To study the effect of differentiator on different waveforms and measuring the frequency and peak to peak voltages of the output waveforms.

 

 

The basic Differentiator Amplifier circuit is the exact opposite to that of the Integrator operational amplifier circuit that we saw in the previous experiment. Here, the position of the capacitor and resistor have been reversed and now the Capacitor, C is connected to the input terminal of the inverting amplifier while the Resistor, R₁ forms the negative feedback element across the operational amplifier. This circuit performs the mathematical operation of Differentiation that is it produces a voltage output which is proportional to the input voltage's rate-of-change and the current flowing through the capacitor. In other words the faster or larger the change to the input voltage signal, the greater the input current, the greater will be the output voltage change in response becoming more of a "spike" in shape. 

Figure 1: The Differentiator Circuit

Analysis of the circuit is similar to that of the integrator. Since the inverting-input terminal represents a virtual ground,

and

Since i_- =0, these two currents must be equal, and

 

The output voltage is a scaled version of the derivative of the input voltage. 

As with the integrator circuit, we have a resistor and capacitor forming an RC Network across the operational amplifier and the reactance (Xc) of the capacitor plays a major role in the performance of a Differentiator Amplifier. The capacitor blocks any DC content only allowing AC type signals to pass through and whose frequency is dependant on the rate of change of the input signal. At low frequencies the reactance of the capacitor is "High" resulting in a low gain (R₁/X_c) and low output voltage from the op-amp. At higher frequencies the reactance of the capacitor is much lower resulting in a higher gain and higher output voltage from the differentiator amplifier. However, at high frequencies a differentiator circuit becomes unstable and will start to oscillate.This is due mainly to the First-order effect, which determines the frequency response of the op-amp circuit causing a Second-order response which, at high frequencies gives an output voltage far higher than what was expected. To avoid this the high frequency gain of the circuit needs to be reduced by adding an additional small value capacitor across the feedback resistor R₁. 

 

If we apply a constantly changing signal such as a Square-wave, Triangular or Sine-wave type signal to the input of a differentiator amplifier circuit the resultant output signal will be changed and whose final shape is dependent upon the RC time constant of the Resistor/Capacitor combination.

 

Figure2: The Output waveforms obtain from the differentiator with respective input waveforms

 

One final point to mention, the Differentiator Amplifier circuit in its basic form has two main disadvantages compared to the previous Integrator circuit. One is that it suffers from instability at high frequencies as mentioned above, and the other is that the capacitive input makes it very susceptible to random noise signals and any noise or harmonics present in the circuit will be amplified more than the input signal itself. This is because the output is proportional to the slope of the input voltage so some means of limiting the bandwidth in order to achieve closed-loop stability is required