Datasheet

I
LOOP
= I
DAC
(1 + + I
AUX
R
1
R
2
)
s
R
2
R
E
A
o
&
o
R
2
R
E
s + A
o
&
o
R
2
R
E
s + A
o
&
o
&
R
1
R
2
)
0 dB
A
o
G
m
R
2
&
o
I
LOOP
= I
DAC
(1 + + I
AUX
R
1
R
2
)
s
s + A
o
G
m
R
2
&
o
A
o
G
m
R
2
&
o
s + A
o
G
m
R
2
&
o
20 log (1 +
A(s) =
s
A
o
&
o
LOOP+
LOOP-
R
1
R
2
+
-
A(s)G
m
I
DAC
I
AUX
-+
I
LOOP
v
e
I
LOOP
A(s)G
m
v
e
r
o
DAC161P997
SNAS515E –JULY 2011–REVISED OCTOBER 2013 www.ti.com
(3)
Figure 17. AC Analysis Model of a Transmitter
The sum of voltage drops around the path containing R
1
, R
2
and v
e
is:
(4)
an assumption is made on the response of the internal amplifier::
(5)
By combining the above the final expression for the I
LOOP
as a function of 2 inputs I
DAC
and I
AUX
is:
(6)
The result above reveals that there are 2 distinct paths from the inputs I
DAC
and I
AUX
to the output I
LOOP
. I
DAC
follows the low-pass, and the I
AUX
follows the high-pass path.
In both cases the corner frequency is dependent on the effective transconductance, G
m
, of the external
transistor. This implies that control loop dynamics could vary with the output current I
LOOP
if G
m
were allowed to
be just native device transconductance g
m
. This undesirable behavior is mitigated by the degenerating resistor
R
E
which stabilizes G
m
as follows:
(7)
This results in the frequency response which is largely independent of the output current I
LOOP
:
(8)
While the bandwidth of the I
DAC
path may not be of great consequence given the low frequency nature of the 4-
20 mA current loop systems, the location of the pole in the I
AUX
path directly affects PSRR of the transmitter
circuit. This is further discussed in PSRR.
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