# Active High Pass Filters Information

Active high pass filters pass signals from high frequencies and reject signals from low frequencies. There are two basic types of products: switched capacitor and continuous. Both are available with first to eighth order filtering. Switched capacitor active high pass filters are clocked devices. The input signal is sampled at a high rate and processed discretely instead of on a continuous-time basis. By contrast, continuous filters have a continuous time operation.

For in-depth background information on electronic filter design and theory, please visit the Electronic Filters Specification Guide.

HPF circuits use at least one operational amplifier connected in a feedback configuration in order to provide stability to the filter, and gain, so the signal is not attenuated as it passes through the filter. Several configuration exist to implement these filters.

**Active RC Single-pole Filters**

The following circuit is the simplest active HPF: a resistor and a capacitor followed by a non-inverting amplifier.

Its amplitude is given by

Or,

Where the amplifier gain, A, is given by

And its -3 dB critical frequency is

The phase shift of this filter is given by

**Second-order Sallen-Key High-pass Filters**

One of most popular configurations for a second-order high-pass filter is shown in the schematic below.

This filter design is a two-pole filter comprised of two single-pole filters followed by a non-inverting amplifier.

The critical frequency of this filter is given by

If the two resistors are equal and the two capacitors are equal, or if

And

Then the critical frequency becomes

The gain of the amplifier is

The amplitude and phase as function of frequency are given by

And

A Bode plot of a second-order Sallen-Key HPF is shown in the following figure.

## Filter Specifications

The most important HPF parameters include the following:

**Cutoff or center frequency.** The filter type determines the specified frequency (f_{c}). For high pass filters, the specified frequency is the cut-on frequency.

**Bandwidth.** Bandwidth is the range of frequencies that an HPF can pass with minimal attenuation.

**Power dissipation.** Power dissipation is the total power consumption of the device. Generally, this value is expressed in watts or milliwatts.

**Number or poles**. This is the order of the filter.

**Filter characteristics.** Filters are specified by the shape and behavior of the frequency response. Specific examples include:

**Bessel filter.**Bessel filters are active filters with a passband that maximizes the group delay at zero frequency, thus showing a constant group delay in the passband. Group delay is a measurement of the time it takes for a signal to move between two points in a network. A constant group delay in the filter passband implies that the time delay will be identical for all signals with frequencies in the passband. This fact is important in many applications, especially audio, video, and radar applications.**Butterworth filter.**Butterworth filters are designed so that the frequency response is flat in the passband.**Chebyshev filter.**Chebyshev filters feature a very steep roll-off, but have ripples in the passband.**Elliptic filter.**Elliptic (or Cauer) filters exhibit equalized ripple in both the passband and the stopband.**Gaussian filter.**Gaussian filters produce no overshoot in response to an input step. They optimize the rise and fall times.**Legendre filter.**Legendre filters are designed to produce the maximum roll-off rate for a given order and a flat frequency response in the passband.