Automatic Neural Model Development for Power Amplifier
description
Transcript of Automatic Neural Model Development for Power Amplifier
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!