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 second-order band pass filter which is:

………………………………….    Equation 1

In the design of band-pass filters, the gain at the mid-frequency  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 (188.2073-145.4213) = 42.786 42.33
BAND 9 200.7422 199.55 (227.2422-175.5821)

= 51.6601

51.01
BAND 13 500.007 570.57 (571.6565-450.5496) = 121.1069 120.94

 

 

 

Calculations:

For band 8 circuit, the calculation of Q, Bandwidth and  are as shown below:

Mid-frequency:

Gain at mid-frequency:

Gain in dB:

Band pass filter quality:

Bandwidth:

For band 9 circuit, the calculation of Q, Bandwidth and  are as shown below:

Mid-frequency:

Gain at mid-frequency:

Gain in dB:

Band pass filter quality:

Bandwidth:

For band 13 circuit, the calculation of Q, Bandwidth and  are as shown below:

Mid-frequency:

Gain at mid-frequency:

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 band-pass 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 Band-Pass Design Example.” Multiple Feedback Band          Pass Design Example – Analog Devices. N.p.

<www.analog.com/media/en/training-seminars/tutorials/MT-218.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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