# Why fast inner current loop and slow outer loop of DC-DC converter

Let say we have a DC-DC converter operates with double loop control (inner and outer) , and with switching frequency of Fs= 20000 Hz. Please ,if you could answer the two following questions:

1- Usually, the inner current loop bandwidth is chosen based on the relation of Fs/10 , = 2000 Hz in this case Way?

2- in a two loop control of DC-DC converter such as : boost converter , always the bandwidth of inner current loop is faster or higher than the outer loop .why? Some paper mentioned that , The outer control loop bandwidth can be calculated as = inner loop bandwidth/10 = 200 Hz in this case Why?

• In any control system the inner loops has to be faster than the outer. The rule of thumb is telling that it should be a factor of 10 at least. To work properly the inner loop has to stabilize quickly in response to any outer loop changes. – Eugene Sh. May 27 '19 at 15:57
• @EugeneSh. You should make that an answer, it sums things up perfectly. – TimWescott May 27 '19 at 16:01
• The reason that multi-loop control systems are designed with a fast inner loop and a slower outer loop is because doing it the other way around basically renders the inner loop pointless. If you can do the job with a fast outer loop and a slow inner loop, then in nearly all cases you can just leave the inner loop off. – TimWescott May 27 '19 at 16:03

The time constants of each loop may be much faster than you suggested depending on the driving rate and energy storage time constants with the output Cap, C*ESR=Tau being one of them to handle very short term transients, such that the bandwidth of that servo must be faster than the cap storage bandwidth $$\f_{-3dB}=0.35/(ESR*C)\$$ in order to regulate step loads.