Contents
What does a pole at the origin mean?
location; poles far from the origin in the left-half plane correspond to components that decay rapidly, while poles near the origin correspond to slowly decaying components. 2. A pole at the origin pi = 0 defines a component that is constant in amplitude and defined by the initial conditions.
What is the quality factor of real axis pole?
Obviously, in a natural system, such a pole must come as part of a pair, and both would yield the same result. For coincident poles on the real axis, this gives a Q of 1/2 (critically damped). For poles on the imaginary axis, that gives a Q of ∞ (undamped).
What is poles and zeros in s plane?
A pole-zero plot can represent either a continuous-time (CT) or a discrete-time (DT) system. For a CT system, the plane in which the poles and zeros appear is the s plane of the Laplace transform. In this context, the parameter s represents the complex angular frequency, which is the domain of the CT transfer function.
How are poles and zeros represented in an S domain?
Usually, you create a pole-zero diagram by plotting the roots in the s-plane (real and imaginary axes). The pole-zero diagram provides a geometric view and general interpretation of the circuit behavior. The zeros, or roots of the numerator, are s = –1, –2. The poles, or roots of the denominator, are s = –4, –5, –8.
What is a good quality factor?
Good high-Q capacitors can have a Q factor value of over 10,000 at 1MHz and over 1,000 at 100MHz, while standard capacitors can have a Q factor as low as 50 at 1kHz. Such capacitors can be used at frequencies of up to 20GHz, which is sufficient for most RF applications.
Where does equation relating pole location to Q come from?
For anyone interested in where the equation relating pole location to Q comes from, It derives from the 2nd order transfer function: A decent discussion of Q and damping in 2nd order systems can also be found here: which gives an excellent review of how the pole placement corresponds to various damping characteristics.
Which is true of a pole and a polar line?
In geometry, the pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section. For a given circle, reciprocation in a circle means the transformation of each point in the plane into its polar line and each line in the plane into its pole.
Which is the first coordinate in the polar grid?
The polar grid is scaled as the unit circle with the positive x x – axis now viewed as the polar axis and the origin as the pole. The first coordinate r r is the radius or length of the directed line segment from the pole.
How is the relationship between Poles and polars reciprocal?
The relationship between poles and polars is reciprocal. Thus, if a point A lies on the polar line q of a point Q, then the point Q must lie on the polar line a of the point A. The two polar lines a and q need not be parallel. There is another description of the polar line of a point P in the case that it lies outside the circle C.