Triangular Signal – Electrical Circuits

Triangular Signals are an important tool in the electronic industry. They are ubiquitous in modern electronics and are almost used in every daily appliance for Voltage, Current, and power amplifiers. In this article, we will study what a triangular signal, how does it look like. We will also represent the Triangular signal mathematically. Later we will discuss the advantages, disadvantages, and some applications of Triangular Electronic Signal. We will conclude the article by summing up what we have learned. The electronics industry especially the communication system uses these signals in various circuits and readers can read about these other signals as well.

What is Triangular Signal ?

Triangular waves are a periodic, non-sinusoidal waveform with a triangular shape. Triangular waves are a form of electronic waveform where the voltage level ramps up linearly and falls away linearly at the same rate for both ramps

Unlike a sine wave, which smooth transition between its positive and negative peaks, a triangular wave has a linear rise and fall. The amplitude of the triangular wave is constant during each half-cycle, and the wave transitions abruptly between the positive and negative peaks. It is a piecewise linear function when plotted on a graph. The period of the wave is the duration of one complete cycle, and the frequency is the number of cycles per unit of time.

Triangular Signal Graph

If we plot the graph representing the magnitude of the triangular signal with time, the graph of the triangular signal looks like this.

Triangular Signal

As we observe, we can see that in a triangular signal the voltage ramps up linearly and falls down linearly. We also see that the signal repeats after a fixed interval of time hence it is a periodic signal.

If we carefully observe the shape of graph we see that the graph has triangles in it hence it has the name triangular signal.

Mathematical Expression of Triangular Signal

Mathematical Expression-of-Triangular-Signal

Using equation of line y₂-y₁=m(x₂-x₁)+c

This pulse can be represented by:

50t 0<t<1 v(t) = -50t+100 1<t<3s . 50t-200 3<t<4

How To Generate A Triangular Pulse ?

Here we will see how we use operational amplifiers to generate triangular pulse.

Triangular Pulse

The circuit for Triangular wave generator is designed using an op amp. We know that if an integrator is fed with a square wave as input the output will be a triangular wave. It means that a triangular wave generator can be generating by simply cascading an integrator and a square wave generator.

Working and Circuit Diagram of Triangular Signal

Triangular Signal Generator

This circuit uses two operational amplifiers. The whole process requires two steps:

Square Wave Generation

Resistor R₁ and capacitor C₁ determine the frequency of the square wave. Resistor R₂ and R₃ forms a voltage divider setup which feedbacks a fixed fraction of the output to the non-inverting input of the IC. The voltage across capacitor C₁ varies from 0 to V_cc using resistor R₁. A fraction of this high voltage is fed back to the non- inverting pin by the resistor network R₂, R₃. When the voltage across the charging capacitor is increased to a point the voltage at the inverting pin is higher than the non-inverting pin, the output of the op amp swings to negative saturation (-V_cc). This cycle is repeated over time and the result is a square wave swinging between +V_cc and -V_cc at the output of the op-amp.

Integrator Output

An active integrator based on op-amp is used. Resistor R₅ in conjunction with R₄ sets the gain of the integrator and resistor R₅ in conjunction with C₂ sets the bandwidth. Square wave is given as input to inverting terminal of op-amp through resistor R₄. The output of this circuit generates a cycle of triangular pulse.

Advantages of Triangular Signal

The advantages of triangular signal are stated below:

• Triangular Signals are very simple and relatively easy to generate thereby making them the best choice for designing.
• Its linear nature along with its periodicity is a vary useful property which is applied in various equipment. As seen in the graph the triangular signal rises and falls linearly and repeats itself after a certain time-period.
• Triangular signals are often used in applications where a frequency sweep is required. For example they are used in induction motor.
• These signals can be easily generated and manipulated to simulate various conditions for testing purposes. They are commonly used in signal processing applications.

Disadvantages of Triangular Signal

The disadvantages of triangular signal are stated below:

• The harmonic content of triangular signal can be disadvantageous in many situations .The presence of odd harmonics may lead to undesired interference in certain systems.
• Due to limited features, these signals have limited applications in communication system. Other signals like sine wave are used more often due to the simplicity and features it offer.
• It has less energy efficiency in systems like power electronics and motor control. This is because the higher harmonics in the triangular waveform can result in increased losses in the system.
• Triangular signals are very sensitive to jitter and noise. In digital systems any imperfections or disturbances in the waveform can impact the performance of systems.

Applications of Triangular Signal

Triangular pulse is used in various applications like:

• Musical Instruments: Triangular waveform is used in musical instruments as it is rich in harmonics and this gives an interesting sound. Triangular wave has a less harsh sound than a square wave which is very rich in harmonics.
• Sweep Circuits: The linearity of triangular waveforms makes triangular wave generators useful in many “sweep” circuits and test equipment. Induction motor uses triangular pulse in PWM(pulse width modulator) circuit.
• Modulation: Triangular waves can be used to modulate other signals These include frequency modulation (FM) and phase modulation (PM) systems and even Amplitude modulation(AM).
• Timing and controllers: Triangular waves can be used to control the timing of digital circuits. These signals are used in digital clocks and timers.
• Oscillators: Triangular waves can be used as a stable, low-distortion, and low-noise source of oscillation in electronic circuits.

Conclusion

As we have seen triangular signals play an important role in modern electronics. We have already discussed the linear nature of this signal along with other properties. As we discuss the uses of this signal we realize it is used in sampling circuits, thyristor firing circuits, frequency generator circuits, tone generator circuits etc for various purposes. These applications signify the need to find appropriate methods to generate Triangular pulse. There are different methods to generate this pulse and one method has been discussed with the readers. There are various other types of signals, each used for a different purpose.

FAQs on Triangular Signal

Q1. What are Triangular waves?

Triangular waves are a periodic, non-sinusoidal waveform with a triangular shape.

Q2. What are sawtooth waves?

The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a saw.

Q3. What is the difference between Triangular pulse and Sawtooth pulse?

People often get confused between the triangle and sawtooth waves. The most important feature of a triangular wave is that it has equal rise and fall times while a sawtooth wave has un-equal rise and fall times.

Q4. What are some other signals?

Some other basic signals are rectangular pulse, square pulse, signum signal and sinc signal.