Active High Pass Filter:11 Facts You Should Know!

In this article, we will discuss about few basic concept related to active high pass filter and try to answer few questions in following sections and we will try to learn about some important application of active high pass filters with advantage.

  • What is an active high pass filter?
  • Working Principle of an active HPF
  • Time Response & Frequency Response
  • Cut-off Frequency of an active HPF
  • What is a transfer function for an active HPF
  • Design a first order active order HPF
  • Second order active HPF
  • Transfer Function for second order HPF
  • Advantages of active High Pass Filter
  • Applications of a HPF
  • FAQS

Active high pass filter definition:

An active high pass filter is nothing but a circuit contains an active component such as a transistor, an operational amplifier(op-amp), etc. These components are mainly used for better performance or better amplification.

What are the components of an active high pass filter?

We can make an active high pass filter by adding an op-amp across a passive high pass filter.

To imply simplicity, time effectiveness and due to growing technologies an op-amp designing, generally, an op-amp is used for an Active High Pass Filter design.

In an active high pass filter, the limitation we have is the op-amp bandwidth. It means that the op-amp will pass the frequency according to its gain and the open-loop characteristics of the op-amp.

Circuit Diagram of active high pass filter:

Active High Pass Filter
Active High Pass Filter

In the above figure, the CR network does the filtering, and the op-amp is connected as a unity-gain follower. The feedback resistor, Rf, is included to minimize the dc off-set.


EQ 1 1

The voltage across the resistor R,

EQ 2 1

Since op-amp gain is infinite, we can therefore derive.

EQ 3 1


EQ 4 1

= Passband gain of the high pass filter,

f = Frequency of the input signal (Hz),

EQ 5

= cut-off frequency of the high pass filter (Hz)

    The Gain Magnitude,

EQ 6

And phase angle (in degree),

EQ 7

Working Principle of an active high pass filter:

First-order filters are the simplest form of any filters that contain only one reactive component, i.e., capacitor, as it is also used in passive filters. To transform it into an active filter, an op-amp is used to the output of a passive filter.

Now, the op-amp is used for different configurations. Each configuration has additional attributes to the performance of the filter.

The main thing to be remembered is a first-order filter’s roll-off rate. The roll-off rate is the rate of change in the gain of a filter in its desired stopband. It shows us the steepness in the curve and how fast the growth tends to increase with frequency.

First-order filters have a roll-off rate of 20dB/decade or 6dB/octave.

        Roll Off Rate = -20n dB/decade = -6n dB/octave

Time Response & Frequency Response of an active HPF


To operate a high pass filter, the verification can be done from the gain-magnitude equation as follows:

At very low frequency, i.e., f<fc,

EQ 8

At f=fc,

EQ 9

At f>>fc,

EQ 10

The bandwidth of the active high pass filter shows the value of frequency from which signals are allowed to pass. As an example, if the bandwidth of that high pass filter is given as 50 kHz, that means the only frequencies from 50 kHz to infinity are allowed to pass the range of bandwidth.

The phase angle of the output signal is +450 at the cut-off frequency. The formula to calculate the phase shift of an active high pass filter is

                     Ø= arctan (1/2πfRC)

Active High Pass Filter Transfer Function

The impedance of the capacitor keeps frequently changing, so electronic filters have a frequency-dependent response.

The complex impedance of a capacitor is given as,

EQ 11

Where, s= σ +jω, ω is the angular frequency in radians per second.

The Transfer Function of a circuit can be found using standard circuit analysis techniques such as Ohm’s Law, Kirchoff’s Law, Superposition Theorem, etc.

The form of a T.F is derived from the ratio of Output Voltage to Input Voltage

EQ 12

The standard form of the transfer function is :

EQ 13


a1 = Amplitude of signal

ω0 = Angular cut-off frequency

Cut-off Frequency:

What do we mean by cut-off frequency ?

By cut-off frequency, we define the useful or essential part of a spectrum. It is simply a frequency level above or below a device or filter cannot response or can be operated properly.

The Cut-off frequency for an active high pass filter is the particular frequency at which the load(output) voltage equals 70.7% of the source(input) voltage. The origin or output voltage is more significant than 70.7% of the input or load voltage and vice versa.

The cut-off frequency also indicates the frequencies at which the power of the output path falls to half its maximum value. These half-power points correspond to a fall in the gain of 3dB(0.7071) relative to the maximum dB value.

Filter Designing of Active High Pass Filter:

To construct an active high pass filter, we need to implement the following steps-

A value of the cut-off frequency,

EQ 14

is chosen.

A value of the capacitance C, usually between 0.001 and 0.1µF, is selected.

The value of the resistance R is calculated using the relation,

EQ 15

Now, the values of R1 and Rf are selected depending on the desired pass-band gain, using the relation,

EQ 16

Second-Order Active High Pass Filter:

What is a second-order filter?

The maximum delay in each sample used in generating each output sample is called the order of that particular filter.

Second-order filters mostly consist of two RC filter, which is connected together to provide a –40dB/decade roll-off rate.

Second-Order Active High Pass Filter

Where DC gain of the amplifier =

EQ 17

The Transfer Function of a second-order active high pass filter can be obtained from the transfer function of the low pass filter by the transformation,

EQ 18 1
  • Substituting s=jω, the transfer function is,
EQ 19

In the above equation, when ωà0, |H(jω)|=0. Thus the low-frequency gain of the filter is zero.

If we compare it with Butterworth filter transfer function, we get

EQ 20
Characteristic curve of a second order HPF

The Frequency response of a second-order active high pass filter is shown in the above diagram. It is noted that the filter has a very sharp roll-off response.

The design procedure for a high pass will be as same as low pass.

The frequency response will be a maximally flat one, i.e., having a very sharp roll-off response.

Advantages of using Active High Pass Filter:

There are so many vital benefits of an active High Pass Filter, some of them are:

  • Whenever there is a small signal is present, an active High pass Filter is used to increase the amplification factor, which also increases the amplitude of those small signals.
  • Due to very high input impedance, active high pass filters can transfer efficient signals without any loss in any preceding circuit.
  • Active filters usually have very low output impedance, which is perfect for transferring efficient signals to its next stage, mostly when they are used in different multistage filters.
  • This type of filters gives us smooth frequencies.
  • They have a sharp roll-off response.
  • Strong broadcasting power to receivers to select desired channel frequency.
  • Best for audio processing in any electrical or electronic device.
  • Active HPF prevents amplification from DC etc.

Application of Active High Pass Filter:

  • To transmit higher frequency in case of video related filters.
  • We use HPF as a treble equalizer.
  • We often use HPF as a treble boost filter.
  • We are changing the frequency depending on different waveforms.
  • Active High Pass filters are also used in oscilloscopes.
  • In the generator, these filters are used.


Frequently Asked Questions

Where are high pass filters used?

      The high pass filters are used in all audio sources to remove unwanted noise that lurks below the important frequencies.

Many unwanted sounds can be hidden by some louder core of a high pitch signal and can be overlooked. We don’t get to hear the rumble due to the limits of hearing as the lowest parts of the spectrums are around 20-40 Hz. High pass filters also eliminate those noises or reduce it that makes them nearly silent.

Can I get the output of a high pass filter as a power source?

A high pass filter is an electronic filter that passes signals with higher frequencies which are above the cut-off frequency range and also attenuates the frequencies which are below the cut-off range.

Now, the output of the specific high pass filter has no DC(0Hz) voltage due to its specified cut-off frequency(fc). The lower cut-off frequency of an active high pass filter is 70.7% or -3dB(dB= -20log Vout/Vin) of the voltage gain which it allows to pass can be used as a power supply as well.

What does corner frequency mean in regards to high pass filter?

The corner frequency, which is also called as cut-off frequency, defines a specific frequency at which the transfer attenuation reaches -3dB below(50%) the magnitude from the 0dB or pass-band level.

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