An Improved Universal CMOS Current-Mode Analog Function

Synthesizer Muhammad Taher Abuelma’atti

King Fahd University of Petroleum and Minerals , Saudi Arabiaand

Nawal Mansour Al-YahiaGirls College of Science, Saudi Arabia

• Analog nonlinear circuits are widely used in instrumentation, communication, neural networks, signal processing and medical equipment.

• Diodes and linear resistors, BJTs JFETs, MOSFETs, BiCMOS operational amplifiers, current conveyors and operational transconductance amplifiers are widely used in designing analog nonlinear circuits.

Numerous nonlinear functions can be approximated by:

55

44

33

2210)( xaxaxaxaxaayxf

1||;66 xxa

For example:* For y=1/(1-x), a0 = a1 = a2 = a3 = a4 = a5 =a6 =1

* For y=ln(1+x), a0 = 0, a1 =1, a2 =-1/2, a3 = 1/3, a4 =-1/4, a5 =1/5, a6 =-1/6

* For y=cos(x), a0 = 1, a1 =0, a2 =-1/2, a3 = 0, a4 =1/24, a5 =0, a6 =-1/720

The traditional class-AB current mirror and its modification to provide squaring unit (SU) and current proportional to the

input current

VDD

VSS

M1 M2

M3 M4

M6

M5

M8

M9

M10

M7

Iq

Iq

Iin

2Iq

IBIA

Using the translinear principle then:

qinqDDqB IIIIIII 2//2// 45

22 8// qinqA IIII

A normalized current proportional to can be obtained using the square-difference identity . Additional SUs can be used to obtain normalized currents proportional to , and .

3x

ABBABA 4)()( 22

4x 5x 6x

Examples with SPICE Simulation Results

In the following examples the bias current

Iq = 1 uA, the input current Iin is changing between 0 and 1 uA, the DC supply voltages are 2 V and x= Iin/ Iq.

Subcircuit for realizing y=1/(1-x)

VDD

VSS2/1

2/1 8/1

8/1

R201

1uA

201

654321 xxxxxx

x

x2

23x

84x

25x

86x

y=1/(1-x)Error < 1% for x<0.5

Subcircuit for realizing y=cox(x)

1/90

R213

2x

1/2

1A

213

VDD

8

4x

VSS

1/3

72024

1

2

11

642 xxx

8

6x

y=cox(x)Error < 1% for x<1

Subcircuit for realizing y=ln(1+x)

2x

VDD 1/2

23x

84x

VSS

R227227

4/32/5

65432

6

1

5

1

4

1

3

1

2

1xxxxxx

2/3 2/1

25x

86x

x

y=ln(1+x) Error < 1% for x<0.675

Conclusion

1. The proposed technique is very flexible. Any nonlinear function can be realized once its Taylor series expansion is obtained.

2. Accuracy can be improved by using additional terms in the Taylor series.

3. No current multipliers are used.