Dynamic Load Carrying Capacity of Mobile-Base Flexible-Link Manipulators: Feedback Linearization Con
1 Digital Cartesian feedback linearization Digital Cartesian Feedback Linearization of Switched Mode...
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1Digital Cartesian feedback linearization
Digital Cartesian Feedback Linearization of Switched Mode
Power AmplifiersAlejandro Viteri, Amir Zjajo, Thijmen Hamoen, Nick van der Meijs
Delft University of Technology
2Digital Cartesian feedback linearization
• Motivation
• Linearization by means of feedback
• Cartesian feedback modeling
• Digital design
• Simulation results
• FPGA synthesis & results
• Conclusions
Outline
3Digital Cartesian feedback linearization
Motivation
• A power efficient switch mode PA in the transmitter
• No power losses due to dissipation• Improves lifetime of batteries• Better use of the solar panels• Non-linear
ISIS Innovative Solutions In
Space
• New version of the transceiver
• Previous version of the transceiver
• A linear mode power amplifier (PA)
4Digital Cartesian feedback linearization
Feedback system with distortion
)()(1
)(
)(1
)()(
)(1
)(
)(
1)( sD
sL
sL
sL
sDsr
sL
sL
ssy fb
fw
Linearization by means of feedback
)()()( ssGsL Loop gain:
• In a feedback system linearity depends on the loop gain
• Distortion in the feedback is not attenuated
• Better control of the system linearity is achieved
5Digital Cartesian feedback linearization
General model
61 TpA
Cartesian feedback
• Stability condition (PM ≥ 60o)
• The signal is decomposed in Cartesian components
• Feedback is applied to each component
• A delay (e-Ts ) will model the latency of the digital domain
6Digital Cartesian feedback linearization
Phase shift problem
Cartesian feedback
Sources of phase shift
• Delays in the loop
• Distortion in the PA and
• Up/Down converters
• To changes and aging
7Digital Cartesian feedback linearization
Mixed signal model
Cartesian feedback
• The dominant poles of this system determine the stability• Oversampling allows to relax the order of the LPFs
• Allows integration
• Reduces area usage and weight in the satellite
• Low power consumption
Benefits
8Digital Cartesian feedback linearization
Stability analysis by root locus
Mixed-signal Cartesian feedback
21 TTApPM 1A
System root locus
60PM
Compensated system root locus
ff
f
zp
pz
10
3
9Digital Cartesian feedback linearization
Mixed-signal Cartesian feedback
seCs
fffs
TsDrPdin
error
0
22)(
Phase regulation
• Source signals modeled as a ramp signal s
fs s
s
2
)(
• Transfer function of phase error
10Digital Cartesian feedback linearization
Mixed-signal Cartesian feedback
DrPdin fffC 20
Phase regulation
• Final value theorem: )( lim)( lim0
sst errors
errort
00
20
s
TsDrPdin
eCs
fff
seCs
fffs
TsDrPdin
error
0
22)(
11Digital Cartesian feedback linearization
Mixed-signal Cartesian feedback
DrPdin fffC 20
IQQIkk
Ct
dt
dshift '')(
21
0
Phase regulation
'sin'' 21 kkIQQI
21
''
kk
IQQIerror
12Digital Cartesian feedback linearization
Digital design
• Delay correction by signal rotation
• Magnitude signal for envelope restoration
13Digital Cartesian feedback linearization
Architecture
14Digital Cartesian feedback linearization
Simulation results
• Amplification of 20 dB
• IMD -40 dBc satisfied
15Digital Cartesian feedback linearization
Logic
Utilization
Used/
Available%
4 input LUTs 428/1536 27%
MULT18x18 2/4 50%
I/O Blocks 87/97 89%
FPGA synthesis
• Spartan3 X3s50-4tq144• 50K System gates• 1536 equivalent logic
cells
16Digital Cartesian feedback linearization
Item Value Units
Bandwidth 9.6 kHz
Loop Gain 10
System delay 400 ns
Bit length 12 bits
Clk freq. 83.33 MHz
Clk cycles 15
Latency 180 ns
Slack 220 ns
Area 27 %
Power 33.31 † mW† Xilinx Xpower Analyzer
Results
• Power budget 1.7 W
• 33.31 mW in a FPGA
• 1.96% of the total power budget
• Latency of 180 ns
• Slack of 220 ns for A/D and D/A
17Digital Cartesian feedback linearization
• Mixed-signal Cartesian feedback proves to be an efficient linearization method for a stable system with sufficient phase margin.
• Feedback improves linearity when provided with an adequate amount of loop gain.
• The results show that the use of the CORDIC algorithm proves to be a simple, low-power and robust solution for the low bandwidth input signal.
Conclusions
18Digital Cartesian feedback linearization
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