Values of TOUT that satisfy this equation give the load stabilty circle. Similarly the load stability circle is found by setting the magnitude of TIN to 1. The center of the source stability circle is at:ĬS =*/(6) This circle is called the source stability circle. Setting the magnitude of TOUT to 1 and solving for TIN gives an equation for a circle. ГOUT is the two port output reflection coefficient. ГIN is the two port input reflection coeffcient, These calculators allow the user to quickly calculate TIN and TOUT given the s parameters of the two port and greatly simplify the calculations.Īn active two port is defined by the following reflection coefficients:
STABILITY CIRCLES ON SMITH CHART DOWNLOAD
Interested readers may download the calculators available in the Signal Processing Group Inc website (under the “Complementary” menu. We must also realize, that when a two port is connected in such a way that it has external load and source impedances, its input and output reflection coefficients change from s11 and s22 ( in terms of s parameters) to TIN and TOUT. (Techniques to stablize an amplifier are discussed in a companion article to be published). Thus, to stabilize an amplifier, for example, we first need to find out what the type a terminations are, and then use a circuit to change the behavior of the amplifier from unstable to stable. Type c terminations are borderline terminations. A third type of termination is also defined. Lets call the terminations that cause reflection coefficients to become 1, type a terminations and terminations that keep the reflection coefficients under 1, type b terminations. If a two port has been found to be potentially unstable then:ġ.0 There are some source terminations that cause the output reflection coefficient to become greater than 1.Ģ.0 There are also some output terminations that cause the input reflection coeffcient to become greater than 1.
To stabilize a virtual or actual two port, we need to investigate what types of termination can result in instability or oscillation. Usually this is the most useful analysis for amplifiers and related circuits. In this monograph, we will focus on two ports and stability circles relating to two ports. Where ZL is the impedance towards the load and ZS is the impedance towards the source.Īnother quantity that is useful in analysis is the Return Loss which is simply the magnitude of the reflection coefficient in dB.įor more on this and related topics please read the book: “Practical Impedance Matching“ by Ain Rehman, published by Amazon. If the source and load impedances are known then the reflection coeffcient can be written as: Reflection coefficient in terms of impedances. Where ρ is the magnitude of the reflection coefficient. The voltage standing wave ratio is given in terms of the reflection coefficient as: Г = +1 (maximum positive reflection line is open circuit at the load). Г = 0 (no reflection from the load and the two port is perfectly matched to the load), Г = -1 (maximum negative reflection, when the line is short circuited at its end.), In the simplest cases where the imaginary part of the reflection coefficient is zero, Г is a complex number and is described by its magnitude and phase angle. Here Vt is the transmitted signal and Vr is the reflected signal from the load. To recap some basic quantities we note that the reflection coefficient is given by:
We limit the stability circle tool description to a two port device. It is understood that many CAD programs can generate these, but it is always useful to understand the stability circle on an intuitive level as a good engineering practice. This monograph presents the stability circle tool for engineers.
STABILITY CIRCLES ON SMITH CHART SOFTWARE
(Note: A free, demo version of smith chart software is available on the web from Fritz Dellsperger). Stability circles are a tool, used to examine and analyze the stability of an amplifier (in the case under discussion) using a graphical technique, with the help of a Smith Chart.
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