Lag and lead compensators using Op amp

Op amp Lag compensator

Definition

A lag compensator is one which adds a pole the system and is used to improve the steady state response of the system. A lag compensator provides phase lag (negative phase) in the frequency response of system.

Op amp Lag compensator Circuit operation

A simple lag compensator realized using Op amp is shown below 

Op amp Lag compenstor circuit

Op amp Lag compensator circuit

Using the concept of virtual ground the opamp lag compensator can be redrawn as shown in the figure

Using voltage divider principle the transfer function of the system is

                                      Vo/Vs =(1+s*C*R1)/(1+(R1+R2)*s*C),

hence the phase added to system is given as

                                   Ω = tan-1(ω*C*R1) – tan-1(ω*C*(R1+R2))

Since R1<R1+R2 and tan-1(x) is increasing function (if a <b, tan-1(a)< tan1(b)) Ω is negative (phase lag).

Op amp Lead compensator

Definition

A lead compensator is one which adds a zero the system and is used to improve the transient response of the system. A lead compensator provides phase lead (positive phase) in the frequency response of system.

Op amp Lag compensator Circuit operation

A simple lead compensator realized using Op amps is shown below

Op amp Leadcompenstor circuit

Op amp Lead compensator circuit

Using the concept of virtual ground the opamp lag compensator can be redrawn as shown in the figure

Using voltage divider principle the transfer function of the system is

                                       Vo/Vs=(1+s*C*R1)/(1+(R1*R2/(R1+R2))*s*C),

hence the phase added to system is given as

                                     Ω =tan-1(ω*C*R1) -tan-1(ω*C*R1*R2/(R1+R2)).

Since R1 > R1*R2/(R1+R2) Ω is positive(phase lead).

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