Filter Project

Jen Lee, Rupa Pandya, Sagar “the man” Rathie

April 18th, 2007 – PHYS 352 – Digital Electronics

 

Design:

            The scope of our design included the combination of a high Q split supply Bandpass-Biquad Filter with the addition of an active High Pass filter. The type of biquad filter utilizes two integrator feedback loops with an inverter. The design also incorporates the use of either a low-pass or band-pass output depending on where you measure the output. The high pass filter was a Twin-T Chebyshev with current feedback amplifiers. In total, we used 5 op-amps for our design. The individual schematics are shown below.

Characterization:

            The combination of the chebyshev high pass filter and the biquad low pass filter created a response like that of a bandstop, or notch, filter.  The output was attenuated to match the low pass and high pass combination transfer functions as shown below.

 

Transfer and other Relevant Functions:

            We were able to find the transfer functions of each respective design (biquad, highpass, and combined) and created charts showing their phase and magnitude bode plots. They are attached.

 

What we learned:

            This lab was very beneficial to us in understanding how applying various filter designs in different configurations can drastically change the output of the device. The active elements of our filters were also a new attribute that we were able to work with, understand and see how the quality factor of these devices compare to simple analog circuits. Additionally, we were able to see hands-on experience as to how mathematical approaches to electronics can be very helpful in the lab.

 

Combined Filters

Biquad Filter

High Pass Filter

Hz

Gain

Phase

Hz

Phase

Gain

Hz

Gain

Phase

1.0E+00

5.4E-14

-98

1.0E+00

174

2.2E-10

1.0E+00

4.0E-13

90

7.9E+00

4.5E-13

-90

7.9E+00

180

2.3E-10

1.6E+01

6.4E-12

90

2.5E+01

3.2E-12

-92

3.2E+01

171

2.8E-09

7.9E+01

6.9E-11

94

3.2E+01

3.1E-12

-91

2.0E+02

0

6.1E-12

7.9E+02

3.3E-10

84

5.0E+01

2.0E-12

92

7.9E+02

0

3.8E-13

3.2E+03

1.2E-09

30

2.0E+02

3.0E-13

94

2.0E+04

-57

5.7E-17

1.3E+04

1.5E-09

10

5.0E+02

1.3E-13

100

6.3E+04

177

3.1E-14

3.2E+04

2.5E-09

-1

2.5E+03

5.4E-14

40

2.0E+05

170

3.4E-13

1.3E+05

1.4E-09

-20

1.6E+04

1.7E-15

1

5.0E+05

156

2.0E-12

3.2E+05

1.0E-09

-43

3.2E+04

5.5E-15

-60

2.0E+06

104

2.1E-11

4.0E+05

9.0E-10

-49

4.0E+04

1.1E-14

60

7.9E+06

16

4.5E-11

1.3E+06

3.7E-10

-66

7.9E+04

5.1E-14

177

 

 

 

1.6E+06

3.1E-10

-66

1.3E+06

1.0E-11

115

 

 

 

4.0E+06

2.2E-10

-71

7.9E+06

3.5E-11

17

 

 

 

5.0E+06

2.2E-10

-83

 

High Pass Characterization

            When choosing a complementary filter to use in conjunction with the biquad the original plan was to build a Sallen Key Chebyshev high pass filter.  However, the break frequency was discovered to be far from the calculated value, thus we built a Twin T Chebyshev high pass filter.  A schematic is provided below.  The relative resistor and capacitor ratios were assigned as indicated to the left of the schematic.  We did not have the exact values of resistors needed, however we used the closest values.  R1 and R2 had values of 820 ohms, R3 390 ohms, C1 .1μF and C2 2.2μF.  With an overall R value of 1000 ohms and a C value of .1μF, the theoretical break frequency was calculated to be about 1.59kHz.  The high pass response was tested using a function generator and an oscilloscope.  It was found that the break frequency occurred at about 1.39 kHz.  Considering that our resistors were not of the exact ratio as expressed in the schematic, this error of 12.6% was expected. 

The graphs above demonstrate the gain and phase behavior of the filter when a sine wave was applied to the filter.  The high pass filter did show the expected behavior of attenuating low frequencies while allowing higher frequencies to pass.  The phase also showed the expected behavior, with the phase change decreasing as the frequency increased.

 

Biquad Characterization

Easily the most important aspect of our filter was the use of the split supply Biquad bessel active filter. This device is a combination of two-integrator feed back loops and an invertor which we characterized to act as a low-pass filter.  This was done by taking the output after the inverter. For our design, we used various resistor combinations to achieve a break frequency at about 10 KHz, however our actual value was around 11.2KHz. An error of 10.71% is understandable considering the error discrepancies and magnitude difference between resistors. We selected our capacitors to be exactly 22uF (C1 and C2) and our resistor values were 227Ω ( R2, R4) and 10KΩ (R1, R3, R5, R6) depending on the feedback desired.  Below, we have 2 graphs indicating the gain and phase when a sinusoidal signal was applied to the filter. Our filter worked well as a low-pass, allowing a majority of signals to pass before cutting off at 11.2Khz.  However, ater the cutoff frequency, the filter started passing signals again. This could possibly be due to the op-amps being used.

 

Combined Filter Characterization

            As per project specifications, we were asked to combine a basic filter with a biquad of some sort. Our group chose the Cheybyshev high pass filter in conjunction with the bandpass biquad low pass filter. With the combination of the low pass bandpass biquad first and then the high pass filter we expected to have a resulting bandstop, also  known as a notch filter. This would collectively limit only a certain frequencies that would pass through the filter. This frequency range was dependent on the characteristics of the filter combinations itself, including the Q factor, active elements, RC combinations, and overall break-frequencies for component circuits. We installed our high-pass filter to input the output from the Biquad at the low-pass port. So essentially we combined the high-passing elements of the Twin-T and the low-passing elemnts of the biquad to create a region of conflicting activity. This collective area is the actual band-stop range. Our break frequency for the HighPass was 1.39KHz and for the Biquad was 11.2KHz. We hypothesized that the Band-Stop range would occur between 1.39Khz and 11.2KHz, however, it was actually larger, occuring between 99Hz and 10.2Khz. We believe the reason for the offset was in response to the respective Q factors of each circuit. The biquad’s Q factor actually decreases with frequency, while the active high pass’ Q factor remains constant. Thus, at lower frequencies, the high-pass filter could “overpower” the effects of the biquad to create a passing element which attenuates at smaller frequencies.   Our circuit diagram is shown above and our graphs of Gain and Phase are attached below. Additonally, we have attached our calculations for determining Poles and Zeros for the filters. Yeay for Filters.