# Tape Stop Filter / Band Stop Filter

By combining a basic RC low-passing filter with an RC high-pass filter, we can create a simple tape passing filter that passes a range or frequency band on both sides of the two cutting frequency points. However, we can also combine these low and high-pass filter sections to produce another type of RC filter network called a band stop filter, which can block or at least severely weaken a frequency band within these two cutting frequency points.

The tape stop filter (Bsf) is another type of frequency selective circuit that works in the opposite way to the tape-passing filter we looked at earlier. The tape stop filter, also known as a tape reject filter, passes all frequencies except those in a certain largely weakened stop band.

If this stop band gets too narrow and weakens at a high rate on a few hertz, the tape stop filter is more commonly referred to as a notch filter, since the Frequency response indicates that there is a deep notch with high selectivity (upright side curve) rather than a flattened wider band.

Also, like a tape-passing filter, the tape stop (tape rejection or notch) filter is a circumstial (bipolar) filter with two cutting frequencies, commonly known as -3dB or half power points. This produces a wide stop band bandwidth between two-3dB points.

The function of a tape stop filter then passes all these frequencies from zero (DC) to the first (lower) cutting frequency point to εl, and passes all these frequencies above the second (upper) cutting frequency εh. However, it blocks or rejects all these frequencies. The filters are then defined as bandwidth, BW: (εH – εL).

Therefore, the actual stop tape of the filters for a broadband stop filter is between the lower and upper-3dB points, as it weakens or rejects any frequency between these two cutting frequencies. Therefore, the frequency response curve of an ideal tape stop filter is given as follows:

## Tape Stop Filter Response

From the amplitude and phase curves above for the tape-passing circuit, we can see that the quantities εL, εH and εC are the same as those used to describe the behavior of the tape-passing filter. This is because the band stop filter is an inverted or complimented form of the standard tape-passing filter. In fact, the definitions used for bandwidth, transition band, stop band and central frequency are the same as before. We can use the same formulas to calculate bandwidth, BW, Central frequency, εC and quality factor, Q.

The ideal tape stop filter will have infinite weakening on the stop band and zero weight loss on both transition bands. The transition between the two transition bands and the stop tape will be vertical (brick wall). There are several ways to design a "tape stop filter", and they all achieve the same goal.

In general, tape-passing filters are created by combining a low-pass filter (LPF) with a serially high-pass filter (HPF). Band stop filters are created by combining low pass and high pass filter sections in a configuration of the "parallel" type as seen together.

## Typical Tape Stop Filter Configuration

The sum of high-pass and low-pass filters means that frequency responses do not conflict, unlike the tape-passing filter. This is due to the fact that the start and end frequencies are at different frequency points. For example, let's say that we have a low-pass filter with a cutting frequency. εL is connected in parallel with a high passing filter with a cutting frequency of 200Hz, εH 800Hz Since the two filters are effectively connected in parallel, the input signal is applied to both filters at the same time as shown above.

All input frequencies below 200hz will be transmitted unattended to the output by the low pass filter. Similarly, all input frequencies above 800hz will be transmitted unattended to the output by the high passing filter. However, the input signal frequencies between these two frequency breakpoints of 200Hz and 800hz, that is, from εl to εh, will be rejected by both filters, which create a notch in the output response of the filters.

In other words, a signal with a frequency of 200Hz or less and a frequency of 800Hz and higher will pass unaffected, but the 500hz signal frequency will be rejected because it is too high to be passed by the low pass filter and too low to be passed by the high pass filter. We can show the effect of this frequency characteristic below.

The transformation of this filter characteristic can be easily applied using a single low-pass and high-pass filter circuits isolated from each other by the non-inverted voltage tracker (Av = 1). The output from these two filter circuits is collected using a third operational amplifier, which then connects as a voltage write (collector), as shown.

## Tape Stop Filter Circuit

The use of operational amplifiers in the design of the tape stop filter also allows us to bring voltage gain to the basic filter circuit. Two voltage trackers that do not reverse can be easily converted into a basic non-reversible amplifier with Av = 1 + Rε/Rin gain with the addition of input and feedback resistors, as seen in our non-inverting op-amp tutorial.

Also, if we need a tape stop filter to have -3dB breakpoints at 1khz and 10khz and a stopband gain of -10db between them, we can easily design a low-pass filter and high-pass filter with these requirements and combine them to create our broadband-passing filter design.

## Tape Stop Filter Example

Design a basic broadband, RC band stop filter with a lower cutting frequency of 200Hz and a higher cutting frequency of 800Hz. Find geometric center frequency, -3db bandwidth, and circuit Q.

The upper and lower cutting frequency points for a tape stop filter can be found using the same formula, as shown for both low and high transition filters.

Assuming a capacitor, the C value for both filter sections of 0.1 uf, the values of the two frequency-determining resistances, RL and RH are calculated as follows.

### High Pass Filter Section

From this we can calculate the geometric center frequency, εC:

## Tape Stop Filter Design

Above, we found that simple tape stop filters can be made using first or second degree low and high pass filters together with an unverted aggregation op-amp circuit to reject a wide frequency band. However, we can design and create tape stop filters to produce a much narrower Frequency response to eliminate certain frequencies by increasing the selectivity of the filter. This type of filter design is called a "notch filter".

## Notch Filters

Notch filters are highly selective, high Q band stop filters that can be used to reject a single or very small frequency band rather than all bandwidth of different frequencies. For example, it may be necessary to reject or weaken electrical noise (such as mains humming), which produces a certain frequency induced into a circuit from inductive loads such as motors or ballast lighting or the removal of harmonics, etc.

But in addition to filtering, variable notch filters are also used by musicians in audio equipment such as graphic equalizers, synthesizers and electronic passages to cope with narrow peaks in the acoustic response of music. Then we can see that notch filters are widely used in the same way as low-pass and high-pass filters.

By design, notch filters have a very narrow and very deep stop band around the Central frequencies, and the notch width, selectivity are described exactly the same as the resonance frequency peaks in the Q and RLC circuits.

The most common notch filter design is the twin-t notch filter network. In its basic form, the twin-T configuration, also called parallel tee, consists of two RC branches in the form of three resistors with contrasting and opposing R and C elements in the tee part of its design and two tee sections using three capacitors. As shown, it creates a deeper notch.

## Basic Twin-T Notch Filter Design

The upper T-pad configuration of resistors 2R and capacitor 2c forms the low-passing filter part of the design, while the capacitors form the lower T-pad configuration high passing filter section of C and resistance R. The frequency at which this basic twin-t notch filter design provides maximum weakening is called "notch frequency", εN and given as follows:

## Twin-T Notch Filter Equation

One of the disadvantages of this basic twin-T notch filter design, which is a passive RC network, is that the maximum value of the output (Vout) below the notch frequency is less than the maximum output value above the notch frequency, partly due to the two series resistance (2R) in the low transition filter section.

In addition to unequal gains on both sides of the notch frequency, another drawback of this basic design is that it has a constant Q value of 0.25 in order of 12dB. This is due to the fact that at the notch frequency, the reactances of the two series capacitors are equal to the resistances of the two series resistances, causing the currents flowing in each branch to be out of phase by 180 degrees.

With positive feedback application connected to the center of the two reference legs, we can improve this by making the notch filter more selective. Instead of connecting junction r and 2C to the ground (0v), instead of connecting it to the central pin of a voltage divider network that works with the output signal, the amount of signal feedback set by the voltage divider ratio determines the Q value, which to some extent determines the depth of the notch.