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Measurement and Instrumentation Dr. Tayab Din Memon Assistant Professor Dept of Electronic Engineering, MUET, Jamshoro. ACTIVE FILTERS and its applications

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Objectives Discuss about the Active filters, its use and applications. Types of filters Important terminologies of Active Filters. Order of Filter Filter Approximations Order of Filter Categories of Filter Responses Active Lowpass Filter Single Order Lowpass Filter & Double Order Lowpass Filter Unity Gain and Variable Gain Active Highpass Filter Single order highpass filter, Second order highpass filter Unity gain and variable gain highpass filter. K Values Table & its discussion Bandpass Filter Wideband & Narrowband Band stop Filter Session-II Lab Work Design and simulation of circuits.

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Filters: An Introduction Filters can be defined as: filters are electrical networks that have been designed to pass alternating currents generated at only certain frequencies and to block or attenuate all others. Filters have a wide use in electrical and electronic engineering and are vital elements in many telecommunications and instrumentation systems where the separation of wanted from unwanted signals – including noise – is essential to their success.

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Filters Applications Filter circuits are used in a wide variety of applications. In the field of telecommunication, band-pass filters are used in the audio frequency range (0 kHz to 20 kHz) for modems and speech processing. High-frequency band-pass filters (several hundred MHz) are used for channel selection in telephone central offices. Data acquisition systems usually require anti-aliasing low-pass filters as well as low-pass noise filters in their preceding signal conditioning stages. System power supplies often use band-rejection filters to suppress the 60-Hz line frequency and high frequency transients.

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Types of Filters Passive Filters Incorporates only passive components like; capacitors, resistors, inductors. Passive filters are difficult to design. Further inductors are difficult to handle. Not only are they expensive, bulky and heavy; they are prone to magnetic field radiation unless expensive shielding is used to prevent unwanted coupling Used for high frequencies (>MHz) Active Filters Along with passive components capacitors and resistors, Additionally it incorporates active components particularly like; op- amp. Due to inductor property at low frequencies, active filters are Used at low frequencies. It overcomes the inductor problems in passive filter.

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Important terminologies in Filters Frequency Response of Filter is the graph of its voltage gain versus frequency. Passband: Those frequencies that are passed by a filter without attenuation. Stopband: Those frequencies that are rejected by filter after cutoff. Transition: The roll-off region between passband and the stopband. Attenuation: Attenuation refers to the loss of signal.

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Order of a Filter The order of an active filter depends on the number of RC circuits called poles it contains. If an active filter contains 8 RC circuits, n=8. In active filters simple way to determine the order is to identify the number of capacitors in the circuit. n= #of capacitors.

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What is the advantage of increasing Order? Answer!!

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Filter Approximation Butterworth Approximation The butterworth approximation is sometimes called the maximum flat approximation. Roll off =20n dB/decade An equivalent roll of in terms of octaves is: Roll-off = 6n dB/octave Chebyshev Approximation In Chebyshav approximation ripples are present in passband, but its roll off rate is greater than 20dB/decade for a single pole. The number of ripples in the passband of a Chebyshav filter are equals to the half of the filter order: #Ripples = n/2 Inverse Chebyshav Approximation In applications in which flat response is required as well as the fast roll-off, a designer may choose Inverse Chebyshav. It has flat passband and rippled stopband. Inverse Chebyshav is not a Monotonic (No Stop Band ripples) Approximation.

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Filter approximation Elliptic Approximation If rippled passband and rippled stopband are accepted designer must choose elliptic approximation. Its major advantage is its highest roll-off rate in transition region. Bessel Approximation Bessel approximation has a flat passband and a monotonic stopband similar to those of the Butterworth approximation. For the same filter order, however, the roll-off in the transition region is much less with a Bessel filter than with a Butterworth filter. The major advantage of the Bessel Filter is that it produces the least distortion of non-sinusoidal signals. No phase change.

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Butterworth Approximation Chebyshav Approximation Elliptic Approximation Bessel Approximation

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Damping Factor Peaking action at resonant frequency is to use the damping factor defined as: For Q=10, the damping factor is 0.1.

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Categories of filters Lowpass It passes frequencies before cutoff. Highpass It passes all frequencies after cutoff. Bandpass It passes all the frequencies in a specific band. Bandstop It rejects all the frequencies of a specific band.

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Response Curves of All types of Filters Fig. Lowpass Filter Fig. Highpass Filter

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Filter Response Curves of all types Fig. Bandpass Filter Fig. Bandstop Filter

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First Order Stage First order stages can only be implemented using Butterworth response. Why?

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Active Lowpass Filter (unity Gain) Fig. Single pole lowpass filter.

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Active Lowpass Filter (Variable Gain) Fig. Single pole lowpass filter.

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Active Lowpass Inverting with variable gain. Fig. Active Lowpass Inverting Circuit.

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Single pole Highpass unity gain Filter Fig. Single Pole Highpass Filter.

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Single pole Highpass with variable gain

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Sallen Key Approach (VCVS) Second order or 2-pole stages are the most common because they are easy to build and analyze. Higher order filters are usually made by cascading second order stages. Each second- order stage has a resonant frequency and Q to determined how much peaking occurs. Sallen Key approach is also known as VCVS (Voltage Controlled Voltage Source) because the opamp is used as a voltage-controlled voltage source.

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VCVS Double Pole Lowpass Filter (Butterworth and Bessel)

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Double Pole Lowpass Peaked Response Peaked Response can be calculated using following three frequencies: f 0 =K 0 f p f c =K c f p f 3dB =K 3 f p f 0 is the resonant frequency where peaking appears, f c is the edge frequency, & f 3dB is the cutoff frequency.

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K values and Ripple depth of Second-Order Stages (Table 1) QK0K0 KcKc K3K3 A p(dB) 0.577---- 1-- 0.707---11 0.750.3330.4711.0570.054 0.80.4760.6611.1150.213 0.90.6200.8741.2060.688 10.7811.2771.25 20.9351.3221.4856.3 30.9721.3741.5329.66 40.9841.3911.53712.1 50.991.41.54314 100.9981.4101.55120 10011.4141.55440

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Discussion of the Table Table gives us K and A p values versus Q. The Bessel and Butterworth have not noticeable frequency, So K 0 and A p values does not apply. When Q is greater than 0.707, a noticeable resonant frequency appears and all K an A p values are present.

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Equal Component Values Second Order Lowpass Filter

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VCVS Second Order Unity Gain High Pass Filters

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VCVS Highpass Filter with Voltage gain greater than unity.

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Bandpass Filter When Q is less than 1, the filter has a wideband response. In this case bandpass filter is designed by cascading lowpass and highpass filter. When Q is greater than 1, the filter has a narrowband response and a different approach is used. A Bandpass filter has a center frequency and a bandwidth.

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Solution!

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Narrowband Filters When Q is greater than 1, we use Multiple Feedback (MFB) filter shown in fig. The input signal is at Inverting terminal. Two feedbacks one from capacitor & resistor. Operation: At low frequencies capacitor appears to be open. Therefore, the input signal cannot reach the opamp, and the output is zero. At high frequencies, the capacitors appear to be shorted. In this case, the voltage gain is zero because feedback capacitor has zero impedance. Between the low and high extremes in frequency, there is a band of frequencies where the circuit acts like an inverting amplifier.

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Narrowband Filters (cont….)

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Narrowband Filter Typical Circuit

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Notch Filter

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VCVS Sallen Key Band stop Filter circuit

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All pass filters All pass filter is widely used in industry. This is called phase filter. It shifts the phase of the output signal without changing the magnitude. Time delay filter.

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Summary Note that in Inverting and Non-Inverting Opamp modes, feedback is – ve. The only difference is that; input is applied at different terminals. Output is 180 0 out of phase with input in Inverting whereas in Non-Inverting Output is in phase with Input.

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