Chapter 5 Active Filter By En. Rosemizi Bin Abd Rahim EMT212 – Analog Electronic II

Introduction Filters are circuits that are capable of passing signals within a band of frequencies while rejecting or blocking signals of frequencies outside this band. This property of filters is also called “frequency selectivity”. Filter circuits built using components such as resistors, capacitors and inductors only are known as passive filters. Active filters employ transistors or op-amps in addition to resistors and capacitors.

Advantages of Active Filters over Passive Filters 1.Active filters can be designed to provide required gain, and hence no attenuation as in the case of passive filters 2.No loading problem, because of high input resistance and low output resistance of op-amp. 3.Active Filters are cost effective as a wide variety of economical op-amps are available.

Applications Active filters are mainly used in communication and signal processing circuits. They are also employed in a wide range of applications such as entertainment, medical electronics, etc.

Active Filters 1.Low pass filters 2.High pass filters 3.Band pass filters 4.Band reject filters Each of these filters can be built by using op-amp as the active element combined with RC, RL or RLC circuit as the passive elements. There are 4 basic categories of active filters:

Active Filters The passband is the range of frequencies that are allowed to pass through the filter. The critical frequency, f c is specified at the point where the response drop -3dB (70.7%) from the passband response. The stopband is the range of frequencies that have the most attenuation. The transition region is the area where the fall-off occur.

Basic Filter Responses 1.Low-pass filter Allows the frequency from 0Hz to critical frequency. The critical frequency can be formula by Ideal response actual response

Basic Filter Responses The critical frequency can be formula by 1.High-Pass filter Only allowing the frequencies above the critical frequency. Ideal response actual response

Basic Filter Responses 3. Band-pass filter Allows frequencies between a lower critical frequency (f c1 ) and an upper critical frequency (f c2 ). Ideal response actual response

Basic Filter Responses The narrower the bandwidth, the higher the quality factor. 3. Band-pass filter Bandwidth, BW = f c2 -f c1 Quality factor (Q) is the ratio of center frequency f o to the BW center frequency, f o

Basic Filter Responses 4. Band-stop filter Opposite of a band-pass. Frequencies above and below f c1 and f c2 are passed. Ideal response actual response

Animation A "Group" of waves passing through a Typical Band-Pass Filter

Filter Response Characteristics Identified by the shape of the response curve 1.Butterworth 2.Bessel 3.Chebyshev Passband flatness Attenuation of frequency outside the passband Three types:

Filter Response Characteristics 1.Butterworth Response Amplitude response is very flat. The roll-off rate -20 dB per decade. This is the most widely used.

Filter Response Characteristics 2. Chebyshev Response Ripples The roll-off rate greater than –20 dB a nonlinear phase response.

Filter Response Characteristics 3. Bessel Response Linear phase response ideal for filtering pulse waveforms

Filter Response Characteristics The damping factor of an active filter determines the type of response characteristic either Butterworth, Chebyshev, or Bessel. The output signal is fed back into the filter circuit with negative feedback determined by the combination of R 1 and R 2. Damping factor (DF) Diagram of an active filter Damping Factor

Filter Response Characteristics Greater 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. Critical Frequency and Roll-off rate First order (one pole) low pass filter

Filter Response Characteristics The number of filter poles can be increase by cascading

Active Low-Pass Filters Basic Low-Pass filter circuit At critical frequency, Resistance = capacitance So, critical frequency ;

Active Low-Pass Filters Low Pass Response Roll-off depends on number the of poles.

Active Low-Pass Filters A Single-Pole Filter

Active Low-Pass Filters The Sallen-Key second-order (two-pole) filter roll-off -40dB per decade For R A =R B =R and C A =C B =C ;

Active Low-Pass Filters Example Determine critical frequency set the value of R 1 for Butterworth response. Critical frequency Butterworth response from table 15.1 floyd, page 744 R 1 /R 2 = 0.586

Active Low-Pass Filters Cascaded LPF – Three pole cascade two-pole and single-pole roll-off -60dB per decade

Active Low-Pass Filters Cascaded LPF – Four pole cascade two-pole and two-pole roll-off -80dB per decade

Active Low-Pass Filters Example Determine the capacitance values required to produce a critical frequency of 2680 Hz if all resistors in RC low pass circuit is 1.8k  C A1 =C B1 =C A2 =C B2 =0.033µf

Active High-Pass Filters Basic High-Pass circuit At critical frequency, Resistance = capacitance So, critical frequency ;

Active High-Pass Filters High Pass Response Roll-off depends on number the of poles.

Active High-Pass Filters A Single-Pole Filter

Active High-Pass Filters The Sallen-Key second-order (two-pole) filter roll-off -40dB per decade Lets R A =R B =R and C A =C B =C

Active High-Pass Filters Cascaded LPF – Six pole cascade 3 Sallen-Key two-pole stages roll-off -120 dB per decade

Active Band-Pass Filters A cascaded of a low-pass and high-pass filter.

Active Band-Pass Filters

The low-pass circuit consists of R 1 and C 1. The high-pass circuit consists of R 2 and C 2. The feedback paths are through C 1 and R 2. Multiple-Feedback BPF center frequency

Active Band-Pass Filters State-Variable BPF 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. R 5 and R 6 set the Q (bandwidth).

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

Active Band-Stop Filters The BSF is opposite of BPF in that it blocks a specific band of frequencies. The multiple-feedback design is similar to a BPF with exception of the placement of R 3 and the addition of R 4.

Assignment on Active Filters Refer to Floyd text book page 766 – 770 Q5, Q10, Q15, Q16, Q19 Due date : 30 th Sept 2005

i)Name the type of circuit. Determine the critical frequency. ii)Modify the circuit to increase roll-off to -120dB/dec. iii)Convert the circuit to become a high pass filter. Quiz on Active Filters

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.

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