AD625

REV. D

–14–

GAIN

1000

1

800

400

200

100

80

40

20

10

8

4

2

1

4

16

64

256

1024

4096

Figure 40. Time to 0.01% of a 20 V Step Input for

SPGA with AD625

DETERMINING SPGA RESISTOR NETWORK VALUES

The individual resistors in the gain network can be calculated

sequentially using the formula given below. The equation deter-

mines the resistors as labeled in Figure 41. The feedback resis-

tors and the gain setting resistors are interactive, therefore; the

formula must be a series where the present term is dependent on

the preceding term(s). The formula

Rk

R

G

G

G

R

Fi

Fj

j

i

i

F

+

=

=

=

=

=

∑

1

0

1

1

0

0

20

1

1

0

(

–

)( –

)

Ω

can be used to calculate the necessary feedback resistors for any

set of gains. This formula yields a network with a total resistance

of 40 k

Ω. A dummy variable (j) serves as a counter to keep a

running total of the preceding feedback resistors. To illustrate

how the formula can be applied, an example similar to the

calculation used for the resistor network in Figure 38 is exam-

ined below.

1) Unity gain is treated as a separate case. It is implemented

with separate 20 k

Ω feedback resistors as shown in Figure 41.

It is then ignored in further calculations.

2) Before making any calculations it is advised to draw a resistor

network similar to the network in Figure 41. The network

will have (2

× M) + 1 resistors, where M = number of gains.

For Figure 38 M = 3 (4, 16, 64), therefore, the resistor string

will have seven resistors (plus the two 20 k

Ω “side” resistors

for unity gain).

0

= 0.

1

= (20 k

Ω – R

2

= [20 k

Ω – (R

0

1

= 15 k

Ω ∴ R

3

= [20 k

Ω – (R

0

1

2

= 18.75 k

Ω ∴ R

mined last. Its value is the remaining resistance of the 40 k

Ω

string, and can be calculated with the equation:

Rk

R

GFj

j

M

=

=

∑

(

–

)

40

2

0

Ω

Ω – 2 (R

40 k

Ω – 39.375 kΩ = 625 Ω

5) If different resistor values are desired, all the resistors in the

network can be scaled by some convenient factor. However,

raising the impedance will increase the RTO errors, lowering

the total network resistance below 20 k

Ω can result in ampli-

fier instability. More information on this phenomenon is

given in the RPGA section of the data sheet. The scale factor

will not affect the unity gain feedback resistors. The resistor

network in Figure 38 has a scaling factor of 650/625 = 1.04,

1

2

3

tor values will match exactly.

6) Round off errors can be cumulative, therefore, it is advised to

carry as many significant digits as possible until all the values

have been calculated.

AD75xx

TO GAIN SENSE

(PIN 2)

20k

20k

TO GAIN SENSE

(PIN 15)

TO GAIN DRIVE

(PIN 5)

TO GAIN DRIVE

(PIN 12)

CONNECT IF UNITY

GAIN IS DESIRED

CONNECT IF UNITY

GAIN IS DESIRED

Figure 41. Resistors for a Gain Setting Network