Experiment 3 : Band Reject Filter Objective: To design an active band reject filter circuit and observe its frequency response. Equipments:
Theory:
• • • • • • • • •
OP –AMP 741 Resistors Capacitors DC power supply (for biasing) Signal Generator Trainer Board Oscilloscope DMM Wires
Band Stop Filter: This kind of filter passes all frequencies above and below a particular range set by the component values. Stopband filters can be constructed using a low-pass and a high pass filter. However, rather than the cascaded configuration used for the pass-band filter, a parallel arrangement is required. A low-frequency f1 can pass through the low-pass filter, and a higher-frequency f2 can use the parallel path. However, a frequency such as fo in the reject-band is higher than the low pass critical frequency and lower than the high-pass critical frequency, and is therefore prevented from contributing to the levels of Vo above 0.707Vmax.
The bandpass filter passes one set of frequencies while reject-ing all others. The band-stop filter does just the opposite. It rejects a band of frequencies, while passing all others. This is also called a bandreject or band-elimination filter. Band-stop filter is exactly opposite to the bandpass filter in performance i.e., it has a bandstop between two cut-off frequencies fH and fL and two passbands, 0 < f < fL and f > fH. f0 is called the centre frequency, since it is approximately at the centre of the passband or stopband.
Like band-pass filters, band-stop filters may also be classified as (i) wide-band and (ii) narrow band reject filters. Wide Band-Stop (or Reject) Filter: A wide band-stop filter using a low-pass filter, a high-pass filter and a summing amplifier is shown in figure. For a proper band reject response, the low cut-off frequency fL of high-pass filter must be larger than the high cut-off frequency fH of the low-pass filter. In addition, the passband gain of both the highpass and low-pass sections must be equal. Narrow Band-Stop Filter: This is also called a notch filter. Because of its higher Q, which exceeds 10, the bandwidth of the narrow band reject filter is much smaller than that of a wide band reject filter. It is commonly used for attenuation of a single frequency such as 60 Hz power line frequency hum. The most widely used notch filter is the twin-T network illustrated in fig. below. This is a passive filter composed of two T-shaped networks. One T-network is made up of two resistors and a capacitor, while the other is made of two capacitors and a resistor.
Twin T active Notch Filter:
The frequency response of the active notch filter is shown below
Notch filters are most commonly used in communications and biomedical instruments for eliminating the undesired frequencies. A notch filter is a band-stop filter with a narrow stopband (high Q factor). Band reject filter rejects a band of frequencies, whereas notch filter rejects one particular frequency.
Twin T passive Notch Filter:
A mathematical analysis of this circuit shows that it acts as a lead-lag circuit with a phase angle, shown in fig. (b). Again, there is a frequency fc at which the phase shift is equal to 0°. In fig. (c), the voltage gain is equal to 1 at low and high frequencies. In between, there is a frequency fc at which voltage gain drops to zero. Thus such a filter notches out, or blocks frequencies near fc. The frequency at which maximum attenuation occurs is called the notch-out frequency given by fn = Fc = 2∏RC Notice that two upper capacitors are C while the capacitor in the centre of the network is 2 C. Similarly, the two lower resistors are R but the resistor in the centre of the network is 1/2 R. This relationship must always be maintained.
Design of band reject filter The best way to implement a band reject filter is to sum together the outputs of a low pass and highpass filter.
Figure: Block diagram of Band reject Filter The best implementation is definitely NOT a low Q (in order to widen the stop band or increase the bandwidth) notch filter.
Some points are worth noting:
The figure shows that although both filters have identical 3 dB points, there is much more rejection of unwanted signals in the stop band with the low pass summed with the high pass than there is with the notch filter - with the single exception of the center frequency.
The performance increase that comes with summing low pass and high pass filter outputs comes at the expense of an additional opamp - the opamp that performs the summing function.
Higher order low pass and high pass filters will improve the performance of the band reject filter.
The farther apart the pass bands are, the better the performance of the band reject filter.
Active Low Pass Filter The most common and easily understood active filter is the Active Low Pass Filter. Its principle of operation and frequency response is exactly the same as those for the previously seen passive filter, the only difference this time is that it uses an op-amp for amplification and gain control. The simplest form of a low pass active filter is to connect an inverting or non-inverting amplifier, the same as those discussed in the Op-amp tutorial, to the basic RC low pass filter circuit as shown. First Order Active Low Pass Filter
This first-order low pass active filter, consists simply of a passive RC filter stage providing a low frequency path to the input of a non-inverting operational amplifier. 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. If a voltage gain greater than one is required we can use the following filter circuit. 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:
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) Thus, the operation of a low pass active filter can be verified from the frequency gain equation above as: 1. At very low frequencies, ƒ < ƒc,
2. At the cut-off frequency, ƒ = ƒc,
3. At very high frequencies, ƒ > ƒc,
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 (= 20log 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 ordB as a function of the voltage gain, and this is defined as: Magnitude of Voltage Gain in (dB)
Active High Pass Filters The basic electrical operation of an Active High Pass Filter (HPF) is exactly the same as we saw for its equivalent RC passive high pass filter circuit, except this time the circuit has an operational amplifier or op-amp included within its filter 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 non-inverting operational amplifier to the basic RC high pass passive filter circuit as shown. First Order Active 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. 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
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) Just like the low pass filter, the operation of a high pass active filter can be verified from the frequency gain equation above as: 1. At very low frequencies, ƒ < ƒc,
2. At the cut-off frequency, ƒ = ƒc,
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 0.707AF, 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: 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 Summing Amplifier The Summing Amplifier is a very flexible circuit based upon the standard Inverting Operational Amplifierconfiguration that can be used for combining multiple inputs. We saw previously in the inverting amplifier tutorial that the inverting amplifier has a single input voltage, ( Vin ) applied to the inverting input terminal. If we add more input resistors to the input, each equal in value to the original input resistor, Rin we end up with another operational amplifier circuit called a Summing Amplifier, "summing inverter" or even a "voltage adder" circuit as shown below. Summing Amplifier Circuit
The output voltage, ( Vout ) now becomes proportional to the sum of the input voltages, V1, V2, V3 etc. Then we can modify the original equation for the inverting amplifier to take account of these new inputs thus:
However, if all the input impedances, (Rin) are equal in value the final equation for the output voltage is given as: Summing Amplifier Equation
We now have an operational amplifier circuit that will amplify each individual input voltage and produce an output voltage signal that is proportional to the algebraic "SUM" of the three individual input voltagesV1, V2 and V3. We can also add more inputs if required as each individual input "see's" their respective resistance, Rin as the only input impedance. This is because the input signals are effectively isolated from each other by the "virtual earth" node at the inverting input of the op-amp. A direct voltage addition can also be obtained when all the resistances are of equal value and Rf is equal to Rin. The Summing Amplifier is a very flexible circuit indeed, enabling us to effectively "Add" or "Sum" together several individual input signals. If the inputs resistors, R1, R2, R3 etc, are all equal a unity gain inverting adder can be made. However, if the input resistors are of different values a "scaling summing amplifier" is produced which gives a weighted sum of the input signals.
Reference: 1. 2. 3. 4.
http://www.electronics-tutorials.ws/filter/filter_5.html http://www.electronics-tutorials.ws/filter/filter_5.html http://www.electronics-tutorials.ws/opamp/opamp_4.html
Chapter 14.8 from Fundamentals of Electric Circuits by Alexander and Sadiku
Data:
R1=10 KΩ R2=3.3 KΩ R3=18 KΩ C1=0.01 µF C2=0.047 µF Data Table: No.
f
Vin
Low Av1= pass Vo2/ O/P,Vo1 Vi
High Pass O/P,Vo2
Av2= Vo2/ Vi
V0
Av= Vo/ Vi
50 Hz … … …
Procedure: 1. Figure out the pin out of the 741 IC. Connect positive bias voltage (+10 V) to pin 7 and connect negative bias voltage (-10 V) to pin 4. Pins 1, 5 and 8 should be left alone.
2. Construct the circuit and connect a signal generator to the input and an oscilloscope channel to the output. 3. Rotate the frequency knob of the signal generator; at low frequencies and at very high frequencies the output signal should be amplified and in the middle the output should be attenuated.
4. Measure Vo for the range of frequencies and record values in the table above. 5. Calculate theoretical cutoff frequencies using the following formula and compare with the practical ones. ωc1=1/ R3C2 ; fc2=1/ 2π R3C2 [Low pass] ωc2=1/ R3C1 ; fc2=1/ 2π R3C1 [High Pass]
Circuit diagram: R1
R1
10k
10k
1
V-
uA741 2
4
-10 Vdc
-
OS1
5
V+
3
+
R1
OS2
Vo2
10k
10k
7
0.01uF
R1
6
OUT
C1
R3 18k 10 Vdc
uA741 2
10k
-
V-
R1
4
-10 Vdc
OS1
OUT
R2
7 3
OS2
OUT 2
-
V-
C2 0.047uF
18k
+
V+
R3
OS1
Vo1
4 -10 Vdc
R1 10k
R1 10k
5 R1 10k
10 Vdc
6
uA741
OS2
3.3k
5
1
+
Vo
6
7
3
10 Vdc
V+
Vin
1
Questions: 1. What is the difference between a band reject filter and a notch filter? What is the relationship between Q factor and Bandwidth? 2. What order high pass and low pass filters have been used in the circuit? Does active high pass filters have infinite frequency response like the passive ones? What limits the frequency response of the active high pass filter? 3. Draw a twin T passive notch filter. What relationships between the resistors and capacitors have to be maintained? 4. Which elements in the circuit you implemented during the experiment will determine the upper and lower cutoff frequencies of the band reject filter. 5. Design a non-inverting active low pass filter circuit that has a gain of ten at low frequencies, a high frequency cut-off or corner frequency of 159Hz and an input impedance of 10KΩ. Assume a value for resistor R1 of 1kΩ. Draw the final circuit. [2 points] 6. A first order active high pass filter has a pass band gain of two and a cut-off corner frequency of 1 kHz. If the input capacitor has a value of 10nF, calculate the value of the cut-off frequency determining resistor and the gain resistors in the feedback network. You have to assume some values. Draw the final circuit. [2 points] 7. Find the output voltage of the following Summing Amplifier circuit. [2 points] Summing Amplifier
