1. University of California San Diego
Linear Dropout Regulator based Power Distribution Design under Worst Loading
Amirali Shayan, Xiang Hu
Chung-Kuan Cheng
University of California San Diego
Christopher Pan
Huawei
Wenjian Yu
Tsinghua University

2. Worst case current synthesis Poles/Zeros based Methodology
Agenda
Introduction and Motivation
LDO based PDN Design under Worst Loading
Worst case current synthesis
Poles/Zeros based Methodology
Experimental Results and Trade offs
Conclusion Remarks

3. Introduction LDO design will enable: LDO design challenges
Localized on die regulation
Relax off chip impedance
Power saving
Finer grain power management
LDO design challenges
Power consumption
Area of the power MOSFET
Stability of the feedback loop
Physical design

4. LDO based PDN Optimization under Worst Loading
Virtually eliminate 1st and 2nd droops
|z|
Original
Optimize Package
With LDO
RPCB
RDIE
RPKG TR VR
Power saving opportunity
LDO
Integrated On-die LDO Shortens the PDN loop
Freq
Bulk
caps
Package
Die MB
caps
LDO
VRM
Motherboard
Adv #1: Better dynamic power management through reduced response time
Adv #2: Maintain low package cost while provide adequate power delivery

5. LDO-PDN Model of Design (1)
Operation region of the power MOSFET depends on the Vds=Vext-Vout comparison with (Vgs-Vth).
In our analysis, power MOSFET is in the linear region.

6. LDO-PDN (2) – Model Approximation

7. Proposed Flow for Worst Case Loading LDO Optimization

8. Problem Formulation P = LDO Power C = Decoupling Capacitor
P0 = Power limit
I peak = Peak loading current of functional block
Vmax = Worst voltage drop based on rogue wave
Z LDO-PDN = impedance profile of ldo-pdn

9. LDO-PDN Output Impedance
impedance zero =
Z1= x 1e9
Z4,5= ± i × 1e9
impedance pole =
p1=
p4,5= ± i × 1e9
Impedance k=

10. Step Response of the LDO-PDN

11. Analytical Worst Step Response

12. “Rogue Wave” Phenomenon
Worst-case noise response: The maximum noise is formed when a long and slow oscillation followed by a short and fast oscillation.
Rogue wave: In oceanography, a large wave is formed when a long and slow wave hits a sudden quick wave.
High-frequency oscillation corresponds to the resonance of the 1st stage
Low-frequency oscillation corresponds to the resonance of the 2nd stage

13. Ideal Worst-Case PDN Noise
Problem formulation I
PDN noise:
Worst-case current [Xiang ’09]:
Zero current transition time. Unrealistic!

14. Rogue Wave based Current Vector Synthesis

15. Algorithm for Vector-based Rogue Wave Generation
for i = 0 to N-window_size Begin sum each current peak of current pattern(i, i+window_size - 1) End sorted_list_des = sorting the sum of the intervals of current peak descending sorted_list_asc = sorting the sum of the intervals of current peak ascending //here is for worst-case calculating for i = 0 to N-window_size and i is increased by window_size //N is the size of impulse_reseponse if impulse_response(i) > 0 current_list = sorted_list_des else current_list = sorted_list_asc for j = 0 to M - window_size + 1 //M is the size of current pattern idx_current = current_list(j) tmp_val = convolution of impulse_response(i, i + window_size - 1) and current_pattern(idx_current, idx_current + window_size -1) if tmp_val > max_val max_val = tmp_val max_current(i, i+window_size -1) = current_pattern(idx_current, idx_current + window_size - 1) break end end //end of for j end //end of for i
Complexity of algorithm =
N= Impulse response size
m= Current windows size

16. Vector-based Synthetic Rogue Wave

17. Rogue-wave Synthesis Resolution Window Sensitivity to Vmax
For the rest of analysis, window resolution = 3nsec is chosen.

18. Vmax LDO-PDN Voltage Drop (Overshoot)
Overshoot is a main concern for:
Reliability of devices
Hold margins

19. Vmin LDO-PDN Voltage Drop (Undershoot)
undershoot is a main concern for:
Functional failures
Optimum Configuration:
Optimal Decap = 350pF
Optimal Power= 20uW
Noise = ~10mV

20. Conclusion and Summary
Introduced a design flow for worst case loading based on LDO poles and zeros.
Proposed an optimization based on the step response and rogue wave in LDO system.
Analyzed LDO power and decap area trade off in the LDO based system.
Experimental result show the target voltage drop budget will be met under worst loading with optimum LDO power and decoupling value.