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Active filterOften you will need to filter signal to adjust it for ADC measurement or remove noise from measured signal. Analog filters are right way to do this. Here is some basic information about analog filter design terms used when designing filters. Active filters give better performance since they can be adjusted not to attenuate signal.

Hundreds if not thousands of different kinds of filters have been developed to meet the needs of various applications. Despite this variety, many filters can be described by a few common characteristics. The first of these is the frequency range of their pass band. A filter's pass band is the range of frequencies over which it will pass an incoming signal. Signal frequencies lying outside the pass band are attenuated. Many filters fall into one of the following response categories, based on the overall shape of their pass band.

Low-pass filters pass low-frequency signals while blocking high-frequency signals. The pass band ranges from DC (0 Hz) to a corner frequency FC.

High-pass filters pass high-frequency signals while blocking DC and low-frequency signals. The pass band ranges from a corner frequency (FC) to infinity.

Band-pass filters pass only signals between two given frequencies, blocking lower and higher signals. The pass band lies between two frequencies, FL and FH. Signals between DC and FL are blocked, as are signals from FH to infinity. The pass band of these filters is often characterized as having a bandwidth that is symmetric around a center frequency.

Band-stop filters block signals occurring between two given frequencies, FL and FH. The pass band is split into a low side (DC to FL) and a high side (FH to infinity). For this reason, it's often simpler to specify a band-stop filter by the width and center frequency of its stop band. Band-stop filters are also called notch filters, especially when the stop band is narrow.

Figure 1 shows how each of these filters operates on a swept-frequency input signal.


Figure 1. Filters are usually characterized by their frequency-domain performance. The effects of a few common filter types on a swept-frequency input signal are shown here.

In the examples, the signal increases continuously in frequency, from a low frequency to a high frequency. When the signal frequency is within the filter's pass band, the filter passes the signal. As the signal moves out of the pass band, the filter begins to attenuate the signal.

Note that the transition from the pass band to the stop band is a gradual process, where the filter's response decreases continuously. Although you can make this transition arbitrarily sharp (at the cost of filter complexity), it can never be instantaneous, at least not in filters physically realizable with today's technology.

The Bode and Phase Plots

Bode plots describe the behavior of a filter by relating the magnitude of the filter's response (gain) to its frequency. An example of this type of plot is shown in Figure 2.


Figure 2. Filter responses are plotted on Bode plots, which are log-log charts of gain (expressed in dB) vs. frequency. A filter's Bode plot can show key features of a filter, such as corner frequency, attenuation rate, and pass-band ripple.

The key feature of this graph is that both axes have logarithmic scales. The horizontal ax[s represents frequency, measured in hertz, and the vertical axis is measured in decibels.

Decibels are a logarithmic measure of power, where an increase of 10 dB represents a 10-fold increase in power. Because power in an electrical signal is related to the square of voltage, a factor of 10 increase in the voltage of a signal is represented by an increment of 20 dB. The advantage of drawing a filter's response curve on a Bode plot is that it provides an easy way to describe the filter's response over several decades of frequency and several orders of magnitude. The decibels of gain of a filter relate to the ratio between input and output voltages:


The low-pass response curve in Figure 2 also illustrates a few characteristics common to many types of filters.

Corner Frequency. Because a real filter rolls off gradually, you usually specify the corner frequency as the frequency at which the response is 1/2 (0.707) of that in the pass band. Because electronic engineers traditionally describe relative signal strengths in decibels, the frequency is also referred to as the –3 dB point.

Attenuation Rate. The transition between the pass band and the stop band is a continuous function, and the rate at which this transition occurs is a common metric used to select a filter. You commonly express the attenuation rate in decibels per decade, where a decade is a factor of 10 in frequency.

A high attenuation rate helps a filter distinguish between signals of similar frequency and is usually a desirable feature. The attenuation rate is also related to the order of a filter. For a low-pass or a high-pass filter, the attenuation rate will be –20 times the filter's order, in dB/decade. For example, a first-order filter will have an attenuation rate of –20 dB/decade, while a fourth-order filter will have an attenuation rate approaching –80 dB/decade.

Pass-Band Ripple. For many types of filters, the response does not decrease monotonically as frequency moves from the center of the pass band out toward the stop band. The magnitude of the response may vary inside the pass band, and this variation is called the pass-band ripple. Again, this metric is also specified in decibels. Pass-band ripple causes the frequency components of a signal to be amplified to different degrees. This has the effect of distorting the waveform of a signal passing through the filter.

In addition to affecting the amplitude of a signal, a filter can also cause changes in the phase of signal components. Figure 3 shows the amplitude and phase responses of a simple low-pass filter.


Figure 3. In addition to attenuating a signal based on frequency, a filter can also shift the relative phase of signals at different frequencies. Phase shift is important because it can distort nonsinusoidal signals in inconvenient ways. 

If you run sinusoidal signals of different frequencies through this filter, not only does the filter attenuate the higher frequency signals, but it also shifts their phase.

Note that the phase-shift plot describes the shift of sinusoidal signals. A filter's phase response is also important in the case of nonsinusoidal signals because phase shifts distort the waveforms. This is because nonsinusoidal signals can be viewed as combinations of sinusoidal signals of varying frequencies. Shifting the phase of these components relative to one another will change the shape of the overall waveform.

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