An electrical network shown in figure What type of compensator is this?

Concept:

Lag compensator:

Transfer function:

If it is in the form of \(\frac{{1 + aTs}}{{1 + Ts}}\), then a < 1

If it is in the form of \(\frac{{s + a}}{{s + b}}\), then a > b

Analysis:

The equivalent Laplace transform network for the given network is,

By applying voltage division,

\({V_2}\left( s \right) = {V_1}\left( s \right)\left( {\frac{{{R_2} + \frac{1}{{Cs}}}}{{{R_1} + {R_2} + \frac{1}{{Cs}}}}} \right)\)

\( ⇒ \frac{{{V_2}\left( s \right)}}{{{V_1}\left( s \right)}} = \frac{{{R_2}Cs + 1}}{{\left( {{R_1} + {R_2}} \right)Cs + 1}}\)

\( = \frac{{{R_2}Cs + 1}}{{\left( {\frac{{{R_1} + {R_2}}}{{{R_2}}}} \right){R_2}Cs + 1}}\)

\( ⇒ \frac{{{V_2}\left( s \right)}}{{{V_1}\left( s \right)}} = \frac{{\tau s + 1}}{{\beta \tau s + 1}},\;\tau = {R_2}C,\;\beta = \frac{{{R_1} + {R_2}}}{{{R_2}}}\)

The above system to be lag compensator, β > 1

\(\beta = \frac{{{R_1} + {R_2}}}{{{R_2}}} > 1\)

⇒ R1 > 0 always

Therefore, at any value of R2 the given system acts as lag compensator.