ch 15 filters

Chapter 15Active Filters

Objectives

Describe the frequency response of basic filters

Describe the three basic filter response characteristics

Analyze the operation of log and antilog amplifiers

Analyze low, high, band-pass, and band-stop filters

Discuss two methods for measuring frequency response

Introduction

Active filters combine solid state amplification and passive filter circuits. The amplification is used to augment a passive filter’s characteristics. The action of the passive filter is no different than when used by itself.

Basic Filter ResponsesThe basic low-pass filter response is from 0Hz to the upper critical frequency (fcu). Note the passband of the ideal (shaded area) versus the realistic. The fcu can be by the formula the formula below.

fcu = 1/2RC

Figure 15–1 Low-pass filter responses.

Thomas L. Floyd Electronic Devices, 7e

Basic Filter ResponsesA high-pass filter effectively blocks below fc and allowing only the frequencies above fc to pass. The same formula is used for the critical frequency for both low and high pass filters.

Figure 15–2 High-pass filter responses.

Basic Filter ResponsesThe band-pass filter allows frequencies between a lower critical frequency (fc1) and an upper critical frequency (fc2) to pass while effectively blocking all others. The narrower the bandwidth, the higher the quality (Q) of the filter. The formula for the Q of a band-pass filter is shown below. f0 = center frequency.

Q = f0/BW

Basic Filter ResponsesThe band-stop filter is just the opposite of a band-pass. Frequencies above and below fc1 and fc2 are passed while effectively blocking the frequencies between.

Filter Response CharacteristicsThe Butterworth, Bessel, and Chebyshev are three response curves that can be produced from filter circuits. These responses are easily identifiable and are produced with selection of certain component values.

Filter Response CharacteristicsThe Butterworth characteristic response is very flat. The roll-off rate –20 dB per decade. This is the most widely used.The Chebyshev characteristic response provides a roll-off rate greater than –20 dB but has ripples in the passband and a nonlinear phase response.The Bessel characteristic response exhibits the most linear phase response making it ideal for filtering pulse waveforms with distortion.

Filter Response CharacteristicsThe damping factor of an active filter determines the type of response characteristic. The output signal is fed back into the filter circuit with negative feedback determined by the combination of R1 and R2. The negative feedback ultimately determines the type of filter response is produced. The equation below defines the damping factor.

DF = 2 - R1/R2

Figure 15–7 First-order (one-pole) low-pass filter.

Filter Response CharacteristicsGreater roll-off rates can be achieved with more poles. Each RC set of filter components represents a pole. Cascading of filter circuits also increases the poles which results in a steeper roll-off. Each pole represents a –20 dB/decade increase in roll-off.

Figure 15–9 Single-pole active low-pass filter and response curve.

Active Low-Pass FiltersThe Sallen-Key low-pass filter is one of the most common configurations for a second-order (two-pole) filter. The cutoff frequency for this type of filter can be determined by the formula below. Greater roll-off can be achieved by cascading.

fc = 1/2 RARBCACB

Figure 15–11

Figure 15–12 Cascaded low-pass filters.

Figure 15–13 Single-pole active high-pass filter and response curve.

Figure 15–14 High-pass filter response.

Active High-Pass FiltersThe Sallen-Key high pass configuration is a second order filter for high pass filters. Note that the positions of the resistors and capacitors are opposite of the low-pass type.

Figure 15–16 Sixth-order high-pass filter.

Active Band-pass FiltersA cascaded arrangement of a low-pass and high-pass filter forms a band-pass filter.

Active Band pass FiltersThe upper and lower cutoff frequencies and center frequencies can be determined with the previously discussed formulas for RC filter circuits.

Active Band-pass FiltersAnother type of filter configuration is the multiple-feedback band-pass filter. The low-pass circuit consists of R1 and C1. The high-pass circuit consists of the of the R2 and C2. The feedback paths are through C1 and R2.

Active Band-pass FiltersThe center frequency for a the multiple-feedback band-pass filter can be determined by the formula below.

f0 = 1/2(R1R3)R2C1C2

Figure 15–19

Active Band-pass FiltersThe state-variable band-pass filter is widely used for band-pass applications. It consists of a summing amplifier and two integrators. It has outputs for low-pass, high-pass, and band-pass. The center frequency is set by the integrator RC circuits. R5 and R6 set the Q (bandwidth).

Active Band-Pass FiltersThe band-pass output peaks sharply the center frequency giving it a high Q.

Figure 15–22

Figure 15–23 A biquad filter.

Active Band-Stop FiltersThe band-stop filter is opposite of band-pass in that it blocks a specific band of frequencies. The multiple-feedback design is similar to a band-pass with exception of the placement of R3 and the addition of R4.

Figure 15–25 State-variable band-stop filter.

Figure 15–26

Filter Response Measurements

Measuring frequency response can be performed with typical bench-type equipment. It is a process of setting and measuring frequencies both outside and inside the known cutoff points in predetermined steps. Use the output measurements to plot a graph.

More accurate measurements can be performed with sweep generators along with an oscilloscope, a spectrum analyzer, or a scalar analyzer.

Figure 15–27 Test setup for discrete point measurement of the filter response. (Readings are arbitrary and for display only.)

Figure 15–28 Test setup for swept frequency measurement of the filter response.

Summary The bandwidth of a low-pass filter is the same as the upper critical frequency. The bandwidth of a high-pass filter extends from the lower critical frequency up to the inherent limits of the circuit. The band-pass passes frequencies between the lower critical frequency and the upper critical frequency. A band-stop filter rejects frequencies within the upper critical frequency and upper critical frequency. The Butterworth filter response is very flat and has a roll-off rate of –20 B.

The Chebyshev filter response has ripples and overshoot in the passband but can have roll-off rates greater than –20 dB. The Bessel response exhibits a linear phase characteristic, and filters with the Bessel response are better for filtering pulse waveforms.

A filter pole consists of one RC circuit. Each pole doubles the roll-off rate.

The Q of a filter indicates a band-pass filter’s selectivity. The higher the Q the narrower the bandwidth. The damping factor determines the filter response characteristic.

Summary

Figure 15–29 Basic block diagram of an FM receiver system.

Figure 15–30 Channel filter board.

Figure 15–31 Channel separation circuits. The circuits on the filter board are shown in the green blocks.

Figure 15–32

Figure 15–33 Multisim file circuits are identified with a CD logo and are in the Problems folder on your CD-ROM. Filenames correspond to figure numbers (e.g., F15-33).

Figure 15–34

Figure 15–35

Figure 15–36

Figure 15–37

Figure 15–38

ch 15 filters

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