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Feedback System Design
4-5
Technical Information
The closed−loop gain is set to 27 dB to allow enough gain from the 3−V signal
to the A+ voltage range. This leaves sufficient low−frequency correction.
Figure 4−4 shows the circuit used for the APA100 feedback. Equation (2)
shows the closed−loop response.
Closed−loop gain + 45
R20
R18
(2)
Resistors R20 and R18 need to be set low to limit noise. Resistor R18 is set
to 2000 Ω and R18 set to 1000 Ω for a closed−loop gain of 22.4 V/V.
To calculate the values for the other resistors and capacitors, the open−loop
response needs to be examined; so, assume that R20 is not placed. Fix the
gain of the TPA2001D1 + TAS5111 = 35 dB = 56 V/V. As Equation (3) shows,
the open−loop gain is the gain of the TPA2001D1 + TAS5111 times the
feedback impedance (Zf) of the integrator circuit/the input resistance (R18).
Open−loop gain + 56
Zf
R18
(3)
The feedback impedance (Zf) is the impedance of C21 in parallel to the
impedance of C25 plus R24.
Zf +
1
sC21
ø
ǒ
1
sC25
) R24
Ǔ
(4)
The feedback impedance can be reduced as shown in Equation 5.
(5)
Zf +
1
s (C21 ) C25
1 ) s R24 C25)
ǒ
1 ) s
R24 C21 C25
C21)C25
Ǔ
The feedback impedance is substituted into the open−loop gain equation as
shown in Equation 6.
(6)
Open−loop gain +
56
s R18 (C21 ) C25
1 ) s R24 C25)
ǒ
1 ) s
R24 C21 C25
C21)C25
Ǔ
From Equation 6, there are two poles and one zero. The first pole is at dc
from the 1/s term. The first pole actually gets pushed out if R21 is installed,
but it is still a very low frequency. The poles and zeros are shown in Equa-
tions 7 and 8.
Fz +
1
2p R24 C25
(Hz)
(7)
Fp +
C21 ) C25
2p R24 C21 C25
(Hz)
(8)
To achieve a 40-kHz bandwidth, the open−loop gain (Equation 6) must equal
22.4 V/V (27 dB) at f = 40 kHz (s = −j 2π f).