Question

Design, simulate, build, and test a passive first-order bandstop filter to remove a 440Hz noise component from an audio signal. Elements available for your design are

1) Resistors (ranging in value from 1Ohm to 1MOhm)

2) Inductors (5mH, 20mH, 100mH, 200mH, 500mH)*

3) Capacitors (ranging in value from 1nF to 10uF)

*Parasitic Resistances RL (0.9 Ohm, 1.9 Ohm, 13 Ohm, 23 Ohm, 73 Ohm

Answer 1

Introduction

The band stop filter is formed by the combination of low pass and high pass filters with a parallel connection instead of cascading connection. The name itself indicates that it will stop a particular band of frequencies. Since it eliminates frequencies, it is also called as band elimination filter or band reject filter or notch filter. We know that unlike high pass and low pass filters, band pass and band stop filters have two cut-off frequencies. It will pass above and below a particular range of frequencies whose cut off frequencies are predetermined depending upon the value of the components used in the circuit design. Any frequencies in between these two cut-off frequencies are attenuated. It has two pass bands and one stop band. The ideal characteristics of the Band pass filter are as shown below:

Where f_L indicates the cut off frequency of the low pass filter

f_H is the cut off frequency of the high pass filter.

The center frequencies fc = √( f_L x f_H)

The characteristics of a band stop filter are exactly opposite of the band pass filter characteristics.

When the input signal is given, the low frequencies are passed through the low pass filter in the band stop circuit and the high frequencies are passed through the high pass filter in the circuit. This is shown in below block diagram.

n practical, due to the capacitor switching mechanism in the high pass and low pass filter the output characteristics are not same as that of in the ideal filter. The pass band gain must be equal to low pass filter and high pass filter. The frequency response of band stop filter is shown below and green line indicates the practical response in the below figure.

Band Stop Filter Circuit using R, L and C

A simple band stop filter circuit with passive components is shown below:

The output is taken across the inductor and capacitor which are connected in series. We know that for different frequencies in the input the circuit behaves either as an open or short circuit. At low frequencies the capacitor acts as an open circuit and the inductor acts like a short circuit. At high frequencies the inductor acts like an open circuit and the capacitor acts like a short circuit.

Thus, by this we can say that at low and high frequencies the circuit acts like an open circuit because inductor and capacitor are connected in series. By this it is also clear that at mid frequencies the circuit acts like a short circuit. Thus the mid frequencies are not allowed to pass through the circuit.

The mid frequency range to which the filter acts as a short circuit depends on the values of lower and upper cut-off frequencies. This lower and upper cut-off frequency values depends on the component values. These component values are determined by the transfer functions for the circuit according to the design. The transfer function is nothing but the ratio of the output to the input.

Where angular frequency, ω = 2πf