Integrator circuits

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  Integrator circuits

Integration is a calculus operation that gives the area under a curve. It gives the result of time-dependent operations. The integral of acceleration, for example, is velocity, and the integral of velocity is distance. Integration is required in many systems. A theoretical circuit is shown over, in (a).

By similar analysis to the inverting circuit, the current through the capacitor C and the resistor R must match, so:

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A practical circuit is shown in (b). Potentiometer RV 1 adjusts for input current offset, which causes the amplifier output to drift slowly  into saturation. Resistor R4 and the switch discharge the capacitor to initialise the circuit.

The response of the practical circuit is shown in (c). For a step input of V volts, the output is a ramp rising (or falling) at V/RC volts per second.

DifTerentiator circuits

Differentiation gives the instantaneous rate of change of time­ varying signals. The differential of distance, for example, is velocity.

Similarly, the differential of velocity is acceleration. A theoretical circuit is shown in (a). By similar analysis to the previous section it's found that:

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In practice a perfect differentiator has a frequency response that rises with frequency, giving impossibly high gains at high frequencies. This is undesirable as it makes the circuit very prone to high frequency noise. A practical circuit, shown in (b), incorporates a limit on the high frequency response.

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The differentiator is formed by R /C 1, giving a response identical to the theoretical circuit at low frequencies. At high frequencies, however R2 and C2 cause the gain to fall. Values are chosen such  that R 1•C1 = R2•C2• The point at which the gain reaches a maximum  and starts to fall is given by:

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The maximum gain is R 1/R 2, and the response is shown in (c).

Filters

Filters are used to shape the frequency response of a circuit. There are basically four types of filter.

A low pass filter blocks frequencies above some fixed value.

Typical application of a low pass filter is to remove higher frequency noise in an audio circuit, and in this case it is often called a scratch filter.

High pass filters only pass frequencies above some particular value. They are used as rumble filters in audio circuits to block out low frequency noise coupled from record player mechanics.

Bandpass filters pass frequencies in a specified range, while notch filters block frequencies in a specified range. A 45-55 Hz notch filter is widely used in instrumentation to block mains-induced noise (which occurs at 50 Hz).

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A range of op-arnp-based filter circuits is shown, along with their design criteria. It should be noted that the cut-off frequencies are the point at which response falls by just 3 dB, and not the point above (or below) which frequencies are blocked. Single-stage filters with a roll-off of 20 dB per decade are shown in (a) and (c), while two­ stage filters with a roll-off of 40 dB per decade are shown in (b) and (d). The latter two circuits can have their damping adjusted by varying the component ratios as shown.

Schmitt trigger

The Schmitt trigger is widely used to convert slowly changing signals into crisp signals with fast edges that can be used in digital

circuits. They also exhibit hysteresis, as shown in (a) and (b). Trigger points are defined by the upper trigger point (UTP) and the lower trigger point (LTP). Hysteresis is a form of backlash and is desirable  as it reduces jitter on the output if the slowly varying input has noise  superimposed on it.

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An op-amp-based Schmitt trigger is shown in (c). The output is either saturated positive or saturated negative. Suppose the input is above UTP; the output is at -Vcc and the non-inverting input is at:

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This is the LTP. As long as Vin stays above LTP the output does not change. If Vin goes below LTP, the output starts to rise, taking the non-inverting input with it. Positive feedback takes place; the output rises rapidly to +Vee and the non-inverting input rises to:

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This is the UTP, and the output stays positive until Vin rises above UTP.

The circuit of (c) has UTP and LTP symmetrical about 0 V. There  are many variations on the circuit to give asymmetrical trigger points. For example, (d) has UTP and LTP of the same polarity (and the circuit works with a single supply).

Most logic families include Schmitt trigger chips: the 7414 in the TTL family or the CMOS 4093 (quad NAND with Schmitt inputs). These ready-made Schmitts, however, have fixed trigger points and restricted input voltage range. Op-amp-based Schmitts allow the user to design a circuit when standard chips are not suitable.

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