Measurement and Instrumentation

Measurement and Instrumentation

Dr. Tayab Din Memon

Assistant Professor Dept of Electronic Engineering, MUET, Jamshoro.

ACTIVE FILTERS and its applications

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.

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.

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.

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.

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.

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.

What is the advantage of increasing Order?

Answer!!

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.

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.

Butterworth Approximation

Chebyshav Approximation

Elliptic Approximation Bessel Approximation

Damping Factor

Peaking action at resonant frequency is to use the damping factor defined as:

For Q=10, the damping factor is 0.1.

Q1

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.

Response Curves of All types of Filters

Fig. Lowpass Filter

Fig. Highpass Filter

Filter Response Curves of all types

Fig. Bandpass Filter

Fig. Bandstop Filter

First Order Stage

First order stages can only be implemented using Butterworth response.

Why?

Active Lowpass Filter (unity Gain)

Fig. Single pole lowpass filter.

+

-

AC

R1

C1

2

11

1

1CR2

1 fcfrequency Cutoff

1 isGain

fcf

A

Av

Active Lowpass Filter (Variable Gain)

Fig. Single pole lowpass filter.

Rf

+

-

AC

R1

C1

2

11

1

1CR2

1 fcfrequency Cutoff

1 isGain

fcf

A

RiRfAv

Ri

Active Lowpass Inverting with variable gain.

C1

Rf

+

-

AC

2

1

1

1R2C21 fcfrequency Cutoff

isGain

fcf

A

RiRfAv

Ri

Fig. Active Lowpass Inverting Circuit.

Single pole Highpass unity gain Filter

2

1

1

1R1C21 fcfrequency Cutoff

1 isGain

ffc

A

Av

+

-

ACR1

C1

Fig. Single Pole Highpass Filter.

Single pole Highpass with variable gain

Rf

2

1

1

1R1C21 fcfrequency Cutoff

1 isGain

ffc

A

RiR

Av f

+

-

ACR1

C1

Ri

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.

VCVS Double Pole Lowpass Filter (Butterworth and Bessel)

0.786Kc 0.577,Q :Bessel1Kc 0.707,Q

:Butterwortfc

f1

1A ,CC0.5Q

CCR21 fpfrequency Cutoff

1Av isGain

41

2

21

+

-ACC1

C2

R R

Double Pole Lowpass Peaked Response

Peaked Response can be calculated using following three frequencies:

f0=K0fp

fc=Kcfp

f3dB=K3fp

f0 is the resonant frequency where peaking appears,

fc is the edge frequency, & f3dB is the cutoff frequency.

K values and Ripple depth of Second-Order Stages (Table 1)

Q K0 Kc K3 Ap(dB)

0.577 ---- ---- 1 --0.707 --- 1 1 ---

0.75 0.333 0.471 1.057 0.0540.8 0.476 0.661 1.115 0.2130.9 0.620 0.874 1.206 0.6881 0.78 1 1.277 1.252 0.935 1.322 1.485 6.33 0.972 1.374 1.532 9.664 0.984 1.391 1.537 12.15 0.99 1.4 1.543 14

10 0.998 1.410 1.551 20100 1 1.414 1.554 40

Discussion of the Table

Table gives us K and Ap values versus Q.

The Bessel and Butterworth have not noticeable frequency, So K0 and Ap values does not apply.

When Q is greater than 0.707, a noticeable resonant frequency appears and all K an Ap values are present.

Equal Component Values Second Order Lowpass Filter

+

-AC

R R

C

C

R1

Rf

RCfc

AvQ

Av RRf

21

31

1 1

VCVS Second Order Unity Gain High Pass Filters

AC

+

-

C C

R1

R2

2121

15.0

1

2

RRCfp

RRQ

Av

VCVS Highpass Filter with Voltage gain greater than unity.

AC

+

-

C C

R

R

CRfp

AVQ

RRfAv

21

31

11

Rf

R1

Bandpass Filter

BWfQ

fff

ffBW

0

210

12

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.

Solution!

HIGH PASSfc=300Hz

LOWPASSfc=3.3KHzVin Vout

Fig. Wideband Filters uses cascadeof lowpass and highpass stages.

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.

Narrowband Filters (cont….)

2121

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Narrowband Filter Typical Circuit

Notch Filter

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v

AQ

RCf

RRA

25.0

21

1

0

1

2

VCVS Sallen Key Band stop Filter circuit

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.

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 1800 out of phase with input in Inverting whereas in Non-Inverting Output is in phase with Input.