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The basic operation of the active high-pass filter (HPF) is the same as the equivalent RC passive high-pass filter circuit. But this time the circuit has an operational amplifier. The simplest form of an active high-pass filter, such as the previous active low-pass filter circuit, will be by connecting a standard inverting or inverting operational amplifier to the basic RC high-pass passive filter circuit, as shown.

Primary High Pass Filter

Technically, there is no such thing as an active high pass filter. An "infinite" Frequency response: Unlike Passive High Passing Filters, an active high-pass filter makes them visible if they become bands, such as the open loop properties of the transactional amplifier used in the maximum pass band frequency or the high frequency closed op-amp and the cut specified by gain, such as limited to bandwidth.

In the op-amp tutorial, we found that the maximum frequency response of an op-amp is limited to the gain/bandwidth product of the op-amp used or open loop voltage gain (Av).

It is a widely available operational amplifier such as Ua741. Ua741's earnings are reduced until it reaches union gain (0dB) or "transition frequency" (εt), which is about 1MHz. This causes the op-amp to have a Frequency response curve very similar to that of the primary low transition filter, which is shown below.

Frequency Response Curve of a Typical Operational Amplifier

Active High Pass Filter
Frequency Response Curve of a Typical Operational Amplifier

The performance of a "high pass filter" at high frequencies is limited to this union gain transition frequency, which determines the overall bandwidth of the open loop amplifier. Op-amp's earnings bandwidth product starts at about 100khz for small signal amplifiers up to about 1 GHz for high-speed digital video amplifiers. Op-amp-based active filters, low-tolerance resistors and capacitors can achieve very good accuracy and performance when used.

Under normal circumstances, the maximum transition band required for the closed loop active high transition or band passing filter is well below the maximum open loop transition frequency. However, when designing active filter circuits, it is very important to choose the right op-amp for the circuit, as the loss of high frequency signals can cause signal distortion.

Active High Pass Filter

As the name suggests, the primary (unipolar) active high-pass filter weakens low frequencies and passes high-frequency signals. It consists only of a passive filter section, followed by an inverted operational amplifier. The frequency response of the circuit is the same as that of the passive filter. However, the amplitude of the signal is increased by the gain of the amplifier, and for an inverted amplifier, the value of the transition band voltage gain is given as 1 + R2/R1, as for the low transition filter circuit.

Active High Pass Filter with Amplification

Active High Pass Filter
Active High Pass Filter with Amplification

This grade II-high passing filter consists only of a passive filter and then an amplifier that does not invert. The frequency response of the circuit is the same as that of the passive filter, but the amplitude of the signal is increased by the gain of the amplifier.

For an inverted amplifier circuit, the size of the voltage gain for the filter and the corresponding input resistance (R1) are given as a function of the feedback resistance (R2) divided by the value:

Gain for Active High Pass Filter

Active High Pass Filter
Gain for Active High Pass Filter

AF = transitional band gain of the filter, (1 + R2 / R1 )
ε = frequency of the input signal in Hertz, (Hz)
εc = Cutting frequency in Hertz, (Hz)

Magnitude of Voltage Gain (dB)

Active High Pass Filter
Magnitude of Voltage Gain (dB)

For a premium filter, the filter's frequency response curve increases by 20dB/decade or 6dB/octave to the specified cutting frequency point, which is always below the maximum gain value of -3dB. As with previous filter circuits, the lower cut or corner frequency (εc) can be found using the same formula:

Active High Pass Filter

The corresponding phase angle or phase shift of the output signal is the same as that given for the passive RC filter. It's the same as the input signal. The cutting frequency is equal to +45o at εc and is given as follows:

Active High Pass Filter

Inverting Operational Amplifier Circuit

Active High Pass Filter
Inverting Operational Amplifier Circuit

Frequency Response Curve

Active High Pass Filter
Frequency Response Curve