# cant find the tranfer function of 2nd order lpf

#### ikhsanrino

Jan 9, 2016
8
Hi guys . I have a a problem to find the transfer function of second order low pass filter. Ive tried it with the pattern of lpf second order filter . and try the TF with matlab but the result is different with the simulation use multisim ( cut off frequency) and also with the cut off equation of 2nd lpf. Anyone can help me to solve this? Thank you for your help , your help means alot for me

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#### LvW

Apr 12, 2014
604
Your circuit is one of the classical 2nd order structures: Unity-gain Sallen-Key lowpass.

#### ikhsanrino

Jan 9, 2016
8
thank you fore your answer, i appreciate alot mate, but im still confuse about the resistor on the negietive input, how about the resistor on the ngetive input ? is that a gain or ? it doesnt gives any impact to the circut and transfer function ?

#### LvW

Apr 12, 2014
604
This resistor is not very imporetant - and it does not influence the transfer function.
The only purpose is as follows: There is always a small dc bias current into the opamp inputs. At the non-inv. input this current produces a small dc voltage which may cause a small dc offset at the output. This dc value can be reduced if we place a resistor with a corresponding value also at the inverting input.
But - as mentioned - you can use such a ressitor or not. It does not alter the transfer function.

#### ikhsanrino

Jan 9, 2016
8
Thank you very much for your explanation mate, it helps me alot. Greeting from indonesia !

May 8, 2012
4,960

#### Ratch

Mar 10, 2013
1,098
thank you fore your answer, i appreciate alot mate, but im still confuse about the resistor on the negietive input, how about the resistor on the ngetive input ? is that a gain or ? it doesnt gives any impact to the circut and transfer function ?

R3 is very important to the operation of the circuit because it provides a conduction path to the negative input of the op-amp, and therefore negative feedback. Its value is not important because it will probably be insignificant compared to the input resistance of terminal 2 of the op-amp. Since the input resistance of terminal 2 swamps out the value of R3, the voltage of terminal 2 and 3 will be the output voltage of the op-amp. Finding the transfer function below is a simple matter of finding the solution of a couple of node equations. Notice that R3 does not enter into the transfer function. The derivation is shown below. e1 is the voltage between R1 and R2.

Ratch

Last edited:

#### LvW

Apr 12, 2014
604
This resistor is not very imporetant - and it does not influence the transfer function.
.
Of course, I mean that the VALUE of this resistor is not very important - and it can be replaced by a simple short. Otherwise, we wouldn`t have a unity-gain amplifier.

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