stability - ECEN 326 Electronic Circuits Stability Dr...

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Unformatted text preview: ECEN 326 Electronic Circuits Stability Dr. Aydın ˙ Ilker Kar¸ sılayan Texas A&M University Department of Electrical and Computer Engineering Ideal Configuration Ideal Configuration ε V fb V o V V i f Σ a(s) a(s) = V o V ε (s) = a o 1- s p 1 A(s) = V o V i (s) = a(s) 1 + a(s)f = a o 1 + a o f 1- s (1 + a o f)p 1 ECEN 326 Electronic Circuits - Aydın ˙ I. Kar¸ sılayan - Stability 1 Gain-Bandwidth Gain-Bandwidth 1-pole amplifier 1+a o f a o 20 log 20 log a o |p 1 | |p 1 | (1+a o f) t ω |a(j )| ω ω log scale-20 dB/dec Gain magnitude, dB |A(j )| ω ECEN 326 Electronic Circuits - Aydın ˙ I. Kar¸ sılayan - Stability 2 Instability and the Nyquist Criterion Instability and the Nyquist Criterion Transfer function of a 3-pole amplifier: a(s) = a o 1- s p 1 1- s p 2 1- s p 3 Nyquist criterion for stability of the amplifier: Consider a feedback amplifier with a stable T(s) . If the Nyquist plot of T(j ω ) encircles the point (-1,0), the feedback amplifier is unstable. ECEN 326 Electronic Circuits - Aydın ˙ I. Kar¸ sılayan - Stability 3 Magnitude & Phase Magnitude & Phase 3-pole amplifier |p 1 | |p 2 | |p 3 180 a(j ω )|, dB | ) ω ω 20 log a o 20 log a 180 |a(j ω-20 dB/dec-40 dB/dec ω-45-90-135-180-225-270 log scale-60 dB/dec ECEN 326 Electronic Circuits - Aydın ˙ I. Kar¸ sılayan - Stability 4 Magnitude & Phase Magnitude & Phase T(s) = a(s)f 1 1 | |p 2 | |p 3 | 180 ) ω T(j |p ω 20 log a o f 1 20 log a 180 ω 1 )|, dB |T(j ω f-20 dB/dec-40 dB/dec ω-45-90-135-180-225-270-60 dB/dec log scale ECEN 326 Electronic Circuits - Aydın ˙ I. Kar¸ sılayan - Stability 5 Nyquist Plot Nyquist Plot T(s) = a(s)f 1 f 1 a o ω positive ω negative ω=ω 180 f 1 a 180 Im ω= Re ω=0 (-1,0) ECEN 326 Electronic Circuits - Aydın ˙ I. Kar¸ sılayan - Stability 6 Magnitude & Phase Magnitude & Phase T(s) = a(s)f 2 1 | |p 2 | |p | ω 3 20 log a o f 180 20 log a 180 f 2 T(j |p 2 )|, dB |T(j ω ) ω-45-90-135-180-225-270-60 dB/dec-40 dB/dec-20 dB/dec log scale ω ω log scale ECEN 326 Electronic Circuits - Aydın ˙ I. Kar¸ sılayan - Stability 7 Nyquist Plot...
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This note was uploaded on 02/08/2009 for the course ECEN 326 taught by Professor Karsilayan during the Spring '09 term at Texas A&M.

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stability - ECEN 326 Electronic Circuits Stability Dr...

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