1. Differential Amplifier
M.S.P.V.L Polytechnic college,
Pavoorchatram.

2. A differentiator circuit produces an output that is proportional to the derivative or rate of change of the input voltage over time.
Differentiator circuit can be constructed as shown using an operational amplifier, a resistor, and a capacitor.
Unlike an ideal integrator circuit where the slightest DC offset in the input eventually drives the output into saturation, for the differentiator we need not be concerned about a DC offset in the input since the derivative of a constant is always zero. For this circuit, it can be shown that:

3. Differentiator Circuit

4. Since the output voltage of a differentiated is proportional to the input frequency, high frequency signals (such as electrical noise) may saturate or cutoff the amplifier.
For this reason: a resistor is placed in series with the capacitor in the input as shown in Figure .
This establishes high frequency limit beyond which differentiation no longer occurs:

5. To achieve greater attenuation at higher frequencies (or prevent oscillation), a feedback capacitor is added in parallel with the feedback resistor.
This establishes another break frequency that can be calculated as in the integrator.
Stable Differentiator Circuit

6. Figure 1. Circuit Diagram for a Dual-Supply Op Amp Differentiator

7. Figure 1. Circuit Diagram for a Single-Supply Op Amp Differentiator

8. The circuits shown in Figures 1 and 2 are differentiator circuits, which are also sometimes referred to as 'differentiation amplifiers'. The main component of these circuits is the operational amplifier, configured in such a way that its output voltage is proportional to the derivative of its input voltage.
The circuit in Fig. 1 operates on two supplies, while that in Fig. 2 is a single-supply differentiator.  However, what makes them both differentiators is the combination of the feedback resistor (R2 in both examples) and the capacitor at the inverting input of the op amp (C1 in both examples).   

9. Cont..,
To illustrate how these circuits perform differentiation, consider the circuit in Figure 1.  Since the current going into the inverting input is ideally zero, then the current through capacitor C1 is practically equal to the current through R2.  The current through C1 is just C1 times the rate of change of the voltage across it, dVc/dt.  If R1 << R2, then this current is approximately C1(dVin/dt). 
The output voltage Vout of this circuit is equal to the negative of this current times the resistance of R2.  Thus, Vout = -R2C1(dVin/dt), which clearly shows that the circuit is indeed a differentiator. As a graphical example, the input voltage in both circuit examples is a triangle wave.  This emerges as a square wave at the output of the circuits (the derivative of a triangle wave is a square wave).
Differentiator circuits like this are commonly seen in wave-shaping and function-generating circuits.  

10. Improved Differentiator Amplifier
 The basic single resistor and single capacitor differentiator circuit is not widely used to reform the mathematical function of Differentiation because of the two inherent faults mentioned above, Instability and Noise.
So in order to reduce the overall closed-loop gain of the circuit at high frequencies, an extra Resistor, R2 is added to the input as shown below.

11. Improved Differentiator Amplifier Circuit
    The circuit which we have now acts like a Differentiator amplifier at low frequencies and an amplifier with resistive feedback at high frequencies giving much better noise rejection. This then forms the basis of a Active High Pass Filter as seen before in the filters section.

12. Applications of Differential Amplifier
Integrator
Differentiators
Difference amplifier
Instrumentation amplifier
AC amplifier
V to I converters
I to V converters

13. Cont.., Buffers Comparators Multi vibrators Triangle wave generator
Square wave generator
Log and anti log amplifiers
Precision rectifiers.