This example shows hyperbolic functions in block diagram using

QFIRE Studio

Introduction

The ordinary trigonometric function are available in

QFIRE Studio

These functions can be described by:

• Hyperbolic sine:
  $$sinh(x) = \frac{e^x-e^{-x}}{2}$$
• Hyperbolic cosine:
  $$cosh(x) = \frac{e^x+e^{-x}}{2}$$
• Hyperbolic tangent:
  $$tanh(x) = \frac{e^x-e^{-x}}{e^x+e^{-x}}$$
• Hyperbolic secant:
  $$sech(x) = \frac{2}{e^x+e^{-x}}$$
• Hyperbolic cosecant:
  $$csch(x) = \frac{2}{e^x-e^{-x}}$$
• Hyperbolic cotangent:
  $$coth(x) = \frac{e^x+e^{-x}}{e^x-e^{-x}}$$

Due to this definition using exponential function, it is possible to create create diagrams for each function.

Simulation

The hyperbolic sine, hyperbolic cosine and hyperbolic tangent diagram are shown in Figure 1, 2 and 3.

Figure 1 - Hyperbolic sine diagram

Figure 2 - Hyperbolic cosine diagram

Figure 3 - Hyperbolic tangent diagram

These diagrams can became subsystems as shown in Figure 4. In this diagram, it was used a Time block as source of the input signal

Figure 4 - Hyperbolic functions in subsystems

Figure 5 - Hyperbolic functions in a Scope

The hyperbolic secant, hyperbolic cosecant and hyperbolic cotangent are represented in Figure 6, 7 and 8. The diagram using subsystems is shown in Figure 9 and the output signals in Figure 10

Figure 6 - Hyperbolic secant diagram

Figure 7 - Hyperbolic cosecant diagram

Figure 8 - Hyperbolic cotangent diagram

Figure 9 - Hyperbolic functions in subsystems

Figure 10 - Hyperbolic functions in a Scope