Automatic Neural Model Development

for Power Amplifier

Na Weicong

04/20/23

Comparison & Conclusion

Content

Problem & Solution

Example: Power Amplifier

Automatic Neural-Network Structure Adaptation with Interpolation Approachesn, j Interpolation

Approaches

Goodlearning

Add a hidden neuron

n-1, j Has it been Trained before?

Training& Test

Goodlearning

UnderlearningStop Add a hidden neuron

No

Yes

Add a hidden neuron

Stop

Overlearning ?

Add training data& test data

Yes

No

Training& Test

Underlearning

Example: MOSFET vs. Power Amplifier

Pin= -5~+5 dBmVdin= 2~3 VRL= 50~60f= 2.1~2.8 kHz

Vgs

···

Vds

Id

Vgs= 0~4 VVds= 0~4 V

Interpolation Algorithm• Select the type of interpolation formula. Linear Function, 2nd order Polynomial Function etc.

• Select the points which can represent the interpolation region.

These points are always the boundary points of the region.

• Calculate the equation to obtain the parameters in the interpolation equation.

• Substitute the coordinates of the interpolated point into the interpolation equation whose parameters we have known, then we will get the final result.

Step1: Select the type of interpolation formula.

Power Amplifier: 3rd order polynomial function

2 2 20 1 1 2 2 4 4 11 1 12 1 2 14 1 4 22

3 3 31

2 4

2 2 4

4

1 4

4

+ + +

x x x x x x x x x

x x bx

x

MOSFET: 2nd order polynomial function

2 20 1 1 2 2 11 1 12 1 2 22 2x x x x x x b

(1) (1) (1) (1) (1) (1) (1) (1) (1) (1)

1 1 1 1 2 4

( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2)

1 1 1 1 2 4

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1 1 1 2 4

(1)

1 4

2 2 22 4 2 4

2 2 22 4 2 4

2 2 22 4 2 4

31

1

1 k k k k k k k k k k

x x x x x x x x x x

x x x x x x x x x x

x x x x x x x x x x

x x

(1)

( 2) ( 2)

1 4

( ) ( )

1 4

(1)

( 2)

( )

3

3 3

3 3

1

4

0

1

2

4

11

12

14

22

44

kk k

b

b

b

x x

x x

k: the number of samples

T -1 T ) ( Ap b p A A A b

(1)(1) (1) (1) (1) (1) (1)

1 1 1 2

( 2)( 2) ( 2) ( 2) ( 2) ( 2) ( 2)

1 1 1 2

( )( ) ( ) ( ) ( ) ( ) ( )

1 1 1 2

0

2 212 2

2 222 2

11

2 2122 2

22

1

1

1 kk k k k k k

bx x x x x x

bx x x x x x

bx x x x x x

MOSFET: 2nd order polynomial function

Power Amplifier: 3nd order polynomial function

Step2: Select the points which can represent the interpolation region.

0 2 40

2

4

k =5+4=9

1 0 0 0 0 0

1 0 4 0 0 16

1 4 4 16 16 16

1 0 2 0 0 4

1 2 4 4 8 16

10 40 0 160 0 0

10 20 20 40 40 40

10 40 20 160 80 40

10 20 0 40 0 0

A

MOSFET:

Power Amplifier: k =64+16=81

6

4

1 0 0

1 1 1

10 0 0

10 10 10

A

64

19

5

16

Step3: Calculate the equation to obtain the parameters in the interpolation equation.

Ap b

T -1 T ( )p A A A b

Problem:

matrix is a singular matrix! T A A

Solution: Change 3rd order polynomial function!

(1) (1) (1) (1) (1) (1) (1) (1) (1) (1)

1 1 1 1 2 4

( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2)

1 1 1 1 2 4

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1 1 1 2 4

(1)

1 4

2 2 22 4 2 4

2 2 22 4 2 4

2 2 22 4 2 4

31

1

1 k k k k k k k k k k

x x x x x x x x x x

x x x x x x x x x x

x x x x x x x x x x

x x

(1)

( 2) ( 2)

1 4

( ) ( )

1 4

(1)

( 2)

( )

3

3 3

3 3

1

4

0

1

2

4

11

12

14

22

44

kk k

b

b

b

x x

x x

(1) (1) (1) (1) (1) (1) (1) (1) (1) (1)

1 1 1 1 2 4

( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2)

1 1 1 1 2 4

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1 1

(1)

1 2 4

(1

1

2 2 22 4 2 4

2 2 22 4 2 4

2 2 22 4 2 4

21

1

1 k k k k k k k k k k

x x x x x x x x x x

x x x x x x x x x x

x x x x x x x x x x

x x

) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1)

1 1 2 1

( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2)

1 1 1 2 1

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1 1

3 2 4 3 4 3 4 2 3 4

2 3 2 4 3 4 3 4 2 3 4

2 3 2 4 3 4k k k k k k k k k

x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x

x x x x x x x x x

(1)

( ) ( ) ( ) ( ) ( ) ( ) ( )

2

( 2)

( )

13 4 2 3 4

1

5

0

1

2

4

11

12

14

22

44

k k k k k k kk

b

b

bx x x x x x x

Comparison （ Example ： Power Amplifier）k

(stage)

# hidden neuron(initial)

# hidden neuron(final)

# train data

# test data

Testerror(%)

CPUtime(s)

NN 21 15 22 782 181 2.1126 1001.4

InterpolationModel

18 15 20 767 181 2.1814 888.1

* tested by the same test data

Thanks!