# Electronic circuits - Signals

Tutorial on electronic circuits 2020-11-20 00:08:24# Electronic Circuits - Signals

A ** Signal ** can be understood as "a representation which gives information about the data present at the source from which they are produced. "This usually varies over time. Thus, a signal can be a ** source of energy that transmits information **. This can easily be represented on a graph.

### Examples

- An alarm gives a signal indicating that it is time.
- A cook's whistle confirms that the food is done.
- A red light indicates danger.
- A traffic light indicates your move.
- A phone rings to signal a call for you.

A signal can be any type that transmits information. This signal produced from electronic equipment is called an ** Electronic Signal ** or ** Electrical Signal **. These are geusually temporal variants.

## Types of signals

Signals can be classified as analog or digital, depending on their characteristics. Both analog and digital signals can be further classified as shown in the following image.

### Analog signal

A continuous signal varying in time, which represents a quantity varying over time, can be called ** Analog signal **. This signal continues to vary over time, depending on the instantaneous values of the quantity that represents it.

### Digital signal

A signal which is ** discrete ** in nature or whose shape is ** non-continuous ** may be referred to as ** digital signal **. This signal has individual values, shown separately, which are not based on previous values, as if they were derived at that particular time.

### Periodic signal and aperiodic signal

TouAn analog or digital signal, which repeats its pattern over a period of time, is called a ** periodic signal **. This signal has its pattern continued over and over and is easy to guess or calculate.

Any analog or digital signal, which does not repeat its pattern over a period of time, is called an ** Aperiodic signal **. This signal has its pattern continued but the pattern is not repeated and is not so easy to guess or calculate.

## Signals and Notations

Among the ** periodic signals **, the most commonly used signals are the sine wave, the cosine wave, the shape triangle wave, square wave, rectangular wave, sawtooth waveform, pulse waveform or pulse train, etc., let's see these waveforms.

### Unit step signal

The unit step signal has the value of one unit from its origin to one unit on the X axis. This is mainly used astest signal. The image of the unit step signal is shown below.

The step function unit is denoted by $ u left (t right) $. It is defined as -

$$ u left (t right) = left {begin {matrix} 1 & t geq 0 0 & t <0 end {matrix} right. $$

### Unity pulse signal

The unity pulse signal has the value of one unit at its origin. Its area is one unit. The image of the unit pulse signal is shown below.

The unit pulse function is denoted by ** ẟ (t) **. It is defined as

$$ delta left (t right) = left {begin {matrix} infty:: if:: t = 0 0:: if:: t neq 0 end {matrix} right. $$

$ $ int _ {- infty} ^ {infty} delta left (t right) d left (t right) = 1 $$

$ $ int _ {- infty} ^ { t} left delta (t right) d left (t right) = u left (t right) $$

$$ delta left (t right) = frac {du left (t right)} {d left (t right)} $$

### Unit ramp signal

The unity ramp signal has its value increasing ex ponentially from its origin. The image of the unit ramp signal is shown below.

The unit ramp function is denoted by ** u (t) **. It is defined as -

$$ int_ {0} ^ {t} u left (t right) d left (t right) = int_ {0} ^ { t} 1 dt = t = r left (t right) $$

$$ u left (t right) = frac {left left (t right)} {dt} $$

### Unit parabolic signal

The unit parabolic signal has its value changing like a parabola at its origin. The image of the unit parabolic signal is shown below.

The parabolic unit function is denoted by $ u left (t right) $. It is defined as -

$$ int_ {0} ^ {t} int_ {0 } ^ {t} u left (t right) dtdt = int_ {0} ^ {t} rleft (t right) dt = int_ {0} ^ {t} t.dt = frac {t ^ {2}} {2} dt = x left (t right) $$

$$ r left (t right) = frac {dx left (t right)} {dt} $$

$$ u left (t right) = frac {d ^ {2} x left (t right)} {dt ^ {2}} $$

### Signum Function

The Signum function has its value equally distributed in the positive and negative planes since its origin. The image of the Signum function is shown below.

The Signum function is denoted ** sgn (t) **. It is defined as

$$ sgn left (t right) = left {begin {matrix} 1:: for:: t geq 0 - 1:: for:: t <0end Danemarkmatrix rireright.$$

$$ sgn left (t right) = 2u left (t right) -1 $$

### Exponential signal

The exponential signal has its value varying exponentially from its origin. The exponential function is in the form of -

$$ x left (t right) = e ^ {alpha t} $$

The form of the exponential canbe defined by $ alpha $. This function can be understood in 3 cases

** Case 1 ** -

If $ alpha = 0 rightarrow x left (t right) = e ^ {0 } = 1 $

** Case 2 ** -

If $ alpha <0 $ then x left (t right) = e ^ { alpha t} where is negative. this form called ** exponential decay **.

** Case 3 ** -

If $ alpha> 0 $ then $ x left (t right) = e ^ {alpha t} $ where $ alpha $ is positive. This shape is called ** exponential increase **.

### Rectangular signal

The rectangular signal has its value distributed in rectangular shape in the positive and negative planes from its origin. The image of the rectangular waveform is shown below.

The rectangular function is denoted $ x left (t right) $. It is defined as follows:

$$ x left (t right) = A: rect left [frac {t} {T} right] $$

### Triangular signal

The rectangular signal has its value distributed in triangular form in the positive and negative planes from its origin. The image of the triangular signal is shown below.

The triangular function is denoted by $ x left (t right) $. It is defined as follows:

$$ x left (t right) = A left [1 - frac {left | t right |} {T} right] $$

### Signal sinusoidal

The sinusoidal signal has its value varying sinusoidally from its origin. The image of the sinusoidal signal is shown below.

The sinusoidal function is denoted by x (t). It is defined as -

$$ x left (t right) = A cos left (w_ {0} t pm phi right) $$

or

$$ x left (t right) = A sin left ( w_ {0} t pm phi right) $$

Where $ T_ {0} = frac {2 pi} {w_ {0}} $

### Sinc function

The signal Sinc has its value which varies according to a particular relation as in the equation given below. It has its maximum value originally and continues to decrease as it moves away. The image of a Sinc function signal is shown below.

The Sinc function is denoted by ** sinc (t) **. It is defined by -

$$ sinc left (t right) = frac {sin left (pi t right)} {pi t} $$

So, these are the different signals that we encounter most often in the field of electronics and communications. Each signal can be defined in a mathematical equation to facilitate the analysis of the signal.

Each signal has a particular waveform as mentioned earlier. Waveform shaping can alter the content present in the signal. Either way, it's up to the design engineer to decide to modify or not a wave for a particular circuit.r change the shape of the wave, there are few techniques that will be covered in other units