A system transfer function is {H}( {s})= { {a}_{1} {s}^{2}+ {b}_{1} {s}+ {c}_{1}}/{ {a}_{2} {s}^{2}+ {b}_{2} {s}+ {c}_{2}} . If {a}_{1}= {b}_{1}=0, and all other coefficients are positive, the transfer function represents a

Correct Answer is : low pass filter

GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 28 of 65

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A system transfer function is

{H}( {s})=\;{ {a}_{1} {s}^{2}+ {b}_{1} {s}+ {c}_{1}}/{ {a}_{2} {s}^{2}+ {b}_{2} {s}+ {c}_{2}} .

{a}_{1}= {b}_{1}=0

, and all other coefficients are positive, the transfer function represents a

Solution:

The standard

2^{\;\text "nd "\;}

order LPF

=\;{ω_{0}^{2}}/{ {s}^{2}+\;{ω_{0}}/{ {Q}} {s}+ω_{0}^{2}}

The standard

2^{\;\text "nd "\;}

order HPF

=\;{ {Ks}^{2}}/{ {s}^{2}+\;{ω_{0}}/{ {Q}} {s}+ω_{0}^{2}}

The standard

2^{\;\text "nd "\;}

order BPF

=\;{s^{2}}/{s^{2}+\;{ω_{0}}/{Q} s+ω_{0}^{2}}

In the given problem

{H}( {s})=\;{ {C}_{1}}/{ {a}_{2} {s}^{2}+ {b}_{2} {s}+ {c}_{2}} \;\;

represents standard LPF

{H}(0)=\;{ {C}_{1}}/{ {C}_{2}}

{H}(∞)=\;{ {Lt}}↙{s → 0} {SH}( {s})

=L_{s-0} \;{s C_{1}}/{a_{2} s^{2}+b_{2} s+c_{2}}=0

∴ {H}(0)=\;{ {C}_{1}}/{ {C}_{2}} ; {H}(∞)=0

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