11.2 Stability. A gain element is an active device. One potential problem with every active circuit is its stability
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1 5/7/ _2 tability 1/2 112 tability eading Aignment: pp A gain element i an active device One potential problem with every active circuit i it tability HO: TABIITY Jim tile The Univ of Kana Dept of EE
2 5/7/2007 tability 1/10 tability Q: o all there i to making a good microwave amplifier i the deign of proper matching network? A: There i one other problem that confront the microwave amplifier deigner That problem i tability (of the amplifier, not the deigner) An untable amplifier i alo known a an ocillator a ource of microwave energy! Q: Under what condition will an amplifier ocillate? A: An amplifier will go untable if either of thee two condition are true: = + > 10 out = + > 10 in In other word, the amplifier will ocillate if either the input or output reflection coefficient of the gain element ha a magnitude greater than one Jim tile The Univ of Kana Dept of EE
3 5/7/2007 tability 2/10 Q: Hey wait! I thought we learned that the maximum value of any reflection coefficient magnitude wa 1 (ie, 10 ) thi defined the validity region of our mith hart! A: emember, the inequality 10 i true for any paive load or device Our gain element i an active device it mut have a D ource of power A a reult, we find that > 10 i quite poible! Q: But, we learned that the region outide the = 10 circle on the mith hart correponded to load with negative value of reitance Doe thi mean that Z in or Z out could have real (ie reitive) component that are negative? A: That exactly what it mean! Q: What i a negative reitor exactly? A: Ohm law till applie negative reitance or not A a reult, we would find for a 10 Ω reitor that: Q:??? V = 10 V = 10I I A: The reult above imply mean that the current through a negative reitor i 180 out-of-phae with the voltage acro it Jim tile The Univ of Kana Dept of EE
4 5/7/2007 tability 3/10 The reitor current i at it minimum value when the voltage acro it i at it maximum and vice vera! Thi behavior drive our amplifier circuit a little wacky, and it begin to ocillate! Q: o how do we avoid thi unfortunate occurrence? A: ecall that amplifier intability occur when: = + > 10 out = + > 10 in Thu, for a given gain element (ie, 11, 21, 22, 12), amplifier tability i determined by the value of and We can olve the above equation to determine the pecific range of value of and that will induce ocillation The reult are provided in page 543 and 544 of your text We find that thee untable value when plotted on the complex plane form a circle Thee circle are know a a tability circle Jim tile The Univ of Kana Dept of EE
5 5/7/2007 tability 4/10 Thee gain circle are defined a a complex value, which pecifie the location of the tability circle center on the complex plane, and a real value, which pecifie the radiu of the tability circle There i one tability circle for (ie, and ) and another for (ie, and ) Typically, the value that lie inide the circle will create amplifier ocillation i r Q: o what do we ue thee tability circle for? A: A an amplifier deigner, we mut make ure that our deign value and lie outide thee circle otherwie, our well-deigned amplifier will ocillate! Jim tile The Univ of Kana Dept of EE
6 5/7/2007 tability 5/10 Jim tile The Univ of Kana Dept of EE i r A table Deign i r An Untable Deign
7 5/7/2007 tability 6/10 Q: Yike! Mut we alway determine thee circle and check our deign for intability? A: Not necearily! ome gain element are unconditionally table A the name ugget, thee gain element reult in table amplifier for any and all realizable value of and Q: o an unconditionally table gain element ha tability circle with zero radiu (ie, 0 = )? A: ould be, but all that i required for a gain element to be unconditionally table i for it tability circle to lie completely outide the = 1 circle i r An Unconditionally table Gain Element Jim tile The Univ of Kana Dept of EE
8 5/7/2007 tability 7/10 For thi condition, we find that the value of and that reult in an untable amplifier mut have a magnitude greater than 1 (ie, > 1 or > 1) But, we can preume that our the load and ource attached to our amplifier will alway have poitive reitance, uch that < 1 and < 1 Thu, an amplifier contructed with an unconditionally table gain element will likewie be unconditionally table! Q: How will I recognize an unconditionally table gain element if I ee one? Mut I determine and plot the tability circle? A: There are tet that we can apply uing the cattering parameter 11, 21, 22, 12 to more directly determine if a gain element i unconditionally table Firt, we find ome neceary condition for a gain element to be unconditionally table are: 2 11 < 1 and 2 22 < 1 If our gain element i unilateral (ie, 12 = 0 or approx ) then the above condition are likewie ufficient for unconditional tability Jim tile The Univ of Kana Dept of EE
9 5/7/2007 tability 8/10 Otherwie, (for 12 0 ) we find that our gain element mut pa two more tet tet that are provided on page 545 of your text Q: Do we really care if our deign i unconditionally table? Aren t we really jut concerned with whether our deign value and lie inide the tability circle? A: emember, the value and are determined for the pecific value of ource and load impedance connected to the amplifier (preumably Z 0) Z V g Z 0 But what if the reulting amplifier i not connected to thee ideal ource? The ideal ource or load impedance Z 0 i never achieved with perfection, and often achieved not at all (conider all the narrow-band device we have tudied!) 20 j V g j Jim tile The Univ of Kana Dept of EE
10 5/7/2007 tability 9/10 Thu, ince we do not pecifically know what ource and load impedance our amplifier might encounter, we had generally deign an amplifier that i table for them all one that unconditionally table! Q: Anything ele we need to know about amplifier tability? A: One lat very important thing ecall that amplifier, like all microwave device, are dependent on frequency Thu, all of the important value involved in our deign (eg,, 11, 21, 22, 12, o) will change a a function of frequency! Q: I ee, amplifier performance, mot notably gain, will change a a function of frequency, and o maximum power tranfer will occur at jut our deign frequency We ve een thi kind of thing before! A: True, but for amplifier there i alo a new twit The amplifier tability condition (ie, tability tet) mut be atified at any and all frequencie! If for even one frequency we find that either: = + > 10 out or = + > 10 in Jim tile The Univ of Kana Dept of EE
11 5/7/2007 tability 10/10 then our amplifier will ocillate even if that frequency i not our deign frequency! Thi make amplifier tability a much more ignificant and difficult problem than you might otherwie think An unconditionally table amplifier mut be unconditionally table at all frequencie! Jim tile The Univ of Kana Dept of EE
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