Active High-pass Filter

The circuit configuration shown on Picture 1 is active high-pass filter. Again, we assume that the input signal is sinusoidal. Thus, we can work in the frequency domain and use the concepts of impedance and reactance. If we look at the circuit we can see that this is an inverting amplifier where the resistor R1 has been replaced with impedance Z1, which is the serial combination of the resistor R1 and the capacitor C. Therefore, we can write:

Z1 = R1 + (1/sC) = (1 + sCR1)/sC

Now, if we write the expression for the output voltage of the inverting amplifier, we will have:

Vo(s) = -(R2/Z1)*Vi(s) = -sCR2/(1 + sCR1) * Vi(s)

So, according to the last expression, the output voltage Vo is large for s large or is small for s small.

Picture 1: Active High-pass Filter


The frequency-domain characteristic of this circuit configuration is shown on the Picture 2. The magnitude of the output voltage is 20 dB for frequencies of the input signal around 40 kHz. The output voltage decreases for 3 dB at frequency of 14.8 kHz and at frequency of 101 kHz. The first frequency is actually the limit frequency of this high-pass filter, or in other words, this circuit will pass the signals which are at frequency of 14.8 kHz and above, while the lower frequencies will be atenuated. The second frequency is actually the first dominant frequency pole for this circuit configuration and its defined by the components used in it. So, this circuit pass through the high frequencies from 14.8 kHz up to 101 kHz, which is actually the upper limit frequency of the circuit.

Picture 2: AC Analysis - output voltage [dB] and its phase [degrees] (frequency-domain)