Table of Contents
- 1 What do you understand by positive real function explain with example?
- 2 What should be the coefficients of numerator polynomial and the denominator polynomial in a transfer function must be *?
- 3 What is the meaning of positive function?
- 4 When S is real the driving point both odd and even parts of a Hurwitz polynomial p/s have roots?
- 5 Which of the system are roots of the denominator polynomial of transfer function?
- 6 How do you know if a transfer function is stable?
- 7 What are the properties of positive real functions?
What do you understand by positive real function explain with example?
For example, if a transfer function is known to be asymptotically stable, then a frequency response with nonnegative real part implies that the transfer function is positive real. to be positive real in terms of its zeros instead of poles.
What do you mean by a Hurwitz polynomial?
In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose roots (zeros) are located in the left half-plane of the complex plane or on the imaginary axis, that is, the real part of every root is zero or negative. Such a polynomial must have coefficients that are positive real numbers.
What should be the coefficients of numerator polynomial and the denominator polynomial in a transfer function must be *?
1. The coefficients of numerator polynomial and the denominator polynomial in a transfer function must be? Explanation: The coefficients of P(s), the numerator polynomial and of Q(s), the denominator polynomial in a transfer function must be real. Therefore all poles and zeros if complex must occur in conjugate pairs.
What do you mean by network synthesis?
Network synthesis is a design technique for linear electrical circuits. Synthesis starts from a prescribed impedance function of frequency or frequency response and then determines the possible networks that will produce the required response. Network synthesis directly addresses both these issues.
What is the meaning of positive function?
The positive part function is a function that takes as input any real number and outputs the same number if it is nonnegative, and 0 if it is negative.
How do you know if a function is positive or real?
Properties of Positive Real Function
- Both the numerator and denominator of F(s) should be Hurwitz polynomials.
- The degree of the numerator of F(s) should not exceed the degree of denominator by more than unity.
- If F(s) is positive real function then reciprocal of F(s) should also be positive real function.
When S is real the driving point both odd and even parts of a Hurwitz polynomial p/s have roots?
Explanation: The roots of the odd and even parts of a Hurwitz polynomial P (s) lie on jω axis not on right half of s plane or on left half of s-plane. Explanation: If the polynomial P (s) is either even or odd, then the roots of P (s) lie on jω axis not on right half of s plane or on left half of s-plane.
When S is real the driving point impedance function is?
9. The real parts of the driving point function Z (s) and Y (s) are? Explanation: The real parts of the driving point impedance function Z (s) and driving point admittance function Y (s) are positive or zero.
Which of the system are roots of the denominator polynomial of transfer function?
The roots of the denominator polynomial, d(s), define system poles, i.e., those frequencies at which the system response is infinite. Thus, p0 is a pole of the transfer function if G(p0)=∞.
What does it mean when a function is positive or negative?
A function is positive when the y values are greater than 0 and negative when the y values are less than zero. Here’s the graph of a function: This graph is positive when x is less than 2 and negative when x is greater than 2.
How do you know if a transfer function is stable?
In order for a system to be stable, its transfer function must have no poles whose real parts are positive. If the transfer function is strictly stable, the real parts of all poles will be negative, and the transient behavior will tend to zero in the limit of infinite time. The steady-state output will be:
How do you calculate overall transfer function with positive feedback?
For a system with a positive feedback, the overall transfer function is the forward path transfer function divided by one minus the product of the forward path and feedback path transfer functions.
What are the properties of positive real functions?
There are four very important properties of positive real functions and they are written below: Both the numerator and denominator of F (s) should be Hurwitz polynomials. The degree of the numerator of F (s) should not exceed the degree of denominator by more than unity. In other words (m-n) should be less than or equal to one.
What is a transfer function in physics?
A transfer function is defined as the following relation between the output of the system and the input to the system . Eq. (1) If the transfer function of a system is known then the response of the system can be found by taking the inverse Laplace transform of .