Basic Elements In Measurement: Sensing Element Signal Conditioning Element Signal Processing Element

Basic Elements in Measurement

Sensing Element

• Input Measurand

Signal Conditioning Element

Signal Processing Element

• Output • Electrical Output

Signal Conditioning • The Measurand, which is basically a physical quantity as is detected by the first stage of the instrumentation or measurement system. • The first stage, with which we have become familiar, is the "Detector Transduces stage''. • The quantity is detected and is transduced into· an electrical form in most of the cases. • The output of the first stage has to be modified before it becomes usable and satisfactory to drive the signal presentation stage which is the third and the last stage of a measurement system. • The last stage of the measurement system may consist of indicating, recording, displaying, data processing elements or may consist of control elements.

Basic structure of D.C. Signal Conditioning

• The signal conditioning or data acquisition equipment in many a situation be an excitation and amplification system for Passive transducers. • Signal conditioning circuits are used to process the output signal from sensors of a measurement system to be suitable for the next stage of operation. DC Excitation Source

Measurand

Transducer

Bridge

Power Supply

Calibration and zeroing network

DC Amplifier

D.C. Signal Conditioning System

Low Pass Filter

Output (DC)

Basic structure of A.C. Signal Conditioning • D.C. systems are generally used for common resistance transducers such as potentiometers and resistance strain gauges. • A.C. systems have to be used for variable reactance transducers and for systems where signals have to be transmitted via long cables to connect the transducers to the signal conditioning equipment.

Transducer

Bridge

Measurand

Carrier Oscillator

Calibration and zeroing network

AC Amplifier

Power Supply

A.C. Signal Conditioning System

Phase Sensitive Demonstra tor Reference

Low Pass Filter

Output (DC)

Wheatstone Bridge (W.B.) It is the most commonly used d.c. bridge for measurement of resistance.

This bridge is used for measurement of small resistance changes that occur in passive resistive transducer like strain gauges, thermistors and resistance thermometers.

Fig.1 Wheatstone Bridge

Wheatstone Bridge (W.B.) • Figure 1 shows the basic circuit of a Wheatstone bridge, which consists of four resistive arms with a source of emf (a battery) and a meter which acts as a detector. • The detector is usually a current sensitive galvanometer. • Measurement may be carried out either by balancing the bridge or by determining the magnitude of unbalance. There are two ways in which W.B. can be used: 1) Null Type

2) Deflection Type

Wheatstone Bridge (W.B.) 1. Null Type Wheatstone bridge: • When using this type of measurement, adjustments are made in various arms of the bridge so that the voltage across the detector is zero and hence no current flows through it. • When no current flow through detector, the bridge is said to be balance.

Under Balance Condition: 𝑅1 = 𝑅2 (𝑅3 /𝑅4 ) • Resistance R1 represents the resistance of a resistive transducer whose value depends upon the physical variable being measured. • The ratio of resistors R3 and R4 is fixed for a particular measurement.

Wheatstone Bridge (W.B.) • In instrumentation work, it is the change ∆R1 in the transducer resistance R1 which is to be found. • The change unbalances the bridge and therefore resistor R2 has to be adjusted by an amount ∆R2 to restore balance. Under Rebalance Condition 𝑅1 + ∆𝑅1 = (𝑅2 +∆𝑅2 )(𝑅3 /𝑅4 ) = 𝑅2 (𝑅3 /𝑅4 ) + ∆𝑅2 (𝑅3 /𝑅4 ) = 𝑅1 + ∆𝑅2 (𝑅3 /𝑅4 ) ∆ 𝑅2 = ∆𝑅1 (𝑅4 /𝑅3 ) Some applications such as temperature measuring systems (where the resistance, R1 of the transducer changes on account of temperature), an automatic bridge balancing control system may be used as shown in Fig. 2.

Wheatstone Bridge • When there is change in resistance R1, it produces a voltage output which is amplified and applied as an error signal to the field winding of a d c. motor. • The motor is coupled to a moving contact. This movable contact is actuated so as to reduce the unbalance and hence the error voltage. • When the bridge is balanced, there is no error voltage and therefore there is no voltage, across the field winding of the motor. The motor stops and thus the slider comes to rest. • The read out scale be calibrated in resistance change values or in terms of temperature or any other physical variable being measured.

Fig. 2 : Self (Automatic) Balance Wheatstone Bridge

Wheatstone Bridge 2. Deflection Type • The null type Wheatstone Bridge is accurate but the problem with this bridge is that balancing, even if done automatically, is not instantaneous. Therefore this bridge is unsuitable for dynamic applications where the changes in resistance are rapid. • For measurement of rapid changing input signals, the Deflection type Bridge is used. When the input changes, the resistances R1 producing an unbalance causing a voltage to appear across the meter. • The deflection of meter is indicative of the value of resistance and the scale of the meter may be calibrated resistance directly.

• For static inputs, an ordinary galvanometer may be used. However for dynamic inputs, output signal may be displayed by a cathode ray oscilloscope or may be recorded by a recorder.

Wheatstone Bridge 2. Deflection Type • The deflection type bridge circuit is provided with a zero setting arrangement as shown in Fig 3. The series resistance Rs is used to change the bridge sensitivity.

Fig. 3: Deflection Type Wheatstone Bridge provided with zero adjustment and sensitivity adjustment arrangements

Wheatstone Bridge • When a deflection type bridge is used, the bridge output on account of the unbalance may be connected either to a high input impedance device or to a low input impedance device. • If the output of the bridge is connected directly to a low impedance devices like a current galvanometer or a PMMC instrument, a large current flows through the meter. In this case, the bridge is called a Current Sensitive Bridge.

• In most of the applications of deflection type bridge, the bridge output is fed to an amplifier which has a high input impedance and therefore the output current 𝑖𝑚 = 0. This would also be the case if the bridge output is connected to a CRO or a digital voltmeter. The bridge thus used is a Voltage Sensitive Bridge.

Voltage Sensitive Bridge Let us assume that the input impedance of the meter is infinite and therefore 𝑖𝑚

=

0.

Hence 𝑖1 = 𝑖2 and 𝑖3 = 𝑖4 , output voltage 𝑒0 = voltage across terminals B and D = 𝑖1 𝑅1 - 𝑖3 𝑅3 .

But 𝑖1 = So 𝑒𝑜 = =

𝑒𝑖 𝑅1 + 𝑅2

and 𝑖3 =

𝑅1 𝑅3 − 𝑅1 + 𝑅2 𝑅3 + 𝑅4 𝑅1 𝑅4 −𝑅2 𝑅3 (𝑅1 + 𝑅2 )(𝑅3 + 𝑅4 )

𝑒𝑖 𝑅3 + 𝑅4

𝑒𝑖 𝑒𝑖

Suppose now 𝑅1 changes by an amount ∆𝑅1 . This causes a change ∆𝑒𝑜 in the output voltage Thus :

Reference fig 1: Basic Wheatstone Bridge

Voltage Sensitive Bridge (𝑅1 + ∆𝑅1 )𝑅4 − 𝑅2 𝑅3 𝑒𝑜 + ∆𝑒𝑜 = (𝑅1 +∆𝑅1 + 𝑅2 )(𝑅3 + 𝑅4 )

1+ =

𝑅2 𝑅3 ∆𝑅1 − ( 𝑅 1 𝑅1 𝑅 4 )

∆𝑅 1 + 𝑅 1 + (𝑅2 /𝑅1 ) 1

𝑒𝑖

𝑒𝑖

1 + (𝑅3 /𝑅1 )

In order to simplify the relationship, let us assume that initially all the resistances comprising the bridge are equal i e., 𝑅1 = 𝑅2 = 𝑅3 = 𝑅4 = 𝑅.

Under these conditions: 𝑒𝑜 = 0 and ∆𝑒𝑜 =

∆𝑅1 𝑅 1

4+2 ∆𝑅1 /𝑅

𝑒𝑖

Voltage Sensitive Bridge It is clear from above equation that the input-output relationship i.e., relationship between ∆ R and ∆ 𝑒𝑜 is non-linear. However, if the change in resistance is very small as compared to initial resistance then we have: 2(∆𝑅1 /𝑅) ≪ 4. ∆𝑒𝑜 =

∆𝑅1 𝑅

4

𝑒𝑖 so ∆𝑒𝑜 = 𝑒𝑖

• For such cases, the input-output relationship is linear. The major disadvantage of a voltage sensitive deflection bridge as compared to voltage sensitive null bridge is that the calibration of the former is dependent upon the value of supply voltage 𝑒𝑖 . • Therefore for constancy of calibration., the input voltage should be absolutely constant.

Current Sensitive Bridge • When using galvanometers at the output, terminals, the resistance of the meter cannot be neglected as galvanometers draw an appreciable current. • Under such circumstances, wherein the measuring device has a low impedance, the deflection is on account of the meter current 𝑖𝑚 , which cannot be assumed to be zero, the bridge is said to be a current sensitive bridge. • In order to find the input-output relationship and the bridge sensitivity for this general case, it is necessary to convert the bridge circuit of Fig. 4, to a Thevenin generator looking into the output terminals B and D.

Fig. 4: Thevenin Equivalent circuit of Wheat stone bridge

Current Sensitive Bridge open circuit voltage of the Thevenin generator (𝑅1 𝑅4 −𝑅2 𝑅3 ) 𝑒𝑜 = 𝑒 (𝑅1 + 𝑅2 )(𝑅3 + 𝑅4 ) 𝑖 The internal resistance of the Thevenin generator is found from looking into terminals B and D and shorting terminals A and C as shown in Fig. 4 (a). The internal resistance of the Thevenin generator looking into the terminals B and D and is :

𝑅1 𝑅2 𝑅3 𝑅4 (𝑅1 𝑅2 )(𝑅3 + 𝑅4 ) + (𝑅3 𝑅4 )(𝑅1 + 𝑅2 ) + = 𝑅1 + 𝑅2 𝑅3 + 𝑅4 (𝑅1 + 𝑅2 )(𝑅3 + 𝑅4 ) The current through the meter is given by : 𝑅𝑜 =

𝑖𝑚 =

𝑒𝑜 𝑅0 + 𝑅𝑚

(𝑅1 𝑅4 −𝑅2 𝑅3 )𝑒𝑖 1 𝑅2 )(𝑅3 + 𝑅4 )+(𝑅3 𝑅4 )(𝑅1 + 𝑅2 )+ 𝑅𝑚 (𝑅1 + 𝑅2 )(𝑅3 + 𝑅4 )

= (𝑅

Let 𝑅1 = 𝑅2 = 𝑅3 = 𝑅4 = 𝑅 and ∆R is the change in R. 𝑖𝑚

(𝑅 + ∆R) 𝑅 − 𝑅2 𝑒𝑖 = (𝑅 + ∆R)(𝑅)(2𝑅) + 𝑅2 (𝑅 + ∆R + 𝑅) + 𝑅𝑚 (𝑅 + ∆R + 𝑅)(2𝑅)

Current Sensitive Bridge When ∆𝑅 ≪ 𝑅 ∆R/𝑅2 𝑒𝑖 We have 𝑖𝑚 = 4 (1+ 𝑅 /𝑅) 𝑚

Voltage output under load conditions is: ∆R/𝑅2 𝑒𝑖 𝑅𝑚 ∆R/𝑅 𝑒 𝑒𝑜𝑙 = 𝑖𝑚 𝑅𝑚 = (1+ 𝑅 /𝑅) 4 = (𝑅+ 𝑅 )𝑖 𝑚

𝑚

𝑅𝑚 4

=

∆R/𝑅 𝑒𝑖 4(1+𝑅/𝑅𝑚 )

From Eqn. 26'55, it follows that open circuit voltage ∆R 𝑒𝑜 = 𝑒 4𝑅 𝑖 The voltage under loaded conditions is : 𝑒𝑜𝑙 =

𝑒𝑜 𝑅𝑚 (𝑅0 + 𝑅𝑚 )

So Ratio of voltage under loaded and no load: 𝑒𝑜𝑙 1 = 𝑒𝑜 (1 + 𝑅0 /𝑅𝑚 )

Operational Amplifiers (Op Amps)

Operational Amplifiers (Op Amps)

• • • • • •

Ideal Op Amp Non-inverting Amplifier Unity-Gain Buffer Inverting Amplifier Differential Amplifier Current-to-Voltage Converter

Ideal Op Amp i

i 1)

v

v

VDD

VSS  v0  VDD

+

vo

-

VSS

v0  Av  v  v  The open-loop gain, Av, is very large, approaching infinity.

2)

i  i  0 The current into the inputs are zero.

Ideal Op Amp with Negative Feedback v

+

v

-

vo

Network

Golden Rules of Op Amps:

1. The output attempts to do whatever is necessary to make the voltage difference between the inputs zero. 2. The inputs draw no current.

Non-inverting Amplifier v

vi

v

R1

+

vo

Closed-loop voltage gain

AF 

-

vo vi

R2 vi  v  v 

AF 

R1 vo R1  R2

vo R  1 2 vi R1

Unity-Gain Buffer vi

v

v

Closed-loop voltage gain

+ -

vo

AF 

vo vi

vi  v  v  vo AF 

vo 1 vi

Used as a "line driver" that transforms a high input impedance (resistance) to a low output impedance. Can provide substantial current gain.

Inverting Amplifier R2

Current into op amp is zero

v  v  0 vi  0 vi ii   R1 R1

ii 

0  v0 v0  R2 R2

vi

ii

ii

R1

v v

+

vi v0  R1 R2 AF 

vo R  2 vi R1

vo

Differential Amplifier R2 Current into op amp is zero

v1

v  v

v2

v1  v i1  R1

R2 v2 R1  R2

R1

v v

+

R1

R2

v  v0 i1  R2 v 

i1

i1

v1  v v  v0  R1 R2

v1 

R2 R2 v2 v2  v0 R1  R2 R1  R2  R1 R2

vo

Differential Amplifier R2

R2 R2 v1  v2 v2  v0 R1  R2 R  R2  1 R1 R2 v0  

v1 v2 2 2

R2 R2 R v1  v2  v2 R1 R1  R2 R1  R1  R2 

R2 R2  R2  v0   v1  1   v2 R1 R1  R2  R1 

i1

R1

v v

i1

+

R1

R2

R2 v0   v2  v1  R1

vo

Current-to-Voltage Converter v

v

ii

+

vo

-

RF

if

ii  i f

v  v  0 0  v0  i f RF

v0  ii RF Transresistance  v0 ii   RF

Photodiode Circuit ii  25 A per milliwatt of incident radiation v

v h

ii

+

vo

-

At 50 mW

RF

if

ii  50  25 106  1.25mA

Assume RF  3.2k

v0  ii RF  1.25  103  3.2  103  4V

Instrumentation Amplifier • Instrumentation amplifier is a kind of differential amplifier with additional input buffer stages. The addition of input buffer stages makes it easy to match (impedance matching) the amplifier with the preceding stage. Instrumentation are commonly used in industrial test and measurement application. The instrumentation amplifier also has some useful features like low offset voltage, high CMRR (Common mode rejection ratio), high input resistance, high gain etc. The circuit diagram of a typical instrumentation amplifier using op-amp is shown below.

Instrumentation Amplifier • The output measuring devices require power for their operation. This power is usually-drawn from the measuring circuit itself. The electromechanical output devices require power which typically ranges from a few micro watt in the case of sensitive moving coil instruments to a few watt in the case of recorders. • In many applications, the measuring circuits cannot supply the power demanded by the output devices. Thus, if an output device is directly connected to the circuit, the signal gets distorted . On account of the loading effects the instrumentation amplifiers, in such cases, are required to supply the necessary power required by the output devices in order that the signal is faithfully measured, displayed or recorded.

Instrumentation Amplifier An instrumentation amplifier should have the following properties: • It should be able to supply power at a specified power level a voltage or a current which is directly proportional to the quantity under measurement, • The power extracted from the measurement system should be as small as possible, • It should faithfully follow the variations in the quantity under measurement • it should operate on the least possible auxiliary power, • it should have a long operating life and a high degree of reliability, • the amplifier should have a high input impedance and low output impedance.

Active Low Pass Filter By combining a basic RC Low Pass Filter circuit with an operational amplifier we can create an Active Low Pass Filter circuit complete with amplification

• Passive filters can be made using just a single resistor in series with a nonpolarized capacitor connected across a sinusoidal input signal. But gain of such filters can not be more than unity. • With Multiple stage this loss in signal amplitude is called “attenuation” can become quiet severe. • One way of restoring or controlling this loss of signal is by using amplification through the use of Active Filters.

Active Low Pass Filter • As their name implies, Active Filters contain active components such as operational amplifiers, transistors or FET’s within their circuit design to boost or amplify the output signal. • Filter amplification can also be used to either shape or alter the frequency response of the filter circuit by producing a more selective output response, making the output bandwidth of the filter more narrower or even wider. • An active filter generally uses an operational amplifier (op-amp) within its design and in the Operational Amplifier tutorial we saw that an Op-amp has a high input impedance, a low output impedance and a voltage gain determined by the resistor network within its feedback loop.

Active Low Pass Filter First Order Low Pass Filter

• The amplifier is configured as a voltage-follower (Buffer) giving it a DC gain of one, Av = +1 or unity gain as opposed to the previous passive RC filter which has a DC gain of less than unity. • The advantage of this configuration is that the op-amps high input impedance prevents excessive loading on the filters output while its low output impedance prevents the filters cut-off frequency point from being affected by changes in the impedance of the load. • While this configuration provides good stability to the filter, its main disadvantage is that it has no voltage gain above one. However, although the voltage gain is unity the power gain is very high as its output impedance is much lower than its input impedance.

Active Low Pass Filter Active Low Pass Filter with Amplification

• The frequency response of the circuit will be the same as that for the passive RC filter, except that the amplitude of the output is increased by the pass band gain, AF of the amplifier. For a non-inverting amplifier circuit, the magnitude of the voltage gain for the filter is given as a function of the feedback resistor ( R2 ) divided by its corresponding input resistor ( R1 ) value and is given as:

Active Low Pass Filter

• Therefore, the gain of an active low pass filter as a function of frequency will be: Gain of a first-order low pass filter

Where: AF = the pass band gain of the filter, (1 + R2/R1) ƒ = the frequency of the input signal in Hertz, (Hz) ƒc = the cut-off frequency in Hertz, (Hz)

Active Low Pass Filter • Thus, the operation of a low pass active filter can be verified from the frequency gain equation above as:

Gain of a first-order low pass filter

1. At very low frequencies, ƒ < ƒc

2. 2. At the cut-off frequency, ƒ = ƒc 3. 3. At very high frequencies, ƒ > ƒc

Active Low Pass Filter • Thus, the Active Low Pass Filter has a constant gain AF from 0Hz to the high frequency cut-off point, ƒC. At ƒC the gain is 0.707AF, and after ƒC it decreases at a constant rate as the frequency increases. That is, when the frequency is increased tenfold (one decade), the voltage gain is divided by 10. • In other words, the gain decreases 20dB (= 20*log(10)) each time the frequency is increased by 10. When dealing with filter circuits the magnitude of the pass band gain of the circuit is generally expressed in decibels or dB as a function of the voltage gain, and this is defined as: Magnitude of Voltage Gain in (dB)

Active Low Pass Filter Frequency Response Curve • Example With corner frequency is 159 Hz

Active High Pass Filter

• The basic operation of an Active High Pass Filter (HPF) is the same as for its equivalent RC passive high pass filter circuit, except this time the circuit has an operational amplifier or included within its design providing amplification and gain control. • Like the previous active low pass filter circuit, the simplest form of an active high pass filter is to connect a standard inverting or noninverting operational amplifier to the basic RC high pass passive filter circuit.

Active High Pass Filter First Order High Pass Filter

• Technically, there is no such thing as an active high pass filter. Unlike Passive High Pass Filters which have an “infinite” frequency response, the maximum pass band frequency response of an active high pass filter is limited by the open-loop characteristics or bandwidth of the operational amplifier being used, making them appear as if they are band pass filters with a high frequency cut-off determined by the selection of op-amp and gain.

Active High Pass Filter • A commonly available operational amplifier such as the uA741 has a typical “open-loop” (without any feedback) DC voltage gain of about 100dB maximum reducing at a roll off rate of -20dB/Decade (-6db/Octave) as the input frequency increases. The gain of the uA741 reduces until it reaches unity gain, (0dB) or its “transition frequency” ( ƒt ) which is about 1MHz. This causes the op-amp to have a frequency response curve very similar to that of a first-order low pass filter and this is shown below. Frequency response curve of a typical Operational Amplifier

Active High Pass Filter • Then the performance of a “high pass filter” at high frequencies is limited by this unity gain crossover frequency which determines the overall bandwidth of the open-loop amplifier. • The gain-bandwidth product of the op-amp starts from around 100kHz for small signal amplifiers up to about 1GHz for high-speed digital video amplifiers and op-amp based active filters can achieve very good accuracy and performance provided that low tolerance resistors and capacitors are used. • Under normal circumstances the maximum pass band required for a closed loop active high pass or band pass filter is well below that of the maximum open-loop transition frequency. • However, when designing active filter circuits it is important to choose the correct op-amp for the circuit as the loss of high frequency signals may result in signal distortion.

Active High Pass Filter • A first-order (single-pole) Active High Pass Filter as its name implies, attenuates low frequencies and passes high frequency signals. It consists simply of a passive filter section followed by a non-inverting operational amplifier. • The frequency response of the circuit is the same as that of the passive filter, except that the amplitude of the signal is increased by the gain of the amplifier and for a non-inverting amplifier the value of the pass band voltage gain is given as 1 + R2/R1, the same as for the low pass filter circuit. Active High Pass Filter with Amplification

Active High Pass Filter • This first-order high pass filter, consists simply of a passive filter followed by a non-inverting amplifier. The frequency response of the circuit is the same as that of the passive filter, except that the amplitude of the signal is increased by the gain of the amplifier. • For a non-inverting amplifier circuit, the magnitude of the voltage gain for the filter is given as a function of the feedback resistor ( R2 ) divided by its corresponding input resistor ( R1 ) value and is given as: Gain for an Active High Pass Filter

Where: AF = the Pass band Gain of the filter, ( 1 + R2/R1 ) ƒ = the Frequency of the Input Signal in Hertz, (Hz) ƒc = the Cut-off Frequency in Hertz, (Hz)

Active High Pass Filter 1. At very low frequencies, ƒ < ƒc 2. 2. At the cut-off frequency, ƒ = ƒc 3. 3. At very high frequencies, ƒ > ƒc

• Then, the Active High Pass Filter has a gain AF that increases from 0Hz to the low frequency cut-off point, ƒC at 20dB/decade as the frequency increases. At ƒC the gain is 0.707*AF, and after ƒC all frequencies are pass band frequencies so the filter has a constant gain AF with the highest frequency being determined by the closed loop bandwidth of the op-amp. • When dealing with filter circuits the magnitude of the pass band gain of the circuit is generally expressed in decibels or dB as a function of the voltage gain, and this is defined as:

Active High Pass Filter Magnitude of Voltage Gain in (dB)

• For a first-order filter the frequency response curve of the filter increases by 20dB/decade or 6dB/octave up to the determined cut-off frequency point which is always at -3dB below the maximum gain value. As with the previous filter circuits, the lower cut-off or corner frequency ( ƒc ) can be found by using the same formula:

• The corresponding phase angle or phase shift of the output signal is the same as that given for the passive RC filter and leads that of the input signal. It is equal to +45o at the cut-off frequency ƒc value and is given as:

Active Band Pass Filter The principal characteristic of a Band Pass Filter or any filter for that matter, is its ability to pass frequencies relatively unattenuated over a specified band or spread of frequencies called the “Pass Band”.

• For a low pass filter this pass band starts from 0Hz or DC and continues up to the specified cut-off frequency point at -3dB down from the maximum pass band gain. Equally, for a high pass filter the pass band starts from this -3dB cut-off frequency and continues up to infinity or the maximum open loop gain for an active filter. • However, the Active Band Pass Filter is slightly different in that it is a frequency selective filter circuit used in electronic systems to separate a signal at one particular frequency, or a range of signals that lie within a certain “band” of frequencies from signals at all other frequencies. This band or range of frequencies is set between two cut-off or corner frequency points labelled the “lower frequency” ( ƒL ) and the “higher frequency” ( ƒH ) while attenuating any signals outside of these two points.

Active Band Pass Filter • Simple Active Band Pass Filter can be easily made by cascading together a single Low Pass Filter with a single High Pass Filter. • The cut-off or corner frequency of the low pass filter (LPF) is higher than the cut-off frequency of the high pass filter (HPF) and the difference between the frequencies at the -3dB point will determine the “bandwidth” of the band pass filter while attenuating any signals outside of these points. One way of making a very simple Active Band Pass Filter is to connect the basic passive high and low pass filters we look at previously to an amplifying op-amp circuit as shown. Active Band Pass Filter Circuit

Active Band Pass Filter • This cascading together of the individual low and high pass passive filters produces a low “Q-factor” type filter circuit which has a wide pass band. The first stage of the filter will be the high pass stage that uses the capacitor to block any DC biasing from the source. This design has the advantage of producing a relatively flat asymmetrical pass band frequency response with one half representing the low pass response and the other half representing high pass response as shown.

Active Band Pass Filter • The higher corner point ( ƒH ) as well as the lower corner frequency cut-off point ( ƒL ) are calculated the same as before in the standard first-order low and high pass filter circuits. Obviously, a reasonable separation is required between the two cut-off points to prevent any interaction between the low pass and high pass stages. The amplifier also provides isolation between the two stages and defines the overall voltage gain of the circuit.

• The bandwidth of the filter is therefore the difference between these upper and lower -3dB points. For example, suppose we have a band pass filter whose -3dB cut-off points are set at 200Hz and 600Hz. Then the bandwidth of the filter would be given as: Bandwidth (BW) = 600 – 200 = 400Hz. • The normalized frequency response and phase shift for an active band pass filter will be as follows.

Active Band Pass Filter Active Band Pass Frequency Response

Active Band Pass Filter • While the above passive tuned filter circuit will work as a band pass filter, the pass band (bandwidth) can be quite wide and this may be a problem if we want to isolate a small band of frequencies. Active band pass filter can also be made using inverting operational amplifier. • So by rearranging the positions of the resistors and capacitors within the filter we can produce a much better filter circuit. For an active band pass filter, the lower cut-off -3dB point is given by ƒC1 while the upper cut-off 3dB point is given by ƒC2.

Active Band Pass Filter Inverting Band Pass Filter Circuit

This type of band pass filter is designed to have a much narrower pass band. The center frequency and bandwidth of the filter is related to the values of R1, R2, C1 and C2. The output of the filter is again taken from the output of the op-amp.