Stability:

• All s_p must be in the negative half of the s-plane
                                               Real parts of all poles must be negative

• Sufficient condition to ensure stability:
                                            
                                               
                                              No s_p can occur on the jw-axis

• w₁₈₀ ... frequency at which the monotone decreasing phase of kA_v (jw) reaches -180o;
  that is:

• Another sufficient condition of stability:

|kA_v (jw₁₈₀)| < 1

No s_p can occur on the jw-axis

Gain margin - measure of stability

Gain margin (in dB) = 20 log |kA_v (jw₁₈₀)|

• Must be negative for stability
  
• It is desirable to obtain a margin of at least 20 dB
  
• Difficult to control ... more often is used the phase margin

w₀ ... frequency at which the monotone decreasing absolute value of a loop gain |kA_v (jw)|

reaches the value 1 (0 dB) ... unit gain frequency

Another sufficient condition of stability:

Phase margin - measure of stability

• The larger the phase margin, the more stable the circuit
  
• It is desirable to obtain a margin of at least 60o or more
  
  

Stability conditions can be checked by using the Bode plots:

At the unity-gain frequency w₀:

• Slope of the logarithmic loop gain versus logarithmic frequency is approximately
  -6m dB/oct

• Angle is around - 90m degrees

m is the number of those poles whose magnitude |s_i| is less than w₀

For a substantial positive phase margin

60o ~ :      m should be less than 2

90o                                               m = 1
                                                            ... only one pole satisfying |s_i| < w₀