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In this post, akellyirl wrote:

As a rule of thumb for design simplicity, the \$G_2H_2\$ loop is designed to be stable with significantly higher bandwidth than the final loop bandwidth so that its phase delay can be neglected in the design of the outer loop; i.e. its phase/magnitude contribution to the overall loop is negligible at crossover.

Is it possible to express that idea mathematically?

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emnha
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  • \$G=\dfrac{G1G^{’}}{G1G^{’}H1+1}\$ approaches 1/H1 – Tony Stewart EE75 Jun 10 '21 at 16:32
  • @TonyStewartEE75 if so then shouldn't he have said `G`` or the closed loop gain of the inner loop NOT just `G2H2` is much larger than the outer loop? – emnha Jun 10 '21 at 18:04
  • More GBW is possible with cascaded linear loops because with G1G2 , Without H2 Then H1 must be bigger meaning more attenuation vs s thus less BW. It’s a generalization for the assumption of high phase margin but not a guarantee. – Tony Stewart EE75 Jun 10 '21 at 18:30
  • @TonyStewartEE75 from your formula of `G`. You'll need G` to be large to be able to simplify it to `1/H1`. What does G` relate to the inner system bandwidth? – emnha Jun 10 '21 at 18:41
  • G’ is assumed to be much larger BW than you need, but permits more BW than without internal compensation H2. so In general, the higher the gain, the lower the BW of the integrator to linearize the loop so it is a 1st order system at 0dB gain open loop in order to achieve decent phase margin – Tony Stewart EE75 Jun 10 '21 at 18:48
  • If the contribution to the overall loop is negligible, the G2~H2 loop is a unity gain TF. – Chu Jun 10 '21 at 21:12
  • @Chu I don't think it is what he meant there. If it is unity gain you wouldn't add it. – emnha Jun 11 '21 at 16:27
  • It hasn't been added, it's part of the system. If it's got a high bandwidth c.f. the G1/H1 loop then its phase angle can be considered zero and its gain can be considered unity, i.e. it doesn't have any significant affect on the G1/H1 loop – Chu Jun 11 '21 at 23:26

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