原创 Design of a Notch Filter

In my last blog, we saw an application in medical electronics. Let’s continue that in this blog too where we will see a circuit that is used to eliminate noise in the signal processed by the ECG.

Coming back to ECG, we know it is a piece of equipment which measures the beating of the heart. We saw the bio-electric amplifier which amplifies the signals generated by the beating for further processing. If we plot the frequency spectrum of such an input signal you are bound to find a peak at about 60 Hz (or 50 Hz in some cases) – something like the diagram below.

http://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Mains_hum_spectrum.png/220px-Mains_hum_spectrum.png

You will see a peak at around 60 Hz. Why is this coming? This is due to 60 Hz noise. And the circuit we will be seeing is called the 60-Hz reject filter with gain.

Why does this peak arise? This noise arises from the interference from other current carrying conductors present in the same room. When current flows through a conductor it tends to induce a small current in any other equipment near it. Suppose we have a wire carrying a high current. According to the laws of electromagnetism, this induces a magnetic field around it. This magnetic field in turn induces some current in any circuit nearby. This noisy signal will be at a frequency of 60 Hz which is the frequency of the mains current in many countries (50 Hz in some). So before processing our required signal we must filter it for this noise. For that purpose we use a notch filter. A notch filter is a type of band-stop filter which has a very steep notch at particular frequency. That is at a particular frequency the signal is completely attenuated.

The notch filter we will use is the twin-T notch filter. This is made up of two T-sections – one of low pass and another high pass section – in parallel. The low pass and high pass sections are designed such that they don’t overlap and they both allow low frequencies below the notch frequencies and those above it but not the frequencies at the notch frequency. Let’s see the circuit for it:

You can see that the input signal is given to a twin-T network. The upper part is the low pass circuit and the lower part is the high pass filter. Remember that at high frequencies the impedance of a capacitor is very low while that of an inductor is very high and vice versa. As a result in the upper network at high frequencies the capacitance will be very low - almost a short. Thus the voltage across it is zero. The similar concept is applied to the high pass section. The design is as follows: notch frequency is given by f =; R0=R1= 2.R2 and C1=C2=C0.

Gain can be introduced in this circuit as the opamp is connected as an amplifier. The gain will be determined by the ratio of  the resistors R4 and R3.

This is the frequency response:

Note the notch at 60 Hz, and also note the quality factor is not too good. For our application, the quality factor must be much better than this.

For that in real life a reject filter with variable Q is used. The circuit is given below:

The Q in this circuit depends on the ratio of resistors R6 and R7.. Increase this ratio and note how the Q varies.

You can check these videos out:

https://www.youtube.com/watch?v=sBEFyMbi2Zo

For another application of notch filter:

https://www.youtube.com/watch?v=01EB6W0HZuk