Investing integrator circuit design

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Conversely, a constant negative voltage at the input results in a linearly rising positive voltage at the output. The rate of change of the output voltage is proportional to the value of the applied input voltage. Output Voltage Calculation From the circuit, it is seen that node Y is grounded through a compensating resistor R1. Node X will also be at ground potential, due to the virtual ground. The negative sign indicates that there is a phase shift of o between input and output, because the input is provided to the inverting input terminal of the op-amp.

The main advantage of an active integrator is the large time constant, which results in the accurate integration of the input signal. Integrator Amplifier as Ramp Generator If the step input of the integrating amplifier is replaced by a continuous time square wave, the change in the input signal amplitude charges and discharges the feedback capacitor. Such a circuit is commonly called a Ramp Generator.

During the positive half-cycle of the square wave input, a constant current I flows through the input resistor R1. Since the current flowing into the op-amp internal circuitry is zero, effectively all of the current flows through the feedback capacitor Cf. This current charges the capacitor. Since the capacitor connected to the virtual ground, the voltage across the capacitor is the output voltage of the op-amp.

During the negative half-cycle of the square wave input, the current I is reversed. The capacitor is now linearly charged and produces a positive-going ramp output. All the high frequency signal components are blocked or attenuated. At 0 Hz, the feedback capacitor behaves like an open-circuit, so there is no feedback from the output to the inverting input of the op-amp. Now, the circuit behaves like an open-loop inverting amplifier with very high gain.

This will result in the saturation of the output voltage. As the input frequency increases, the capacitor gets charged. At higher frequencies, the capacitor acts like a short circuit. Op-amp Integrator with DC Gain Control To avoid the saturation of the output voltage and to provide gain control, a resistor with high value of resistance can be added in parallel with the feedback capacitor Cf.

Consequently, at low frequencies of the input signal the circuit behaves normally like an integrator. At high frequencies, the capacitor acts as a short circuit and by-passes the resistor R2. The frequency response of an AC integrating amplifier with DC gain control is as shown in the figure above. At lower frequencies of the input, the capacitor remains uncharged and acts as an open-circuit.

As the input signal frequency increases, the feedback capacitor gets charged and acts almost like short-circuit, bypassing the feedback resistor R2. Provided that these conditions are met, then the action of the integrator is opposite to that of the differentiator circuit described in Filters and Wave shaping Module 8. With a square wave input and the correct relationship between the periodic time of the wave and the time constant of the circuit, Fig 8. The output is now considering the waveforms as simple graphs , a graph of the changing area beneath the input wave.

The integrator has converted the square wave input to a triangular wave at the output, the slope of this wave describes the increase in area beneath the square wave moving from left to right. For the circuit to act effectively as an integrator, the periodic time of the wave must be similar to, or shorter than the circuit time constant i.

The higher the frequency of the input wave for a particular time constant, the better the shape of the output wave will be, but the smaller its amplitude. Also notice that, unlike the differentiator, the integrator does not block any DC component of the input wave.

Therefore the reduced amplitude output wave will have a DC component, which igoring the resistance of any load placed on the output will be the same as the average DC level of the input wave. The output at these low frequencies is not a graph of the changing area beneath the input wave, the circuit is acting as a low pass filter and removing the high frequency components of the square wave that were responsible for the rapid vertical changes at each half cycle.

When the input to the integrator circuit is a triangular wave, the output seems to become a sine wave. Remember however, that the integrator circuit is also a low pass filter that has the effect of removing the higher frequency harmonics present in the complex triangular wave at its input, leaving just the fundamental sine wave and possibly a few lower frequency harmonics.

At low frequencies, the output from the integrator circuit is therefore a rounded form of the triangular input wave. The main purpose of a passive CR integrator is to produce a good triangular wave shape from a square wave input, which it can do very well and at very low cost only two components are needed although the output will be reduced in amplitude.

Any lack of amplitude may be overcome by combining the passive CR circuits described in this module with an op-amp to create an active filter, differentiator or integrator as described in Amplifiers Module 6. Hons All rights reserved.

Revision So the output can be expressed mathematically for one period as,. Thus it can be seen that the output of an integrators is a cosine waveform for a input. Due to inverting integrators, the output waveform is as shown in the Fig.

The operation amplifier has input offset voltage V ios and the input bias current I b. In the absence of input voltage or at zero frequency d. The input offset voltage gets amplified and appears at the output as an error voltage.

The bias current also results in a capacitor charging current and adds its effect in an output error voltage. The two components, due to high d. After some time, output of op-amp may achieve its saturation level. Hence there is a possibility of op-amp saturation due to such an error voltage and it is very difficult to pull op-amp out of saturation.

Thus the output of an ideal integrators in the absence of input signal is likely to be offset towards the positive or negative saturation levels. In the presence of the input signal also, the two components namely offset voltage and bias current, contribute an error voltage at the output. Thus it is not possible to get a true integration of the input signal at the output. Output waveform may be distorted due to such an error voltage. Another limitation of an ideal integrators is its bandwidth, which is very small.

Hence an ideal integrator can be used for a very small frequency range of the input only. Due to all these limitations, an ideal integrators is not used in practice. Some additional components are used along with the basic integrator circuit to reduce the effect of an error voltage, in practice.

Such an integrator is called Practical Integrators Circuit. The limitations of an ideal integrators can be minimized in the practical integrators circuit, which uses a resistance R f in parallel with the capacitor C f. The resistance R comp is also used to overcome the errors due to the bias current. The resistance R f reduces the low frequency gain of the op-amp.

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