Filter Circuit & Coupled Circuit Study Notes for GATE and Electrical Engineering Exams

By Yash Bansal|Updated : July 25th, 2021

In this article, we will discuss the Filter Circuit & Coupled Circuit which contains the topics Low Pass, High Pass & Band Pass Filter & Magnetic Coupled Circuit.

Table of Content

In this article, we will see about Filter Circuit & Coupled Circuit which contains the topics Low Pass, High Pass & Band Pass Filter & Magnetic Coupled Circuit.

Filter Circuit

A filter is a circuit arrangement that is capable of passing certain frequencies while attenuating the rest of the frequencies. Thus, a filter circuit can pass the desired important frequencies from signals.

In the electronics industries, there are many practical applications for filters. Examples include:

1) Radio communications: Filters allow radio receivers to only "watch" the desired signal while rejecting all other unwanted.

2) DC power supplies: Filters used to eliminate undesired high frequencies (i.e. noise) that are present in AC input lines. Additionally, filters are also used on a power supply output to reduce ripple.

3) Audio electronics: A crossover network is a type of network of filters that are used to channelize the low-frequency audio to woofers while mid-range frequencies to midrange speakers, and high-frequency sounds to tweeters.

4) Analog-to-digital conversion: Filters are placed in front of an ADC input to minimize the aliasing effect.

Filters are linear circuits that can be represented as a two-port network:

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Filter are basically Classified as: 

1) Passive filter

2) Active filter

Passive filters are the type of filter circuits that are developed using resistor, inductor and capacitor as their major elements. They are mostly responsive to a frequency range from100Hz to 300MHz. 

 

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Active filters are those filter circuits that are designed using transistor and op-amp as their basic elements. Along with these elements, circuits of active filters will also contain resistor and capacitor, but not inductors.

Active filters are capable of dealing with very low frequencies (approaching 0 Hz), and can provide a high voltage gain (passive filters cannot).

Active filters can also be used to design the high-order filters without using any type of inductors. However, active filters are least suitable for very-high-frequency applications because of the issue of amplifier bandwidth limitations.

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Filters are further classified on the basis of frequency responses:-

1)  Low-Pass Filter

2) High-Pass Filter

3) Band-Pass Filter

4) Band Stop Filter

5) All-Pass Filter

1) Low Pass Filter: It is a type of filter that passes signals with a frequency lower than a desired cutoff frequency and attenuates signals with frequencies higher than that of the preset cutoff frequency.

2) High Pass Filter: It is a type of filter that passes signals with a frequency higher than a desired cutoff frequency and attenuates signals with frequencies lower than that of the preset cutoff frequency.

3) Band Pass Filter: It is a type of filter that passes signals frequencies within a specific range and cancel (attenuates) frequencies outside that course.

4) Band Stop Filter or Band Rejection Filter: It is a type of filter that passes all frequencies unaltered, but attenuates those in a preset range.

5) All-Pass Filter: It is a signal processing filter that passes all frequencies of the signal.

Some technical terms are mentioned below  that are commonly used when describing filter response curves:

  1. A) -3dB Frequency. This "minus 3dB frequency", corresponds to the input frequency of the signal that causes the output signal to drop by 3dB relative to the input signal. This -3dB frequency is also referred to as the cutoff frequency, and it is the frequency at which the output power is reduced by one-half. This is this frequency is also called the "half-power frequency". 
  2. B) Center frequency (f0) This term used for band-pass type filter and notch type filters, it is a central frequency that occurs between the upper and lower cutoff frequencies. The center frequency is commonly referred to as either the arithmetic mean or the geometric mean of the lower cutoff frequency and the upper cutoff frequency.
  3. C) Bandwidth (B.W). The bandwidth is the space length of the pass-band, and the pass-band is the band of frequencies that do not experience attenuation when moving from the input to the output of the filter.
  4. D) Stop-band frequency (fs). It is a particular frequency at which the attenuation reaches a specified value.

In case of low-pass filter and high-pass filters, frequencies beyond the stop-band frequency are considered as the stop-band.

 For band-pass and notch type filters, two stop-band frequencies do exist. The frequencies between these two stop-band frequencies are considered as the stop-band.

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Coupled Circuits

An electrical circuit is considered to be a coupled circuit if there exists a mutual inductance between the coils.

There are two types of Classification of Coupling:-

1) Electrical Coupling

2) Magnetic Coupling

1) Electrical Coupling: 

Electrical coupling occurs when there exists a physical connection between two coils (or inductors). This coupling can be of aiding type or opposing type. It is based totally on the current direction i.e whether it enters at the dotted terminal or leaves the dotted terminal.

1.1) Coupling of Aiding type

Consider the following electric circuit, having two inductors that are connected in series.

Since the two inductors are connected in series. Hence the same current I will flow through the inductors having self-inductance L1 and L2

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In this case, the current I enter the dotted terminal of each inductor. Hence, the induced voltage in each inductor will have positive polarity at the dotted terminal.

On Applying KVL in the loop we get

 

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The above equation is in the form of:

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Hence  the equivalent inductance of series combination will be Leq = L1+L2+2M

In this case, the equivalent inductance increased by 2M factor. Hence the above electrical circuit is an example of aiding type.

1.2) Coupling of Opposing type

Consider the below electric circuit, having two inductors that are connected in series.

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In the above circuit, the current I enter at the dotted terminal of the inductor L1. Hence it induces a positive voltage in the other inductor having an inductance of L2.

In the above circuit, the current I leave from the dotted terminal of the inductor L2. Hence it induces a negative voltage in the other inductor having an inductance of L1.

On Applying KVL in the loop we get

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The above equation is in the form of

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Hence  the equivalent inductance of series combination will be Leq = L1 + L2 −2M

In this case, the equivalent inductance decreased by 2M factor. Hence the above electrical circuit is an example of an opposing type.

2) Magnetic Coupling:

Magnetic coupling exists when there is no physical connection between two coils. This coupling can be of aiding type or opposing type.

It is based totally on the current direction i.e whether it enters at the dotted terminal or leaves the dotted terminal.

2.1) Coupling of Aiding type

Consider the electrical equivalent circuit of transformer, having two coils and these are called as primary coils and secondary coils.

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The currents flow through primary and secondary coils are i1 and i2 respectively. In this condition, current enters at the dotted terminal of the coil. Hence, the induced voltage in each coil will have positive polarity in the dotted terminal due to the flow of current in another coil.

On Applying KVL in the around primary coil.

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On Applying KVL in the around secondary coil.

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In 1 and  2, the self-induced voltage and mutually induced voltage will have the same polarity. Hence above transformer circuit is an example of magnetic coupling and of aiding type.

2.2) Coupling of Opposing type

Consider the electrical equivalent circuit of transformer, having two coils and these are called as primary coils and secondary coils.

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The currents flows through primary and secondary coils are i1 and i2 respectively. In this condition, the current, i1 enters at the dotted terminal of primary coil. Hence induces a voltage in secondary coil. So positive polarity of the induced voltage  present at the dotted terminal of the secondary coil.

In the above circuit, the current, i2 leaves from the dotted terminal of secondary coil. Hence, it induces a voltage in primary coil. So negative polarity of the induced voltage present at the dotted terminal of this primary coil.

On Applying KVL in the around primary coil.

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On Applying KVL in the around secondary coil,

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In 3 and 4, self-induced voltage and mutually induced voltage are having opposite polarity. Hence above transformer circuit is an example of magnetic coupling and of opposing type.

The Filter Circuit & Coupled Circuit an important chapter of the Network theory most commonly asked in the GATE EE, SSC JE EE, ESE IES EE, ISRO EE, and other electrical branch exams.

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