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## LINEAR WAVE SHAPING & DIFFERENT TYPES OF WAVEFORMS

Timing circuits networks composed of resistors, capacitors and inductors are called linear network and they do not change the waveform of a sine wave when it is transmitted through them. On the other hand when non-sinusoidal waveforms, (e.g. step, ramp, exponential) are applied to the input of such networks the output signal may have very little resembles with the input waveform. The action of a linear network in producing a waveform at its output different from its input is called linear wave shaping. The wave shaping is used to perform any one of the following functions.

- To hold the waveform to a particular d.c. level.
- To generate one wave form the other
- To limit the voltage level of the waveform of some presenting value and suppressing all other voltage levels in excess of the present level.
- To cut-off the positive and negative portions of the input waveform.

Shaping circuits may be either series RC or series RL circuits. The series RC and RL circuits electrically perform the mathematical operation of integration and differentiation. Therefore, the circuits used to perform these operations are called integrators and differentiator. The differentiator circuits are used to generate sharp narrow pulses either from distorted pulse waveform or from rectangular wave forms. The integrator circuits are required to generate a voltage, which are required to generate a voltage, which increases or decreases linearly with time.

## Non-sinusoidal Waveforms

Any waveform whose shape is different from that of sinusoidal wave is called a non-sinusoidal waveform. For example pulse square, symmetrical square triangular and saw-tooth are non-sinusoidal waves. When one quantity is dependent upon some other variable quantity varies with respect to others. In case of electronic circuits function usually means that current or voltage varies with respect to time. All these waveform are the function voltage or current with respect to time such as step, ramp and exponential are explained as under:

### Step Function:

A step function shown in Fig. 1(a), makes an instantaneous jump from one steady value to another steady value. A step means an instantaneous change in level.

In such a case, voltage maintains zero value for all times t < 0 and maintains the value V for all times t > 0 is called a step voltage.

### Ramp Function:

A ramp function shown in Figure 1(b) isone that voltage increases or decreases linearly with time. Slope of the function is constant. In such a case, voltage is zero for t < 0 and increases linearly with time for t > 0.it is linear change in function with respect to time called a ramp.

### Exponential Function:

An exponential function is a function of voltage that increases or decreases exponentially with time. In such a case, voltage is zero for t < 0 and increases nonlinearly with time t called an exponential voltage. The terms used for exponential are e^{x} and e^{-x}. Exponential quantity gap is known as an exponential curve.

## Different Types of Waveforms

Let us now discus the pulse square, symmetrical square, Triangular and saw-tooth waveforms.

### Pulse waveform

Figure 2(a) shows the waveform of an ideal pulse. The pulse amplitude is V and the pulse duration is t_{p}. It** **is evident from Fig. 2(b) and (c) that the pulse may be considered as the sum of the step voltage +V, whose discontinuity occur at t = 0 and a step voltage —V, whose discontinuity occurs at t = t_{p}. The pulse waveform find extensive use is almost every field of electronics such as communication, computer, defense** **equipment, etc.

### Square waveform

A waveform which maintains itself at one constant voltage level V_{1} for a time T_{1} and at another constant level V_{2} for time T_{2} and is repetitive with a period T = T_{1} + T_{2} as shown in Fig. 2 (a) is called a square waveform. The square waveform is used in digital electronic circuits, radars and as synchronizing pulses in television.

### Symmetrical square waveform

A square waveform for which T_{1} = T_{2} = T/2 as shown in Fig. 3(b) is called a square waveform. It may be noted that because of the symmetry, the voltage levels V_{1} and V_{2} are equal and opposite V_{1} = —V_{2}. The symmetrical square waveform is very useful in digital electronic circuits.

### Triangular waveform

A waveform which increase linearly with time to a voltage level V for a time T/2 and then decreases linearly to its original level for a time T/2 and is repetitive with a period T as shown in Fig. 4(a) is called triangular waveform. It may be noted from this figure, that a triangular wave may be considered as the sum of ramp voltage, which incre.ases at a rate of 2V/T for a time T/2 and the ramp voltage which decreases at a rate of —2V/T for the remaining time T/2. The triangular waveform is used in scanning circuits, where a uniform left-to-right scan is required as in computer displays. These are also used in timing circuit for electronics applications.

### Sawtooth waveform

A waveform increases linearly with time to a voltage level V for a time T and then changes abruptly to its original level and is repetitive as shown in Fig. 4(b) is called sawtooth waveform. It is also called sweep waveform or time-base waveform. The sawtooth waveform is used in the scanning circuit of cathode ray oscilloscopes and televisions.