Figure 5.105 displays a two-op-amp instrumentation amplifier. Derive an expression for V0 in terms of V1 and V2. How can this amplifier be used as a subtractor?

Question

Figure 5.105 displays a two-op-amp instrumentation amplifier. Derive an expression for { V }_{ 0 } in terms of { V }_{ 1 } and { V }_{ 2 }. How can this amplifier be used as a subtractor?

Accepted Answer

The output, [latex]{ V }_{ a }[/latex], of the first op amp is,

[latex]{ V }_{ a } = (1 + (R2/R1)){ V }_{ 1 }[/latex] (1)

Also, [latex]{ V }_{ 0} = (-{ R}_{ 4 }/{ R}_{ 3 }){ V }_{ a } + (1 + ({ R }_{ 4}/{ V }_{ 3 })){ V }_{ 2 } [/latex] (2)

Substituting (1) into (2),

[latex]{ V }_{ 0 } =(-{ R}_{ 4 }/{ R}_{ 3 })(1 + ({ R}_{ 2 }/{ R}_{ 1 })){ V}_{ 1 }+ (1 + ({ R}_{ 4 }/{ R}_{ 3 })){ V }_{ 2 }[/latex]

Or, [latex]{ V }_{ 0 } = (1 + ({ R}_{ 4 }/{ R}_{ 3 })){ V }_{ 2 } – ({ R}_{ 4 }/{ R}_{ 3 } + ({ R }_{ 2 }{ R }_{ 4 }/{ R }_{ 1 }{ R }_{ 3 })){ V }_{ 1 }[/latex]

If [latex]{ R }_{ 4 } = { R }_{ 1 } and { R }_{ 3 } = { R }_{ 2 }[/latex], then,

[latex]{ V }_{ 0 } = (1 + ({ R}_{ 4 }/{ R}_{ 3 }))({ V }_{ 2 } – { V }_{ 1 })[/latex]

which is a subtractor with a gain of [latex](1 + ({ R}_{ 4 }/{ R}_{ 3 })).[/latex]

Question 5.87: Figure 5.105 displays a two-op-amp instrumentation amplifier...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions