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a question in the book "Understanding Delta-Sigma Data.

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sethtalk

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hi,
I have a question about stability criterior in negative feedback circuit,
i hope somebody who have read "Understanding delta-sigma converter",Temes,G.C.
can tell me the answer..
In circuit theory, we know in a nagative feedback system,the loop gain L1(f) is
stable if |L1(f)|<1 at 180 degree phase shit location,say f=f1,
my question is:
in section 4.2.1,fig4.7 (bode plot for the 5'th order loop filter).in the paragraph
the author said ".... Kmin=1/1.83 = 0.547,is the lowest allowable quantizer gain
as indicated in Fig4.6",it seem contradict to my belief,I thought 0.547 should be
the maximum value,not minimum value,because |L1|>1 at f1 location for every value
k >= 0.547..
could everybody can tell me what mistake i made??
 

in fig 4.6 for k>kmin u r inside the unit circle so u are stable,
in the bode plot u can consider decreasing k as shifting the mag. curve downward while keeping the phase unshifted , so u are reaching the unity gain freq. earlier which happens to be more close to the -180 degree
 

safwatonline,very thanks for your enthusiastic reply ...
but i still don't quite catch on the reason you mentioned before,
for example, let k=0.2, then the loop gain < 1
before the phase shit reach 180 degree,
so the loop is stable? isn't it?
 

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