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Wednesday, March 5, 2014

Instrumentation Amplifier

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  • Instrumentation AmplifierOne drawback of the differential amplifier is that its input impedance ($R_3+R_4$) may not be high enough if the output impedance of the previous stage is not low enough. To overcome this problem, two non-inverters with high input resistance can be used each for one of the two inputs to the differential amplifier. The resulting circuit is shown below:
    InstrumentationOpAmp.gif
    The analysis of this circuit is very simple. As the output impedance of the non-inverter is low, the three op-amp circuit can be considered as three independent circuits. The outputs of the two non-inverters are:

    \begin{displaymath}V'_1=V_1\left(1+\frac{R_f}{R_1}\right),\;\;\;\;\;\;\;\;\; V'_2=V_2\left(1+\frac{R_f}{R_1}\right) \end{displaymath}


    The output voltage of the differential amplifier is:

    \begin{displaymath}V_{out}=\frac{R_4}{R_3}(V'_2-V'_1)=\frac{R_4}{R_3}\left(1+\frac{R_f}{R_1}\right)(V_2-V_1) \end{displaymath}


    Of course the two resistors $R_1$ can be combined to become $R_0=2R_1$, i.e., $R_1=R_0/2$, then the output can be written as:

    \begin{displaymath}V_{out}=\frac{R_4}{R_3}\left(1+\frac{2R_f}{R_0}\right)(V_2-V_1) \end{displaymath}


    Alternatively, we consider the current going from $V'_1$ to $V_'_2$:

    \begin{displaymath}\frac{V'_1-V_1}{R_f}=\frac{V_1-V_0}{R_1}=\frac{V_0-V_2}{R_1}=\frac{V_2-V'_2}{R_f} \end{displaymath}


    From the equation of the first two terms we get:

    \begin{displaymath}V'_1=\left(1+\frac{R_f}{R_1}\right)V_1-\frac{R_f}{R_1}V_0 \end{displaymath}


    From the equation of the second two terms we get:

    InstrumentationOpAmp.gif$R_3+R_4$\begin{displaymath}V'_2=\left(1+\frac{R_f}{R_1}\right)V_2-\frac{R_f}{R_1}V_0 \end{displaymath}


    Using the equation of the differential amplifier above, we get the same result as above:

    \begin{displaymath}V_{out}=\frac{R_4}{R_3}(V'_2-V'_1)=\frac{R_4}{R_3}\left(1+\frac{R_f}{R_1}\right)(V_2-V_1) \end{displaymath}






sumber : http://fourier.eng.hmc.edu/e84/lectures/opamp/node3.html

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