Texas Instruments APA100 manual Feedback System Design

Feedback System Design

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.

1		1
Zf +		ø ￿		) R24￿
	sC21		sC25		(4)

The feedback impedance can be reduced as shown in Equation 5.

Zf +			1	1 ) s		R24	C25)
	s		(C21 ) C25	￿1 ) s	R24 C21			C25	￿		(5)
						C21)C25
The feedback impedance is substituted into the open−loop gain equation as
shown in Equation 6.
Open−loop gain +			56			1 ) s	R24 C25)
		s	R18 (C21 ) C25		￿1 ) s			R24	C21 C25	￿	(6)
								C21)C25

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		(Hz)
	2p		R24	C25			(7)
Fp +			C21 ) C25			(Hz)
		2p	R24	C21	C25		(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 2 π f).

Technical Information 4-5