Multiple Feedback Bandpass Filter (MTB) filter circuit.
Introduction:
To develop the frequency response of a second–order band pass filter, we first apply the transformation equation of to the first order low pass transfer function:
Then replacing s with, we get the general transfer function for a secondorder band pass filter which is:
…………………………………. Equation 1
In the design of bandpass filters, the gain at the midfrequency and the quality factor (Q) (which represents the selectivity of the band pass filter) are the main parameter of interest.
Therefore, we replace with and with 1/Q in Equation 1 above to obtain the following equation below:
………………………. Equation 2
Figure 1 below shows the gain responses of a second order band pass filter, which has been normalized, for different Qs. The graph also shows that the frequency response gets steeper with rising Q, thus making the second order band pass filter to be more selective.
Procedure:
Use band 8, 9, and 13 as it can be seen in table 1 below.
The circuits for band 8, 9, and 13 were constructed on multism by following figure 3 below.
Band 8 circuit was achieved by constructing it in multism by following figure 3 above but the value of the following components was changed as follows: ,, , , and finally
The resulting circuit looked as figure 4 shown below:
Figure 4
The second circuit of band 9 was achieved by constructing it in multism by following figure 3 above but the value of the following components was changed as follows: (theoretical value), , , , and finally
The resulting circuit looked as figure 5 shown below:
Figure 5
The third and last circuit of band 13 was achieved by constructing it in multism by following figure 3 above but the value of the following components was changed as follows: (theoretical value), , , , and finally
The resulting circuit looked as figure 6 shown below:
Figure 6
Results:
After simulation in multism, the following results were observed. For Band 8, the result is as shown in figure 7 and 8 below.
Figure 7 Figure 8
For the second circuit two, Band 9, the result are as shown in figure 9, 10, 11, 12 and 13 below.
Figure 9 Figure 10
Band 9 by using Oscilloscope in the lab:
Figure 11 Figure 12
Band 9 by using spectrum Device:
Figure 13
For the third and last circuit, Band 13, the result is as shown in figure 14 and 15 below.
Figure 14 Figure 15
Measured Centre Frequency (Hz)  Calculated Centre Frequency (Hz)  Measured
Bandwidth (Hz)

Calculated
Bandwidth (Hz) 

BAND 8  164.6183  165.58  (188.2073145.4213) = 42.786  42.33 
BAND 9  200.7422  199.55  (227.2422175.5821)
= 51.6601 
51.01 
BAND 13  500.007  570.57  (571.6565450.5496) = 121.1069  120.94 
Calculations:
For band 8 circuit, the calculation of Q, Bandwidth and are as shown below:
Midfrequency:
Gain at midfrequency:
Gain in dB:
Band pass filter quality:
Bandwidth:
For band 9 circuit, the calculation of Q, Bandwidth and are as shown below:
Midfrequency:
Gain at midfrequency:
Gain in dB:
Band pass filter quality:
Bandwidth:
For band 13 circuit, the calculation of Q, Bandwidth and are as shown below:
Midfrequency:
Gain at midfrequency:
Gain in dB:
Band pass filter quality:
Bandwidth:
Discussion:
The calculated parameter and the measured parameters are in harmony with each other, with little variations. For example, the measured mid frequency for band 8, 9, and 13 are 164.6183 Hz, 200.7422 Hz, and 500.007 Hz in that order. On the other hand, the calculated values are 165.58 Hz, 199.55 Hz, and 570.57 Hz respectively. The slight difference between the measured and the calculated is as a result of components variation. For instance, the exact resistor may be not available and so we use the approximately available resistor. Also, resistor tolerance and temperature drift contribute to the variation of the measured and calculated values especially the Centre frequency as we have seen in our result and calculation.
Conclusion:
To conclude, multiple feedback bandpass filter has an advantage of not using a bulky and expensive inductor. It also requires only one op amp device making it simple to create and use. Getting the circuit parameters by calculation and by experiment was easy and simple making the filter ideal for many occasion. The only disadvantage of this filter is that adjusting the center frequency is not independent.
References:
Zumbahlen, Hank. “Multiple Feedback BandPass Design Example.” Multiple Feedback Band Pass Design Example – Analog Devices. N.p.
<www.analog.com/media/en/trainingseminars/tutorials/MT218.pdf>.
Kugelstadt, Thomas. “Chapter 16 Active Filter Design Techniques.” Chapter 16 – Active Filter Design Techniques – Electro. N.p.
<electro.uv.es/asignaturas/ea2/archivos/sloa088.pdf>.
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