Question 8-38D5

An RC integrator's function is to output a voltage proportional to the integral of its input voltage. When a square wave is applied, the capacitor in the RC circuit charges when the input is high and discharges when the input is low. The crucial condition is that the square wave's period is "much less than one time constant" (RC). This means the capacitor does not have enough time to fully charge or discharge before the input voltage flips. In the initial phase of charging or discharging, the capacitor's voltage changes nearly linearly over time. Therefore, as the capacitor charges from the high input, the output voltage rises linearly; and as it discharges from the low input, the output voltage falls linearly. This continuous linear rising and falling motion creates a **triangle wave**. A differentiator, on the other hand, would produce narrow spikes (C). A sine wave (B) is usually generated by oscillators or heavy filtering, not a simple RC integrator. While related, a sawtooth wave (A) is typically asymmetric, with a fast rise/slow fall or vice-versa, whereas an integrator with a symmetric square wave produces a symmetric triangle. This principle is fundamental to waveform generation and shaping in radio circuits.