in excitation changes form of the o/p.

eg:- time invarient :suppose you get a particular constant speed for dwnloadin then if start a file which gets completed in 30 mins. if u start dwnlodin at 2.00 pm it will end at 2.30 pm. if u start at 10 pm it will end at 10.30 pm. thus delay in excitaion delays o/p but does not change its form.

time varient: if same file u r dwnlodin but this time u get double speed between 2.00 pm to 2.30 pm then file will be completed at 2.15pm and u get normal speed between 10pm to 10.30 pm then dwnlod will be complete at 10.30. So due to delay in i/p since o/p form is changed it is time varient.

This happens when internal systems quantities are time varying.

Any LCR ckt is time invarient

• Points: 2

#### electronics_kumar why transfer function?

it is also called as static sensitivity of a circuit

##### Member level 3 Re: why transfer function?

see the transfer function means output/input so this will give you the efficiency of the system.you will come to know about TF in control engg and Electrical etc

#### ziyas

##### Member level 1 Re: why transfer function?

A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. The transfer function is commonly used in the analysis of single-input single-output analog circuits. It is mainly used in linear, time-invariant system theory, signal processing, communication theory, and control theory.

In its simplest form for continuous-time signals, the function is often written as

H(s) = \frac{Y(s)} {X(s)}

where H(s) is the symbol for the transfer function, Y(s) is the output function, and X(s) is the input function (see Laplace transform). In discrete-time systems, the function is similarly written as H(z) = Y(z) / X(z) (see Z transform).

#### zhi_yi

##### Full Member level 4 Re: why transfer function?

hi all, thank you very much..

how about the discrete time? what is the discrete time? and why do we find the discrete time equation? what is the purpose?

thank you..

#### jetset

##### Full Member level 3 Re: why transfer function?

Discrete time signals are related to signals that are going to be processed by a digital system, since computers are not sensitive to continuos analog signals, they rather take a measure of the analog signal in a periodic time(T), which its inverse is commonly called sampling frequency (f = 1/T) , then transform the measure of the signal to a digital magnitude. Then discrete time signals are related to digital signal processing and digital control systems... for analog control systems we use the continuos time methodes like Laplace and so on.

#### ferrite

##### Member level 1 Re: why transfer function?

zhi_yi said:
in control engineering, we learn about transfer function, what is the "function" of the transfer function?

thanks..

because this fucntion tersely gives many important features of the system regarding its input/output. it is essentially a frequency-domain concepts

#### LBdgWgt

##### Member level 5 Re: why transfer function?

zhi_yi said:
hi all, thank you very much..

how about the discrete time? what is the discrete time? and why do we find the discrete time equation? what is the purpose?

thank you..

Yes, since nowadays, all control systems are based on microcontrollers, microprocessors, signal processors, etc. so the analog signal value which are measured, firstly sampled and quantized (discrete time, discrete value - basic concepts of digital signal) for further being processed.

#### leoren_tm Re: why transfer function?

why transfer function?
when using a matlab... it is easer if you present it in a transfer function.....
and you can easily know the properties of it....
refer to the book"modern control eng'g by dorf"
and also control eng'g by nice......
there you will learn much,.......[/url]

#### jjohn

##### Banned why transfer function?

A transfer function is a mathematical representation of the relation between the input and output of a system.

K

#### kkeiser

##### Guest why transfer function?

Without it control system will paralise itself. It heavily depends on Transfer Function.. for stability purpose....

#### maharshi_qis

##### Full Member level 5 Re: why transfer function?

Transfer function is not only b/n i.p and o/p.u can get the relation b/n 2 nodes in a ckt....i.e gain b/n those nodes..

#### jasmin_123

##### Full Member level 3 Re: why transfer function?

v_c said:
By the way, the terms "input" and "output" can be confusing. Take for example the impedance of a network at a port. Impedance is the ratio of voltage/current. So current is the "input" and voltage is the "output". But these are measured at the same port -- so you have to be a little more careful. I tend to use excitation (instead of input) and response (instead of output), with the transfer function given by response/excitation.

You should not be too careful: impedance also is a transfer function!

See for example: "On impedance evaluation in feedback circuits," by Francesco Corsi, Cristoforo Marzocca, and Gianvito Matarrese.

#### rabel126

##### Member level 3 Re: why transfer function?

it is used in ploting root locus and frequency response of a system
by ploting root locus though transfer function u will be able to analyse a sytem abt a its stability

#### mma

##### Newbie level 4 Re: why transfer function?

simply transfer function is used to get a relation between the input and the output
without solving the circuit you can get it by using laplace transform and u it used to draw a diagrams for filter from this diagrams we can known the type of the filter

#### sivakumar_tumma

##### Full Member level 4 Re: why transfer function?

zhi_yi said:
in control engineering, we learn about transfer function, what is the "function" of the transfer function?

thanks..

Transfer function will give relation between input and output. so If u know the input , u can find output of that particular system whch is having that transfer function..............

Status
Not open for further replies.