The diagram shown below demonstrates one of the simplest type of active filters. It is composed of a resistor-capacitor passive filter that is followed by a non-inverting amplifier for the purpose of restoring or possibly increasing the amplitude of the signal.
With the values that are shown in the figure, the voltage gain level of the amplifier comes out to be 1.56. Shown below is the graph that displays the signals in this filter when it is supplied with a 1 V sinusoid at 1 kHz
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The RC network filters make the input of sinusoid (which is a dark grey line). At the output of the network (light grey) the filtered signal has amplitude of just 0.7 V. This has not only changed. The output reaches its peak levels of 125 μs behind the input. This is a delay of one-eighth of the period of the signal. When we talk in terms of angle, this is 360/8 equals to 45 degrees. The value is negative because it is a delay. The output is out of phase with, or lags the input, by -45 degrees. The black curve is used to denote the output of the op-amp. The values that are shown for RF and RA, the gain of the amplifier has the value of 1.56. The output coming from the RC network has amplitude value of 0.7 V, so the overall gain of the active filter is calculated by multiplying 0.7 with 1.56 that equals to 1.1. The amplitude level of the output comes out to be 1.1 V.
Gain: Gain of non-inverting amplifier is equal to (RA + RF)/RA
The amplifier does not change the phase any further, so the output lags the input by 45o.
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