DAC161S997_15 Datasheet, PDF (20/39 Pages) Texas Instruments – DAC161S997 16-Bit SPI-Programmable DAC for 4-20 mA Loops

DAC161S997
SNAS621A – JUNE 2013 – REVISED DECEMBER 2014
Application Information (continued)
LOOP+
www.ti.com
I_DAC
DAC161S997
+
A(s)
-
BASE
G_m
g_m r_o
C_X3
RE
R_X1
I_AUX
C_X1 C_X2
R₁
R₂
COMA
C_X4
OUT
Figure 18. Capacitances Affecting Control Loop
LOOP-
Here it is assumed that the internal amplifier dominates the frequency response of the system, and it has a single
pole response. The BJT’s response, in the bandwidth of the control loop, is assumed to be frequency
independent and is characterized by the transconductance g_m and the output resistance r_o.
As in previous sections I_DAC and I_AUX represent the filtered output of the ∑Δ modulator and the quiescent current
of the companion devices.
The circuit in Figure 18 can be further simplified by omitting the on-board capacitances, whose effect will be
discussed in Stability, and by combining the amplifier, the external transistor and resistor R_E into one G_m block.
The resulting circuit is shown in Figure 19.
By assuming that the BJT’s output resistance (r_o) is large, the loop current I_LOOP can be expressed as:
(3)
LOOP+
A(s)G_mv_e
I_LOOP
I_DAC
A(s)G_m
+
v_e
r_o
-
I_AUX
R₁
R₂
I_LOOP
LOOP-
Figure 19. AC Analysis Model of a Transmitter
The sum of voltage drops around the path containing R₁, R₂ and v_e is:
(4)
An assumption is made on the response of the internal amplifier:
A(s)
=
A_o_o
s
(5)
20
Submit Documentation Feedback
Copyright © 2013–2014, Texas Instruments Incorporated
Product Folder Links: DAC161S997