Analog Devices AN584 Application Notes

AN-584

a

APPLICATION NOTE

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Using the AD813x

THEORY OF OPERATION

The AD813x differs from conventional op amps by the
external presence of an additional input and output. The
additional input, V

, controls the output common-

OGM

mode voltage. The additional output is the analog
complement of the single output of a conventional op
amp. For its operation, the AD813x makes use of two
feedback loops as compared to the single loop of con­ventional op amps. While this provides significant
freedom to create various novel circuits, basic op amp
theory can still be used to analyze the operation.

One of the feedback loops controls the output common­mode voltage, V

. Its input is V

OUT,cm

(Pin 2) and the

OCM

output is the common-mode, or average voltage, of the
two differential outputs (+OUT and –OUT). The gain of
this circuit is internally set to unity. When the AD813x is
operating in its linear region, this establishes one of the
operational constraints: V

OUT,cm

= V

OCM

.

The second feedback loop controls the differential opera­tion.

Similar to an op amp, the gain and gain-shaping of
the transfer function is controllable by adding passive
feedback networks. However, only one feedback net­work is
constrain the
desired, two
possible as a

required to “close the loop” and fully

operation. But depending on the function
feedback networks can be used. This is
result of having two outputs that are each

inverted with respect to the differential inputs.

DEFINITION OF TERMS

C

F

R

F

R

G

+D

IN

V

OCM

–D

IN

+IN

–IN

R

G

AD813x

R

F

C

F

–OUT

+OUT

R

V

,dm

L

OUT

,dm

Figure 1. Circuit Definitions

Differential voltage refers to the difference between two
node voltages. For example, the output differential volt­age (or equivalently output differential-mode voltage) is
defined as:

VVV

V

+OUT

=+(–)

OUT,dm OUT OUT

and

V

refer to the voltages at the +OUT and –OUT

–OUT

–

(1)

terminals with respect to a common reference.

Common-mode voltage refers to the average of two
node voltages. The output common-mode voltage is
defined as:

VVV

=+(+)/2

OUT,cm OUT OUT

–

(2)

PIN FUNCTION DESCRIPTIONS

Pin No. Mnemonic Function

1 –IN Negative Input
2V

OCM

Voltage applied to this pin sets the
common-mode output voltage with
a ratio of 1:1. For example, 1 V

dc
on VOCM will set the dc bias level
on +OUT and –OUT to 1 V.

3 V+ Positive Supply Voltage
4 +OUT Positive Output. Note: The voltage

is inverted at +OUT.

at –D

5 –OUT

IN

Negative Output. Note: The voltage
at +DIN is inverted at –OUT.

6 V– Negative Supply Voltage
7 NC No Connect
8 +IN Positive Input

GENERAL USAGE OF THE AD813x

Several assumptions are made here for a first-order
analysis, which are the typical assumptions used for the
analysis of op amps:

• The input impedances are arbitrarily large and their
loading effect can be ignored.

• The input bias currents are sufficiently small so they
can be neglected.

• The output impedances are arbitrarily low.

• The open-loop gain is arbitrarily large, which drives
the amplifier to a state where the input differential
voltage is effectively zero.

• Offset voltages are assumed to be zero.

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© Analog Devices, Inc., 2002

AN-584

While it is possible to operate the AD813x with a purely
differential input, many of its applications call for a circuit
that has a single-ended input with a differential output.

For a single-ended-to-differential circuit, the RG of the
undriven input will be tied to a reference voltage. For
now this is ground. Other conditions will be discussed
later. Also, the voltage at V

, and hence V

OCM

OUT,cm

will be
assumed to be ground for now. Figure 2 shows a gener­alized schematic of such a circuit using an AD813x with
two feedback paths.

R

F1

R

G1

+

R

G2

R

F2

Figure 2. Typical Four-Resistor Feedback Circuit

For each feedback network, a feedback factor can be
defined, which is the fraction of the output signal that is
fed back to the opposite-sign input. These terms are:

β1/( )

=+RRR

111

GGF

β2/( )

=+RRR

222

GGF

(3)

(4)

The feedback factor ␤1 is for the side that is driven, while
the feedback factor ␤2 is for the side that is tied to a ref­erence voltage (ground for now). Note also that each
feedback factor can vary anywhere between 0 and 1.

A single-ended-to-differential gain equation can be
derived that is true for all values of ␤1 and ␤2:

G 2 (1 1) / ( 1 2)=× +–

βββ

(5)

This expression is not very intuitive. One observation
that can be made right away is that a tolerance error in
␤1 does not have the same effect on gain as the same
tolerance error in ␤2.

For RF1/RG1 = RF2/RG2 the gain equation simplifies to G = RF/RG.

BASIC CIRCUIT OPERATION

One of the more useful and easy to understand ways to
use the AD813x is to provide two equal-ratio feedback
networks. To match the effect of parasitics, these net­works should actually be comprised of two equal-value
feedback resistors, R
tors, R

. This circuit is diagrammed in Figure 1.

G

and two equal-value gain resis-

F

Like a conventional op amp, the AD813x has two
dif

ferential inputs that can be driven with both a differen­tial-mode input voltage, V
voltage, V

. Another input, V

IN,cm

conventional op amps, but provides another
consider on the AD813x. It is totally separate
above inputs. There are also two complementary

, and a common-mode input

IN,dm

OCM

, is not

present on

input to

from the

outputs
whose response can be defined by a differential-mode
output, V

and a common-mode output, V

OUT,dm

OUT,cm

.

Table I indicates the gain from any type of input to either
type of output.

Table I. Differential and Common-Mode Gains

Input V

V

IN,dm

V

IN,cm

V

OCM

OUT,dm

RF/R
0 0 (By Design)
0 1 (By Design)

The differential output (V
tial input voltage (V

) times RF/RG. In this case, it does

IN,dm

G

OUT,dm

V

OUT,cm

0 (By Design)

) is equal to the differen-

not matter if both differential inputs are driven, or only
one output is driven and the other is tied to a reference
voltage, like ground. As can be seen from the two zero
entries in the first column, neither of the common-mode
inputs has any effect on this gain.

The gain from V

IN,dm

to V

is 0 and to first-order does

OUT,cm

not depend on the ratio matching of the feedback net­works. The common-mode feedback loop within the
AD813x provides a corrective action to keep this gain
term minimized. The term “balance error” describes the
degree to which this gain term differs from zero.

The gain from V

IN,cm

to V

does directly depend on

OUT,dm

the matching of the feedback networks. The analogous
term for this transfer function, which is used in conven­tional op amps, is “common-mode rejection ratio” or
CMRR. Thus, if it is desirable to have a high CMRR, the
feedback ratios must be well matched.

The gain from V

IN,cm

to V

is also ideally 0, and is

OUT,cm

first-order independent of the feedback ratio matching.
As in the case of V

IN,dm

to V

, the common-mode

OUT,cm

feedback loop keeps this term minimized.

The gain from V

OCM

to V

is ideally 0 only when the

OUT,dm

feedback ratios are matched. The amount of differential
output signal that will be created by varying V

OCM

is

related to the degree of mismatch in the feedback networks.

–2–

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V

controls the output common-mode voltage V

OCM

OUT,cm

with a unity-gain transfer function. With equal-ratio
feedback networks (as assumed above), its effect on
each output will be the same, which is another way to
say that the gain from V

OCM

to V

is zero. If not

OUT,dm

driven, the output common-mode will be at mid-supplies.
It is recommended that a 0.1 µF bypass resistor be con­nected to V

OCM

.

When unequal feedback ratios are used, the two gains
associated with V

become nonzero. This signifi-

OUT,dm

cantly complicates the mathematical analysis along
with any intuitive understanding of how the part oper­ates. Some of these configurations will be in another
section.

AN-584

In the case of a single-ended input signal (for example if
–D

is grounded and the input signal is applied to +DIN),

IN

the input impedance becomes:



R

IN,dm




=






R

G

1

R

–

2

RR

×+

()

GF

The circuit’s input impedance is effectively higher than it
would be for a conventional op amp connected as an
inverter because a fraction of the differential output voltage
appears at the inputs as a common-mode signal, partially
bootstrapping the voltage across the input resistor R







F




(8)

G

.

ESTIMATING THE OUTPUT NOISE VOLTAGE

Similar to the case of a conventional op amp, the differ­ential output errors (noise and offset voltages) can be
estimated by multiplying the input referred terms, at +IN
and –IN, by the circuit noise gain. The noise gain is
defined as:





R

F

1





R





G

(6)

G

=+

N

To compute the total output referred noise for the circuit
of Figure 1, consideration must also be given to the
contribution of the resistors

R

and

F

R

. Refer to Table II

G

for estimated output noise voltage densities at various
closed-loop gains.

Table II. Recommended Resistor Values and Noise Performance
for Specific Gains

Output Output

R

GRF

Gain (⍀)(⍀) –3 dB AD813x

Bandwidth Noise Noise

AD813x + RG, R

F

1 499 499 360 MHz 16 nV/Hz 17 nV/Hz
2 499 1.0 k 160 MHz 24.1 nV/Hz 26.1 nV/Hz
5 499 2.49 k 65 MHz 48.4 nV/Hz 53.3 nV/Hz
10 499 4.99 k 20 MHz 88.9 nV/Hz 98.6 nV/Hz

CALCULATING AN APPLICATION CIRCUIT’S INPUT
IMPEDANCE

The effective input impedance of a circuit such as that in
Figure 1, at +D

and –DIN, will depend on whether the

IN

amplifier is being driven by a single-ended or differen­tial signal source. For balanced differential input signals,
the input impedance (R

) between the inputs (+D

IN,dm

IN

and –DIN) is simply:

=×

R2R

IN,dm G

(7)

INPUT COMMON-MODE VOLTAGE RANGE IN SINGLE­SUPPLY APPLICATIONS

The AD813x is optimized for level-shifting “ground”

ref­erenced input signals. For a single-ended input this
would imply, for example, that the voltage at –DIN in Figure 1
would be zero volts when the amplifier’s negative power
supply voltage (at V–) was also set to zero volts.

SETTING THE OUTPUT COMMON-MODE VOLTAGE

The AD813x’s V

pin is internally biased at a voltage

OCM

approximately equal to the mid-supply point (average
value of the voltages on V+ and V–). Relying on this
internal bias will result in an output common-mode voltage
that is within about 100 mV of the expected value. In
cases where more accurate control of the output common
mode level is required, it is recommended that an external
source, or resistor divider (with R

< 10 kΩ), be used.

SOURCE

APPLICATION NOTES FOR THE AD813x DIFFERENTIAL AMPS
ADC DRIVING
High-Performance ADC Driving

The circuit in Figure 3 shows a simplified front-end
con

nection for an AD813x driving an AD9224, a 12-bit,
40 MSPS A/D converter. The A/D works best when
driven differentially, which minimizes its distortion as
described in its data sheet. The AD813x eliminates the
need for a transformer to drive the ADC and performs
single-ended-to-differential conversion, common-mode
level-shifting, and buffering of the driving signal.

The positive and negative outputs of the AD813x are
connected to the respective differential inputs of the
AD9224 via a pair of 49.9 Ω resistors to minimize the effects
of the switched-capacitor front-end of the AD9224. For
best distortion performance it is run from supplies of ±5 V.

-

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–3–