If an RC integrator uses a 47 $\mu \mathrm { F }$ capacitor, a 12$\mathrm { k } \Omega$ resistor and a square wave input with a frequency of 200 kHz , its approximate output is _______
A) a square wave with a frequency of 100 kHz
B) a near dc voltage of about half the peak square wave voltage
C) 0 V
D) a square wave with a frequency of 200 kHz

Question

If an  RC  integrator uses a 47 $\mu \mathrm { F }$ capacitor, a 12$\mathrm { k } \Omega$ resistor and a square wave input with a frequency of  200 kHz , its approximate output is _______
A) a square wave with a frequency of  100 kHz
B) a near dc voltage of about half the peak square wave voltage
C)  0 V 
D) a square wave with a frequency of  200 kHz

Quizplus · Accepted Answer

An RC integrator circuit will produce an output that is proportional to the integral of the input waveform. For a square wave input, the output of the integrator will be a ramp waveform up to a maximum voltage and then a ramp down to zero before starting over again.

The frequency response of an RC integrator is given by:

$$
H(j\omega) = \frac{1}{1 + j\omega RC}
$$

where $\omega$ is the frequency of the input signal, $R$ is the resistor value, and $C$ is the capacitor value.

At high frequencies, the capacitor acts like a short circuit and the output voltage is attenuated. At low frequencies, the capacitor acts like an open circuit and the output voltage approaches the DC input voltage. At the cutoff frequency, the output voltage is reduced to $1/\sqrt{2}$ or approximately 0.707 times the DC input voltage.

The cutoff frequency is given by:

$$
f_c = \frac{1}{2\pi RC}
$$

Plugging in the values given in the question, we get $f_c = 227.91$ Hz.

Since the input frequency of 200 kHz is much higher than the cutoff frequency, the output of the integrator will be attenuated significantly. However, it will still produce an output waveform that is proportional to the integral of the input waveform.

The output will be a ramp waveform that starts at zero and increases linearly until it reaches a maximum voltage determined by the peak voltage of the input square wave. The slope of the ramp will be proportional to the amplitude of the input square wave.

Since the output waveform starts at zero and goes up to a maximum voltage before ramping down to zero again, the average or DC value of the waveform will be approximately half the peak voltage of the input square wave. Therefore, the best choice is B, a near DC voltage of about half the peak square wave voltage.

If an RC Integrator Uses a 47 μF\mu \mathrm { F }μF

If an RC Integrator Uses a 47 $\mu \mathrm { F }$