Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.
Welcome to our site! Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.
Given conditionaly stability and s parameter of a equation, how do we know it's laying inside the circle or outside the circle?
Like |rL| = | S11 + [S21 S12 rL / 1 - S22 rL] | = 1 and |rout| = | S22 + [S21 S12 rs / 1 - S11 rs] | = 1 ?
Any complex quantity can be expressed in Cartesian coordinates like a + jb where a is the real part and b is the imaginary part. That same quantity can be expressed in polar coordinates (r, θ) where the radial component r is equal to:√a²+b², and θ= arctan (b/a).
If the magnitude of r > 1 you are outside the unit circle, and if the magnitude of r < 1 you are inside and if r = 1 you are on the unit circle. For circles of other sizes located at places other than the origin you can apply constants of translation or scaling but the idea is the same as for the unit circle.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.