Reject Band Active Filters

Francesca Ríos Miller

A reject band activate filter is a filter that is able to block any potency between a selected interval. To understand this type of filter we have to know some terms like active filters of low pass and high pass, adder, and Butterworth filters. An activate filter is an analog circuit characterized because it has at least one activate component besides of the capacitors and resistances. One of the advantages of this type of circuit is that it produces a response very close to the one we want, making them more effective than passive filters.

Active filters can be design to control the frequency that are going to pass and the ones that not, these frequency is known as cutting frequency. There are four types of active filters: high pass, low pass, band pass, and reject band. Each one of this filters have a specific function that repel or let it pass a wide band determined by the cutting frequency. A high pass filter let pass every frequency greater than it cutting frequency. On the other hand a low pass filter let only pass a frequency smaller than it cutting frequency. These terms are important to understand what a reject band filter is because this filter is a combination of these two basic filters.

Another concept that we should know is the adders. These components are use to join the basics filters and construct the reject band desire filter. An adder is an operational amplifier with negative feedback. The exit of the adder is equal to the negative of the sum of the voltages connected to the inverse entrance multiply by the ratio of the resistance of feedback and the resistance of the entrances:

Vout=-R_f/R_in ∑_(i=1)^n▒〖V_i 〗

where n is the total of entrance of the adder assuming that they all have the same resistance. This concept is the one use to make a reject band filter because the entrances would be the voltages of exit of the low pass and high pass filters. For this reason the filter is designed with the exit of the adder with the desire parameters.

The last concept that we should know is the Buttersworth filter, an activate filter with two poles. The rejected amplitude decline more quickly when it has a greater quantity of poles in the filter, making it to react quick than a pole of one filter. This model is selected also because the response of this filter is closer to the desire response compare to the response of other filters. To determine the cutting frequency we choose the values of the resistance and capacitors to calculate the equation that define the Butterworth filter which is

f_c=1/2πRC

An example of this type of filter is one that is able to pass any frequency smaller than 500Hz and greater than 5kHz. This filter could be designed with three op-amps. The capacitors are fixed to be 33nF for the low pass and high pass filters, to select the desire cutting frequencies which are 500Hz and 5kHz. For the low pass filter can be use a resistance of 10kΩ and for the high pass filter one of 1kΩ. With this values, that were choose with the equation of f_c, the values of R and C required can be determine to make the equality.

To construct this circuit the entrance is connected to two Buttersworth filters, the superior is low pass and the inferior is high pass. The exits of the two filters enter to an adder, which exit is finally the reject band signal. The rejected wide of band is of 500Hz to 5kHz.