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

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 Active filters can be designed to provide required gain, and hence no attenuation as in the case of passive filters No loading problem, because of high input resistance and low output resistance of op-amp. 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 There are 4 basic categories of active filters: 1. Low pass filters High pass filters Band pass filters 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.

Active Filters The passband is the range of frequencies that are allowed to pass through the filter. The critical frequency, fc is specified at the point where the response drops by 3dB from the passband response (i.e. to 70.7% of 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 occurs

Basic Filter Responses 1. Low-pass filter Allows the frequency from 0 Hz to critical frequency fH (also known as cutoff frequency). Ideally, the response drops abruptly at the critical frequency fH. Fig 15-1a Ideal response

Basic Filter Responses 1. Low-pass filter In an RC low-pass filter, the critical frequency can be calculated from the expression: Fig 15-1a

Basic Filter Responses Actual response

Basic Filter Responses 2. High-Pass filter Allows the frequencies above the critical frequency fL. (also known as the cutoff frequency. Ideally, the response rises abruptly at the critical frequency Ideal response

Basic Filter Responses 2. High-Pass filter In an RC high-pass filter, the critical frequency can be calculated from the expression;

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Basic Filter Responses Fig 15-2a High pass filter response actual response

Basic Filter Responses 3. Band-Pass filter Allows frequencies between a lower cutoff frequency (fL) and an upper cutoff frequency (fH). Fig 15-3 Ideal response

Basic Filter Responses Fig 15-3 actual response

Basic Filter Responses 3. Band-Pass filter Fig 15-3 Bandwidth,

Basic Filter Responses 3. Band-Pass filter Center frequency, Fig 15-3

Basic Filter Responses 3. Band-Pass filter Quality factor (Q) is the ratio of center frequency fo to the BW; Fig 15-3

Basic Filter Responses 4. Band-stop filter Opposite of a band-pass. Frequencies above fc1 (fL) and above fc2 (fH) are passed Fig 15-4 Ideal response

Basic Filter Responses Fig 15-4 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 Passband flatness Attenuation of frequency outside the passband Three types: 1. Butterworth 2. Bessel 3. Chebyshev Fig 15-5 Three response types

Filter Response Characteristics Fig 15-5 Three response types

Filter Response Characteristics 1. Butterworth Response Amplitude response is very flat. The roll-off rate -20 dB per decade (per filter order). This is the most widely used. Fig 15-5 Three response types

Filter Response Characteristics 2. Chebyshev Ripples. The roll-off rate greater than –20 dB. a nonlinear phase response. Fig 15-5 Three response types

Filter Response Characteristics 3. Bessel Linear phase response. ideal for filtering pulse waveforms. Fig 15-5 Three response types

Filter Response Characteristics Damping Factor 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 R1 and R2. Fig 15-6 general active filter

Filter Response Characteristics Damping Factor Fig 15-6 general active filter Diagram of an active filter

Filter Response Characteristics Critical Frequency and Roll-off rate 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 Fig 15-8 cascaded filters

Filter Response Characteristics Fig 15-8 cascaded filters First order (one pole) low pass filter

Filter Response Characteristics The number of filter poles can be increased by cascading Fig 15-8 cascaded filters

Filter Response Characteristics Fig 15-8 cascaded filters

Active Low-Pass Filters Basic Low-Pass filter circuit At critical frequency, Resistance = capacitive reactance i.e. Fig 15-10 Sallen-Key low pass or

Active Low-Pass Filters Basic Low-Pass filter circuit So, critical frequency; Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Low Pass Response Roll-off depends on number the of poles. Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters A Single-Pole Filter One pole Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters A Single-Pole Filter Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters The Sallen-Key second-order (two-pole) filter roll-off -40dB per decade Fig 15-10 Sallen-Key low pass Two-pole Low-pass circuit

Active Low-Pass Filters The Sallen-Key For RA = RB = R and CA = CB = C; Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Example For the following circuit; Determine critical frequency Set the value of R1 for Butterworth response Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Example (cont’d) Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Solution Critical frequency Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Solution Butterworth response from Table 15.1 Floyd, page 744, R1/R2 = 0.586; Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Cascaded LPF – Three-pole cascade two-pole and single-pole roll-off -60dB per decade Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Cascaded LPF – Four pole cascade two-pole and two-pole roll-off -80dB per decade Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Example For the fourth order filter circuit shown in the following figure, determine the capacitance values required to produce a critical frequency of 2680 Hz if all resistors in RC low pass circuit is 1.8 k. Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Example (cont’d) Fig 15-10 Sallen-Key low pass

Active Low-Pass Filters Example – SOLUTION Fig 15-10 Sallen-Key low pass

Active High-Pass Filters Basic High-Pass circuit At critical frequency, Resistance = capacitive reactance i.e; Fig 15-10 Sallen-Key low pass or; or;

Active High-Pass Filters Basic High-Pass circuit So, critical frequency ; Fig 15-10 Sallen-Key low pass

Active High-Pass Filters High Pass Response Roll-off depends on number the of poles. Fig 15-10 Sallen-Key low pass

Active High-Pass Filters A Single-Pole Filter Fig 15-10 Sallen-Key low pass Circuit

Active High-Pass Filters A Single-Pole Filter Response curve Fig 15-10 Sallen-Key low pass

Active High-Pass Filters The Sallen-Key second-order (two-pole) filter roll-off -40dB per decade Fig 15-10 Sallen-Key low pass

Active High-Pass Filters The Sallen-Key Fig 15-10 Sallen-Key low pass

Active High-Pass Filters The Sallen-Key Lets RA = RB = R and CA = CB = C; Fig 15-10 Sallen-Key low pass

Active High-Pass Filters Cascaded HPF – Six pole cascade 3 Sallen-Key two-pole stages roll-off -120 dB per decade Fig 15-10 Sallen-Key low pass

Active Band-Pass Filters A cascade of a low-pass and high-pass filter. Fig 15-17a

Active Band-Pass Filters Fig 15-17b band-pass curve

Active Band-Pass Filters Fig 15-17b band-pass curve

Active Band-Pass Filters Fig 15-18 Mult feedback band-pass

Active Band-Pass Filters Multiple-Feedback BPF The low-pass circuit consists of R1 and C1. The high-pass circuit consists of R2 and C2. The feedback paths are through C1 and R2. Center frequency; Fig 15-18 Mult feedback band-pass

Active Band-Pass Filters State-Variable BPF State-Variable BPF is widely used for band-pass applications. Fig 15-20

Active Band-Pass Filters State-Variable BPF 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). Fig 15-20

Active Band-Pass Filters The band-pass output peaks sharply the center frequency giving it a high Q. Fig 15-21 state-variable curve

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 R3 and the addition of R4. Fig 15-23 Mult.-feedback band stop

Active Band-Stop Filters Fig 15-23 Mult.-feedback band stop

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.

Summary 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

Summary 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.

Active Filters EXAMPLE With reference to the following circuit; Name the type of circuit. Determine the critical frequency Modify the circuit to increase roll-off to 120dB/decade. Convert the circuit to become a high pass filter. Fig 15-23 Mult.-feedback band stop

Active Filters EXAMPLE (cont’d) Fig 15-23 Mult.-feedback band stop

Active Filters SOLUTION (i) Type of circuit: FOUR-POLE LOW-PASS ACTIVE FILTER Critical frequency Fig 15-23 Mult.-feedback band stop

Active Filters SOLUTION (cont’d) Fig 15-23 Mult.-feedback band stop

Active Filters SOLUTION (cont’d) (ii) Modification Add the following 3rd stage to the output of the 2nd stage Fig 15-23 Mult.-feedback band stop

Active Filters SOLUTION (cont’d)

Assignment on Active Filters Due date : 30th Sept 2005 Refer to Floyd text book page 766 – 770 Q5, Q10, Q15, Q16, Q19 Fig 15-23 Mult.-feedback band stop