What is - 3dB Frequency Response? And applications

• 📘 Overview & Theory
• 📘 Application of -3dB Frequency Response
• 🧮 MATLAB Codes
• 🧮 Online Digital Filter Simulator
• 📚 Further Reading

• Filters
• What is -3dB Frequency Response?

 

Remember, for most passband filters, the magnitude response typically remains close to the peak value within the passband, varying by no more than 3 dB. This is a standard characteristic in filter design.

The term '-3dB frequency response' indicates that power has decreased to 50% of its maximum or that signal voltage has reduced to 0.707 of its peak value. Specifically,

The -3dB comes from either 10 Log (0.5) {in the case of power} or 20 Log (0.707) {in the case of amplitude}.

Viewing the signal in the frequency domain is helpful. In electronic amplifiers, the -3 dB limit is commonly used to define the passband. It shows whether the signal remains approximately flat across the passband. For example, in pulse shaping, the signal magnitude is nearly constant within the -3 dB bandwidth.

The term "-3 dB" refers to the allowable drop from the peak in the passband, not the high- or low-frequency cutoff itself. For example, one might say "between 100 Hz and 18 kHz, the signal remains flat within -3 dB." A filter's passband is considered flat if the magnitude does not deviate more than 3 dB from the peak value.

Maintaining signal integrity within the passband is critical. A signal that falls below 50% of its original power (a 3 dB reduction) is typically considered outside acceptable limits. Well-designed filters ensure that the variation in magnitude response within the passband remains within a 3 dB tolerance to preserve signal quality, especially in audio and communication applications.

Application of -3dB Frequency Response

All types of filters often use the -3 dB point (low pass, band pass, high pass) to indicate where the output power is halved. Within the passband, the signal is considered approximately flat.

For digital filters, a bandpass filter passes frequencies in a range (e.g., h1 to h2 Hz). Frequencies within this range are transmitted; others are attenuated. The passband is "flat" if the magnitude does not vary by more than 3 dB.

Band-Pass Filter: −3 dB Cutoff Frequencies

In a band-pass filter, there are two cutoff frequencies where the output amplitude falls to 0.707 of its peak value. This corresponds to a −3 dB drop in amplitude. These frequencies are:

• Lower −3 dB frequency (f_L)
• Upper −3 dB frequency (f_H)

Both cutoff points are −3 dB — never +3 dB — because they represent a drop from the peak amplitude, not an increase.

Visualization

Amplitude (dB)
   0 dB |                         Peak
        |                          *
        |                         ***
 -3 dB |---------------------*---------*----------------------
        |                   **           **
        |                 **               **
        |               **                   **
        |             **                       **
 -∞ dB |_________________________________________________________
              fL                       f0                     fH
             (-3 dB)             (center freq)              (-3 dB)

                          Frequency →

Key Points

• The peak amplitude occurs at the center frequency (f₀).
• At both f_L and f_H, the signal drops to 0.707 of the peak.
• This drop equals −3 dB, defining the filter's bandwidth.
• Bandwidth = f_H − f_L

 

Further Reading 

1. MATLAB Code for understanding - 3 dB Frequency Response of a Bandpass Filter
2. Why Half-Power (−3 dB) Is Used 
3. Filters
4. Online Digital Filter Simulator