# RF Filter Bandwidth (with a calculator)

A filter is a product that as the name suggests, filters signals of interest and rejects everything else. In this post we discuss a key specification of filters namely, Bandwidth. We also provide a filter bandwidth calculator in addition to some practical considerations and examples.

## Background

### What is Filter Bandwidth?

Filter bandwidth is the frequency range within which a filter allows signals to pass through with minimal attenuation. It is determined by the filter’s frequency response, which describes how the filter responds to different frequencies. The bandwidth is typically specified as the range of frequencies between the two points where the filter’s response drops by 3 dB or half the power of the input signal.

Different applications require filters with specific bandwidths to achieve desired performance characteristics. For example, in an FM radio system, the ideal filter bandwidth ensures that signals within the desired frequency range of 88 MHz to 108 MHz are reproduced accurately without distortion.

Here is a video that discusses Filter Bandwidth

### How to calculate filter bandwidth

As a Radio Frequency engineer I’m often reviewing data sheets that have the start and stop frequencies of a SAW filter for example. From this I want to know where the passband begins and ends. As well, where is the filter centered.

The formula for this calculation is:

FC = FL+(FH-FL)/2

where

• FC is the center frequency
• FH is the upper end of the band
• FL is the lower end of the band

The bandwidth (B) is simply given by B = FH-FL

## Types of Filters

Filters can be categorized into different types based on their frequency response and the range of frequencies they allow to pass.

The common types of filters include:

### Low-Pass Filter

A low-pass filter (LPF) allows frequencies below a specific cut-off frequency to pass through while attenuating higher frequencies. It is commonly used to remove or reduce high-frequency noise or signals. In power supplies a LPF will be used prevent high frequency signals from entering other parts of the circuit or the main supply.

### High-Pass Filter

A high-pass filter (HPF) allows frequencies above a specific cutoff frequency to pass through while attenuating lower frequencies. It is often used to remove or reduce low-frequency noise or signals.

### Band-Pass Filter

A band-pass filter (BPF) allows a specific range of frequencies, known as the pass band, to pass through while attenuating frequencies outside the pass-band. It is used to isolate or extract a specific range of frequencies from a signal. Receivers typically use SAW bandpass filters to reject out of band signals.

### Band-Stop Filter

A band-stop filter, also known as a notch filter, attenuates a specific range of frequencies, known as the stop-band, while allowing frequencies outside the stop-band to pass through. It is commonly used to eliminate or suppress unwanted frequencies in a signal. FM notch filters are commonly used to reject strong signals that can interfere with the neighboring Airband frequencies.

## Filter Specifications

There are three key attributes of a filter. The table below lists these specifications for Band pass, Low pass and High pass filters.

In the case of a notch filter, the center frequency and bandwidth refers to the range of frequencies that the filter will reject.

The Insertion Loss and Rejection are specified in decibels (dB). In general, the pass band insertion loss should be as small as possible. In practical filters typically this number varies between 1 dB and 5 dB. The out-of-band rejection or insertion loss should be as high as possible. Theoretically, the further away in frequency a signal is from the pass band, the higher the rejection. However this is not generally true in practice. Below is a plot of a Mini-Circuits filterâ€™s rejection. The pass band of this filter is from 2570 MHz to 3440 MHz.

There are two things that really stand out here:

• The filter is not symmetric in its ability to reject signals, i.e. a signal that is 2500 MHz to the left of the center will be rejected more than a signal that is 2500 MHz away to the right.
• The rejection of the filter increases with an increase in frequency but only up to around 5300 MHz. Beyond that, the rejection actually decreases. Note that the rejection is only 9 dB at 12500 MHz.

## Filter Bandwidth Calculator

This tool calculates the bandwidth and center frequency of a filter from its start and stop frequencies.

FLow and FHigh are the start and stop frequencies respectively.

## Example Calculations

### Low Pass Filter Bandwidth

To calculate the bandwidth of a Low Pass Filter, enter FL=0. FH is the cutoff frequency. For a cutoff frequency of 10 MHz, the bandwidth is also 10 MHz. For a LPF, the bandwidth is the same as the cutoff frequency.

### High Pass Filter Bandwidth

In theory the bandwidth of a high pass filter is infinite. The picture below shows an ideal HPF.

However in practice, this is not true. The picture below shows a high pass filter specified to have a pass band of 6700-13000 MHz. In an ideal world, you would expect there to be no upper limit. The insertion loss of the filter starts increasing at 13 GHz and has a value of 10 dB at 20 GHz. Expect it to increase even more after that.

## Related Posts

• Pi Filter Design Calculator – A Pi Filter consists of a Î  configuration of inductors and capacitors. This tool can be used to design either a LPF, HPF or BPF