REV. B

AD633

–4–

0.1 F

+15V

E

W =

10V

8

7

6

5

1

2

3

4

AD633JN

0.1 F

X1

X2

Y1

Y2

W

Z

–15V

C

R

R1

1k

R2

3k

Figure 5. ”Bounceless” Frequency Doubler

At

ω

° (and is

attenuated by

√2), and the Y input lags the X input by 45° (and

is also attenuated by

√2). Since the X and Y inputs are 90° out of

phase, the response of the circuit will be (satisfying Equation 3):

W

V

E

t

E

t

E

V

t

oo

o

+°

(

)

−°

(

)

)

1

10

2

45

2

45

40

2

2

sin

sin

sin

ωω

ω

(Equation 4)

which has no dc component. Resistors R1 and R2 are included to

restore the output amplitude to 10 V for an input amplitude of 10 V.

The amplitude of the output is only a weak function of fre-

quency: the output amplitude will be 0.5% too low at

ω =

0.9

ω

ω

ω

Generating Inverse Functions

Inverse functions of multiplication, such as division and square

rooting, can be implemented by placing a multiplier in the feed-

back loop of an op amp. Figure 6 shows how to implement a

square rooter with the transfer function

WV E

=−

( )

10

(Equation 5)

for the condition E<0.

0.1 F

+15V

E

8

7

6

5

1

2

3

4

AD633JN

0.1 F

X1

X2

Y1

Y2

W

Z

–15V

W =

–(10V)E

0.1 F

0.1 F

R

10k

1N4148

R

10k

+15

–15

AD711

Figure 6. Connections for Square Rooting

0.1 F

+15V

E

8

7

6

5

1

2

3

4

AD633JN

0.1 F

X1

X2

Y1

Y2

W

Z

–15V

W = –10V

E

0.1 F

0.1 F

R

10k

1N4148

R

10k

+15

–15

AD711

Figure 7. Connections for Division

Likewise, Figure 7 shows how to implement a divider using a

multiplier in a feedback loop. The transfer function for the

divider is

WV

E

=−

( )

10

(Equation 6)

0.1 F

+15V

8

7

6

5

1

2

3

4

AD633JN

0.1 F

X1

X2

Y1

Y2

W

Z

–15V

R1

R2

W =

+ S

10V

X

INPUT

Y

INPUT

(R1 + R2)

R1

1k

R1, R2

100k

S

Figure 8. Connections for Variable Scale Factor

Variable Scale Factor

In some instances, it may be desirable to use a scaling voltage

other than 10 V. The connections shown in Figure 8 increase

the gain of the system by the ratio (R1 + R2)/R1. This ratio is

limited to 100 in practical applications. The summing input, S,

may be used to add an additional signal to the output or it may

be grounded.

Current Output

The AD633’s voltage output can be converted to a current

output by the addition of a resistor R between the AD633’s W

and Z pins as shown in Figure 9 below. This arrangement forms

10V

1

R

X

INPUT

0.1 F

+15V

–15V

8

7

6

5

1

2

3

4

AD633JN

0.1 F

X1

X2

Y1

Y2

W

Z

Y

INPUT

1k

R

100k

R

Figure 9. Current Output Connections