4 Stability

Now that the loop gain, T, has been defined from the application parameters it is possible to use this to determine system stability and hence calculate the correct compensation components. To calculate the stability we will use a simple procedure invoking the Nyquist Stability Theorem. A special case of this theorem states that the stability of a system can be determined by analysis of the phase margin. To calculate the phase margin the crossover frequency, fc, first needs to be determined. This is defined as the frequency where the magnitude of the loop ( |T| ) is unity, equal to 0 dB. The phase of the loop gain, T, can then be calculated at this frequency and the difference between it and 180 degrees is the phase margin. Expressing it as an equation:

To design for an exact phase margin we need to know the desirable range for which our switching regulator should reside. If phase margin is less than or equal to 0 degrees the system will be unstable. Therefore a positive number is always required. But increasing the phase margin excessively causes the system to become over-damped, while a lower phase margin will create an under-damped response. For the sake of simplicity it will be stated that a good value for the LM3478 phase margin is in the range of 30 to 100 degrees.