Analysis: Designing an Active Notch Filter

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  • Topic: Low-pass filter, High-pass filter, Band-pass filter
  • Pages : 11 (1978 words )
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  • Published : October 15, 2010
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1. Objectives:
o To design a active notch filter which have a bandwidth of 500kHz o To analyses the designed notch filter

2. Equipments and Components :
o Power supply of + 15V x 1 o Function generator x 1 o Oscilloscope x 1 o LM318 op-Amp x 2 o Resistor 3.3KΩ x 3 o Resistor 10kΩ x 3 o Resistor 1kΩ x 1 o Capacitor 0.1uF x 2

3. Theory:

Figure 1

One of the design of the active filter is by using a bandpass filter cascadeted with a summing amplifier as shown in figure 1. notch filter is made by subtracting the output of a bandpass filter from the original signal. For the frequencies in the notch filter’s passband, the output of the bandpass filter section approaches zero. Therefore, input Ei is transmitted via adder input resistor R1 to drive Eo to a value equal to –Ei. Thus Eo =-E1 in both lower and upper passband of the notch filter. Suppose that the frequency of the Ei is adjusted to resonant frequency fr of the narrow bandpass filter component(fr of the bandpass sets the notch frequency). Ei will exit from the bandpass as –Ei and then is inverted by R1 and R to drive Eo to +Ei. However, Ei is transmitted via R2 to drive Eo to –Ei. Thus, Eo responds to both inputs of the adder and becomes Eo = Ei-Ei = 0V at fr.

In practice, Eo approaches zero only at fr. The depth of the notch depend on how closely the resistor and capacitors are matched in the bandpass filter and judicious fine adjustment of the resistor R1 at the inverting adder’s input.

The notch or band reject filter is named for the characteristics shape of its frequency response curve as show in figure 2. unwanted frequency are attenuated in the stopband B. The desired frequencies are transmitted in the passband that lies on the either side of the notch. Notch filter usually have a passband gain of unity or 0dB. The equations for Q, B, fl, fh and fr are identical to those of its associated bandpass filter.

Figure 2

Figure 3

From notch filter in figure 3, the formula use to get the B, Q, fr, R, C Rr is as follow:

B = fL - fH where fL is lower cutoff frequency fH is Upper cutoff frequecy

Q = fr / B where fr is resonant frequency/notch frequency

Fr = √fLfH

R = 0.1591 / BC

Rr = R / (2Q2- 1)

4. Procedure/ Metrology to design a notch filter

1. The lower cutoff frequency and upper frequency is determined for the desired notch filter. In this design, the fL = 500kHz and fH = 1MHz. 2. By fixing the value of the capacitor used and using the formula given in the theory, a bandpass filter that has the same resonant frequency fr, bandwidth B, and consequently Q as the notch filter is made. 3. Connect the inverting adder as shown in the figure 3 by selecting equal values of R. usually, R = 10kΩ and by using a simulation software, the circuit is simulated to conform the result desired before constructing the circuit. 4. Construct the circuit as shown in the figure 3, and the input voltage and output voltage is measured at different frequency at lower frequency, notch frequency and upper frequency. 5. from the measured...
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