Passive Filters Information

Passive filters use only passive electronic components: resistors, capacitors, and inductors. For low frequency applications (less than 100 kHz) it is typically sufficient to use only resistors and capacitors. These filters are called RC networks or RC filters. Inductors play a more important role in high-frequency applications. Filters that also employ inductors are called RLC networks or RLC filters. An example RC filter schematic is shown below.

passive filter rc circuit schematic

Because passive components do not have amplification capabilities, the magnitude or amplitude response maximum gain is unity at the lowest frequency for low-pass filters (0←f ); at the highest frequency for high-pass filters (f→∞); at the maximum frequency of the passband for band-pass filters (max f in interval f1<f<f2); and at the minimum frequency of the lower passband and the highest frequency of the upper passband of band reject filters. The value of unity gain normally happens at one point only, and for any other frequency there is attenuation. This implies that the output of the filter is always less than the input, or in equation form:

For much more detailed information on the theory and design of electronic filters, please visit the Electronic Filters Specification Guide.

Types

Filters are grouped and specified according to the type of frequencies they suppress or attenuate. The four common filter classifications are listed below.

  • Low-pass filters attenuate or suppress signals with frequencies above a particular frequency called the cutoff or critical frequency. For example, a low-pass filter (LPF) with a cutoff frequency of 40 Hz can eliminate noise with a frequency of 60 Hz.
  • High-pass filters suppress or attenuate signals with frequencies lower than a particular frequency, also called the cutoff or critical frequency. For example, a high-pass filter (HPF) with a cutoff frequency of 100 Hz can be used to suppress the unwanted DC voltage in amplifier systems, if desired.
  • Band-pass filters attenuate or suppress signals with frequencies outside a band of frequencies. They are common in TV or radio tuning circuits.
  • Band-reject, or notch filters attenuate or suppress signals with a range of frequencies. For instance, a notch filter can reject signals with frequencies between 50 Hz and 150 Hz.

Filter Terminology

Electronic filters employ their own unique terminology to describe each device's filtration characteristics:

  • Passband: The range of frequencies where the output has a gain.
  • Stopband: The range of frequencies where the output is zero or very small.
  • Passband ripple: The variations or oscillations in the bandpass, or error band. These oscillations typically occur around the nominal value of 1.0, or at 0 dB, if the amplitude is expressed in decibels. The ripple value is 2a1, where a1 is a parameter dependent on the circuit components.
  • Stopband ripple represents the variations in the stopband region. The ripple is equal to the parameter a2, which is determined by the circuit component attributes.
  • Critical frequency, fc: This is the frequency at which the response leaves the passband ripple. For certain filter types (Butterworth filters, for instance), at this frequency the amplitude of the response is  of the nominal amplitude.
  • Stopband frequency, fs, is the frequency at which the maximum stopband ripple (a2) occurs.
  • Transition band: This represents the range (fs - fc) of frequencies between the critical and cutoff frequencies. The slope of the transition region is related to the number of poles in the transfer function of the response, also known as the filter's order. A pole is a root of the denominator of the transfer function. For a standard Butterworth filter, every pole adds -20 dB/decade or -6 dB/octave to the slope of the response. The slope of the line is called the roll-off of the transition. Also, a pole represents one RC stage in the circuit, as shown below. 

Resources

Circuits Today—Active and Passive Filters

Electronics Tutorials—Filters articles (includes all passive filter types)