Sketch the output voltage of the circuit shown in Figure Pl 4.74 to scale versus time Sometimes,

step 1 Question number 14 .74. Question is, sky the output voltage of the circuit shown in 14 .74 to sc

Sketch the output voltage of the circuit shown in Figure Pl...

Sketch the output voltage of the circuit shown in Figure $\mathrm{Pl} 4.74$ to scale versus time Sometimes, an integrator circuit is used as a (approximate) pulse counter, Suppose that the output voltage is -10 V. How many input pulses have been applied (assuming that the pulses have an amplitude of $5 \mathrm{V}$ and a duration of $2 \mathrm{ms}$, as shown in the figure)?

Key Concepts

Operational Amplifier Integrator

An op-amp integrator is a circuit configuration that uses an operational amplifier along with a resistor and a capacitor to produce an output voltage proportional to the time integral of the input voltage. This means the circuit effectively sums the input over time, transforming a series of voltage pulses into a continuously varying output voltage.

Pulse Integration

When a constant voltage pulse is applied to an integrator, the output voltage changes linearly during the pulse duration because the integrator accumulates charge on the capacitor. Each pulse contributes a predictable voltage step determined by the pulse's amplitude and duration, making the integrator useful for summing discrete events.

Pulse Counting Using Integration

Pulse counting with an integrator involves using the cumulative integration of individual pulses to track the number of pulses received. Each pulse causes a fixed change in the output voltage, so by measuring the total voltage change, one can calculate how many pulses have been integrated into the output.

Voltage Change per Pulse Calculation

The change in output voltage due to an individual pulse is determined by the integration of the pulse's constant amplitude over its duration and is scaled by the circuit's RC time constant. Understanding this relationship allows one to determine the number of pulses required to achieve a specific voltage change in the integrator's output.

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