L292
CLOSED-LOOP SYSTEM STEP RESPONSE
a) Small - signals analysis.
The transfer function (3) can be written as follows:
s
IM
VI
(s)
=
0.044
Rs
1+
2ξωo
1+
2 ξs + s2
ωo ω o 2
(7)
where
wo
=
√GmoRs
R4 C RF CF
is the cutoff frequency
ξ
=
√R4C
4 RF CF Gmo Rs
is the dumping factor
By choosing the ξ value, it is possible to determine
the system response to an input step signal.
Examples :
1) ξ = 1 from which
IM
(t)
=
0.044
Rs
[
1
−
e
−
t
2RF
CF
(1
+
4
t
RF
CF)
]
•
Vi
(where Vi is the amplitude of the input step).
2) ξ
=
1
√2
from which
IM (t)
=
0.044
Rs
(1
−
cos
2
t
RF
CF
e
−
2
t
RF
CF
)
Vi
Figure 8. Small Signal Step Response
(normalized amplitude vs.
t / RFCF).
V7 = 200 mV/div.
IM = 100 mA/div.
t = 100 µs/div.
with VI = 1.5 Vp.
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