Stability problems

Electronic Circuits II

1. Academic Year 2018-19 EC6401 Electronic Circuits II Stability problems Mrs.R.Chitra , AP/ECE, Ramce Institute f Technology, Rajapalayam

2. Stability Problem A negative feedback amplifier designed for a particular frequency range may be broken into oscillation at some high or low frequency. Gain and Phase shift of an amplifier change with frequency Gain gets decreased at low and high frequencies from the mid frequency range. When phase shift changes at high frequencies, then some of the feedback signal adds to the input signal. Due to this positive feedback, the amplifier breaks out into oscillation at some high and low frequencies.

3. Contd.... Stability of feedback amplifier is depend on the loop gain The frequency at which phase angle become 180˚, loop gain A(j ω ) β (j ω ) will be real number with a negative sign. Thus at this frequency, the feedback will become positive, it will behave like an Oscillator.

4. Nyquist criteria Nyquist plot can be used to test the stability of the feedback amplifier It is a plot of real and imaginary components of complex function of loop gain A β It is used to plot gain and phase shift as a function of frequency on a complex plane. The points in complex plane obtained for the value of A β corresponding to values of f from -∞ to ∞ locus of │1+A β │ = 1 represents a circle of unit radius with centre at -1+j0

5. Criterion of Nyquist is that amplifier is unstable if this curve encloses the point -1+j0 Amplifier is stable if the curve does not enclose this point

6. Gain margin and phase margin Gain margin (GM) is defined as the value of │A β │ in dB at the frequency at which the phase angle of A β is 180 ˚ Phase margin is defined as the angle of 180 ˚ minus the magnitude of the angle of A β at which │A β │ is unity (0 dB)

7. Pole location Stability of an amplifier can be determined directly by its poles. For an amplifier to be stable, it is necessary that its poles should lie in the left half of S-plane If poles are left half of the j ω axis, the system is globally stable and decaying oscillatory response If poles are right half of the j ω axis, the system is unstable and rise to growing oscillations A pair of poles on the j ω axis, give rise to sustained oscillations

8. Effect of feedback amplifiers on poles

9. The pole of amplifier is shift towards left from imaginary axis and it never enters the right-half of the s-plane. Single pole amplifier introduce a maximum phase shift of 90˚ Because of this, a single pole amplifier s stable for any values of β and hence such an amplifier is also known as unconditionally stable amplifier

10. Amplifier with two pole response Maximum phase shift is 180˚ (90˚ per pole). However, this phase shift is reached at ω = ∞ and hence he feedback of amplifier is always negative for entire frequency range

11. If Feedback amplifier has more than two poles , the phase angle of loop gain could exceed 180 ˚ beyond certain frequency, then amplifier cab be unstable .

12. References: Sedra and Smith, “Micro Electronic Circuits”; Sixth Edition, Oxford University Press, 2011. Jacob Millman , ‗Microelectronics‘, McGraw Hill, 2nd Edition, Reprinted, 2009.