Crash course part 2. Frequency compensation
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1 Crash course part Frequecy compesatio
2 Ageda Frequecy depedace Feedback amplifiers Frequecy depedace of the Trasistor Frequecy Compesatio Phatom Zero Examples Crash course part
3 poles ad zeros I geeral a trasfer fuctio ca be writte as: H ( s),,, m are zeros p, p,, p are poles poles ad zeros are show i the s-plae poles are draw as zeros as k s s p s s p s m s p Crash course part 3
4 System with oe pole Pole placemet Magitude Step respose Crash course part 4
5 System with complex pole pair Pole placemet Magitude Step respose Crash course part 5
6 Complex poles close to jω-axis Pole placemet Magitude Step respose Crash course part 6
7 Discrepacy factor, frequecy depedace Discrepacy factor ca be writte as: A A ( s) ( s) N( s) (0) P( s) N( s) (0) P( s) Iterpretatio of the above: zeros i A (s) is zeros i A t A A A P( s) (0) N( s) A (0) N( s) Roots of equatio P(s) - A (0)N(s) = 0 are poles i A t The system poles depeds o the loop gai A (0) P(s) - A (0)N(s) is called the caracteristic polyome Crash course part 7
8 Root locus Root locus is a graphical represetatio of how the system poles moves with icreasig A (0) Arrows i root locus shows icreasig A (0) Loop poles are p, p,, p System poles are p, p,, p Crash course part 8
9 High frequecy model for BJT Capacitaces are icluded i the hybrid- -model C capacitace betwee base ad emitter C capacitace betwee base ad collector C is much less tha C ad is assumed to have o importace i our calculatios. C (ad r o ) are eglected if ot stated otherwise! Crash course part 9
10 Trasit frequecy f T At very high frequecies the CE-stage has o gai f T is the frequecy whe H(s) = i o /i i = for a curret drive CE-stage with a short circuit at the output f T gm ( C C ) f T varies heavily betwee differet types of trasistors N6 f T ~ khz but today there are trasistors havig f T > 50GHz Crash course part 0
11 H(j ) Maximal flat magitude Ofte you wat to have costat gai for all sigal frequecies This is equal to havig the system poles i Butterworth positio They are located o a half circle equally spaced i left half plae [rad/s] Crash course part
12 Loop-gai-Poles-product (LP-product) The characteristic polyomial for a system havig two loop poles ad o loop zeroes is: P(s) - A (0)N(s) = s - (p + p )s + [ - A (0)]p p The same system with poles i Butterworth positio is: Idetifyig: P(s) - A (0)N(s) = s - (p a + p b )s + = [ - A (0)]p p is the maximum possible badwidth for the system. Föreläsig
13 LP-product defiitio The LP-product for a system with two loop poles: LP A (0) p p I geeral the LP-product is: LP A (0) With the poles i Butterworth positio the bad width is, 0: p 0 LP A (0) p Crash course part 3
14 Poles i Butterworth Poles i Butterworth is foud from: s a s a 0 där a 0 Locatio for the poles are (:d ad 3:rd order) :d order - 0 j 3:rd order - 0, - 0 j 3 Crash course part 4
15 Flow chart for bad width estimatio Caculate the LP-product Estimate the bad width Choose the locatio of the system poles (Butterworth) for estimated bad width Calculate the sum of the loop poles ad the sum of the system poles Check that the loop poles are domiat If a o-domiat pole exists remove the most egative oe ad re-calculate Fiished Crash course part 5
16 Phatom zero, grafical iterpretatio A t is made frequecy idepedat Crash course part 6
17 Where to put the phatom zero (:d order) Idetificatio of s-terms gives p p 0 p p Place the zero at System poles sum, A (0) 0 ( p p ) p p Characteristics p +p Butterworth 0 MFM Bessel Real double polee - 0 Crash course part 7
18 Implemetatio of phatom zero should icrease for higher frequecies ( s) (0) s Three places to put a phatom zero i I the feedback et At the amplifiers output At the amplifiers iput Crash course part 8
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