# loop gain and closed loop gain

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#### engrvip

##### Full Member level 2
does loop gain and closed loop gain transfer functions have same poles adn zeros or are they have different pole-zeros?????

and if yes then why it is so ....since pole-zero positions r decided by R-C values at a particular node and those nodes remains same in two cases???

Hi
see any basic control books.
regards

Loop gain is a "partial" transfer function; it depends on a part of the circuit, and its equation does NOT necessarily include all the circuit parameters. Whereas closed loop gain is a "total" transfer function, whose equation does include all the circuit parameters.
Since equations deffer, so do the poles and zeros.

A(closed)=A(open)/[1+A(open)•β]

A(closed) is closed loop gain.

A(open)•β is loop gain.

But doesnt poles and zeros at nodes which fall under both loop gain and closed loop gain appear same in two equations.

engrvip said:
does loop gain and closed loop gain transfer functions have same poles adn zeros or are they have different pole-zeros?????

and if yes then why it is so ....since pole-zero positions r decided by R-C values at a particular node and those nodes remains same in two cases???

Definitely they have different pole and zero.. bcoz in closed and open looped , the impedance or output impedance at certain node in the circuit will change according to the open loop gain.

for example, Rout is open loop output impedance

Rcl is close looped output impedance, and u can relate in formula as below

Rcl= Rout/ 1+GH, where G=open looped gain and H is feedback gain..

and pole frequency is F=1/Rc

as R become smaller in close looped, then the pole will shift to higher frequency.

hope u understand..

surely,they differ.so whenever you design a op,you should always consider the mismatches causing by the poles and zeros

engrvip said:
does loop gain and closed loop gain transfer functions have same poles adn zeros or are they have different pole-zeros?????

and if yes then why it is so ....since pole-zero positions r decided by R-C values at a particular node and those nodes remains same in two cases???

No, the open loop is use to determine the system stability

it depends on the feedback network if it's resistive they have the same poles and zeros.
you can refer to "analysis ans design of analog integerated circuits" by gray,hursr, lewis,meyer

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