What is a Band Pass Filter?

Problem:
What is a Band Pass Filter?

Solution:
A Band Pass filter is a filter that passes frequencies in a desired range and attenuates frequencies below and above. A closely related Knowledgebase item discusses the concept of the Q of a filter. The Knowledgebase makes a distinction between high Q band pass filters and low Q bandpass filters. While there are separate terms for the opposite of a bandpass filter - the notch and band reject - there are no corresponding terms to differentiate between a high Q bandpass filter - covered by this item - and a low Q bandpass filter. This knowledgebase item is geared towards the single tone, narrowband RF, and IF type of filters. The audio, speech, and broadband communications type of filter are covered in the low Q bandpass filter item.

The amplitude response of a band pass filter is flat from the center frequency down and up to points where it begins to roll off. The standard reference points for these roll-offs are the points where the amplitude has decreased by 3 dB, to 70.7% of its original amplitude. This is the passband of the filter. The regions above the passband to infinity, and below the passband to zero (or near zero) are the stop bands of the filter.

The -3 dB points and -20 dB amplitude points of the filter are determined by the size of the passband in relation to the center frequency, in other words the Q of the filter. The Q knowledgebase item will have additional information, but it is hard to talk about the roll-off points of a bandpass filter without defining the Q, which is the center frequency divided by the bandwidth. In the case of the figure below:

• The -3 dB points are at about 1 kHz and 100 kHz for a Q of 0.1 and a center frequency of 10 kHz. The low and high frequency roll offs look exactly like what would be expected from a single pole high pass and single pole low pass. At one tenth the frequency of the lower -3 dB point and ten times the frequency of the upper 3 dB point, the response is down 20 dB from the center frequency. This means that the two pole filter bandpass filter is effectively putting a single pole on the low frequency end and a single pole on the high frequency end of the passband. This is not always desirable, as cascading subsequent stages to get more rejection in the stop bands will merely add more single poles on each end. An alternative technique that provides much better performance will be described in the low Q bandpass filter knowledgebase item.
  
  
• The -3 dB points are at about 600 Hz and 1.6 kHz for a Q of 1 and a center frequency of 10 kHz. The -20 dB points, however, are now at about 1 kHz and 100 kHz, which are NOT at one tenth and 10 times the lower and upper -3 dB frequency, respectively. The shape of the curve is also different, looking like a rounded 90 degree angle more than a single pole characteristic. The single pole performance has been lost in the region between the -20 dB points, or within ten times the bandwidth. Outside of this region, however, the single pole response of the bandpass filter returns. Therefore, for Q values between 0.1 and 1, the response of a bandpass circuit will change to whatever is required to satisfy the requirements of the - 3 dB points, as determined by the Q, and an ultimate slope of - 20 dB per decade for the region between 10 and 100 times the bandwidth. This is a final value of slope, and will be maintained at higher multiples of the bandwidth.
  
  
• The response of the bandpass filter with a Q of ten dramatically illustrates this effect. Between the -20 dB points, the shape of the response is completely opposite what it was for a Q of 10. The initial -3 dB points are so close to the center frequency that they have not been highlighted, but the -20 dB points are the same as -3 dB points for a Q of 1. In the region between 10 and 100 times the bandwidth, the slope continues to change to its final value of -20 dB per decade at 100 times the bandwidth.
  
  
• So - what is the ultimate limit? Does this mean that any Q is possible? Unfortunately, no. At very high Q values, the response of the circuit will begin to have overshoot and undershoot that will destroy the integrity of the peak. The frequency that was supposed to be passed may actually be rejected.

The phase response of a band pass filter shows the greatest rate of change at the center frequency. The rate of change becomes more rapid as the Q of the filter increases.

The group delay of a bandpass filter is greatest at the center frequency, and becomes longer as the Q of the filter increases.