Digitally-Assisted Compensationfor Timing Skew in ATE Systems

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Digitally-Assisted Compensation for Timing Skew in ATE Systems

K. Asami T. Tateiwa T. Kurosawa H. Miyajima H. Kobayashi

Advantest Corporation Gunma University

IEEE International Mixed-Signals, Sensors, and Systems Test Workshop

May 2011

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Research Goal

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 Fine time resolution

 Linear phase

Features of Proposed Digital Filter

τ Fine time shift

F(t)

F(t-τ)

(5)

Linear Phase FIR Filter Impulse Response

0 3 6

0 3

6

0 3 7

0 3

7 (1)Case 1

odd # of taps ・even symmetry

(2) Case 2

even # of taps・even symmetry

4 4

(7)

Frequency Characteristics

Case 1

Case 2

Case 3

Case 4

Phase : proportional to ω (linear phase) Time resolution of group delay Ts/2

(8)

Ideal LPF

：Sampling Frequency Frequency Characteristics

1.0

Impulse Response

Fourier Transform

1 2 3 4 5 -5 -4 -3 -2 -1

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Discrete-Time Representation of Ideal LPF

Fourier Transform

FIR (Finite Impulse Response)

zero

(11)

Impulse Response Time-Shift

1 2 3 4 5 -5 -4 -3 -2 -1

No change of Gain

Δt time-shift of impulse response

(12)

Time-Shift and Filter Coefficients

FIR filter

1 2 3 4 5 -5 -4 -3 -2 -1

IIR Filter

Time Shift

Ideal Delay-Filter

zero

(13)

2-Tap Filter: Model

1 0

(15)

2-Tap Filter: Delay Model

0 1

1 2 3 4 5 -5 -4 -3 -2 -1

FIR

IIR

(16)

2-Tap Filter: Delay Model

0 1

IIR FIR

(17)

Proposed Delay Digital Filter

(a) FIR Filter (b) Ideal Delay Filter

(c) Delay Digital Filter

Window

(18)

Frequency Characteristics of Proposed Delay Digital Filter

Case 1

Case 2

Case 3

Case 4

（）

(19)

Comparison of 2-Tap Filter Impulse Responses

5 10 15 20 25 30

-0.2 0 0.2 0.4 0.6

2 taps FIR Filter

5 10 15 20 25 30

-0.2 0 0.2 0.4 0.6

Delayed Filter (0.3 samples delay)

２-tap FIR coefficients

Impulse response changes.

Proposed Delay Filter

（

0.3 samples delay

）

2-Tap FIR Filter

zero

Non-zero

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Comparison of

2-Tap Filter Frequency Characteristics

-0.5 0 0.5

-20 -15 -10 -5 0

Gain [dB]

-0.5 0 0.5

-2 0 2

Normalized Frequency (Fs=1.0)

Phase [radian]

No change of gain

Phase slope changes

Proposed delay filter

Original filter Original filter and proposed delay filter

(22)

Hann

Finite Tap Truncation of Proposed Delay Filter

10 20 30 40 50 60

-0.2 0 0.2 0.4 0.6

61 taps Cosine Roll-off Filter

0.2 0.4 0.6

Delayed Filter with Hann window (0.3 samples delay)

61

タップコサインロールオフフィルタ

10 20 30 40 50 60

-0.2 0 0.2 0.4 0.6

61 taps Cosine Roll-off Filter

10 20 30 40 50 60

-0.2 0 0.2 0.4 0.6

Delayed Filter (0.3 samples delay)

Delay Filter

（

0.3 samples delay

）

61-Tap Cosine Roll-off Filter

Delay Filter

（

0.3 samples delay

）

Rectangular window

(23)

Effects of Window

0 0.05 0.1 0.15 0.2 0.25

-10 -5 0

Gain [dB]

0 0.05 0.1 0.15 0.2 0.25

30.299 30.2995 30.3 30.3005 30.301

Normalized Frequency (Fs=1.0)

Group Delay [samples]

Hann window

Rectangular window

Frequency characteristics of delay filter with 61-tap truncation

Gibbs oscillation of group delay

(24)

How to Apply Window

1 2 3 4 5 -5 -4 -3 -2 -1

Δt Ts

1 2 3 4 5 -5 -4 -3 -2 -1

Δt Ts

t Ts

Window

Centered at origin

Centered at

impulse response center

Window center shifted by Δt

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0 0.1 0.2 0.3 0.4 0.5 -100

-50 0

Power [dB]

マルチレート・フィルタの周波数特性(非対称)

0 0.1 0.2 0.3 0.4 0.5

-100 -50 0

Normalized frequency

Phase [rad]

0 0.1 0.2 0.3 0.4 0.5

-100 -50 0

Power [dB]

マルチレート・フィルタの周波数特性(対称)

0 0.1 0.2 0.3 0.4 0.5

-100 -50 0

Phase [rad]

Frequency Characteristics of Delay Filter after Applying Window

Delay 0.3 samples Filter Tap 100 taps

Window centered at origin Window centered at impulse response

Gain[dB]Phase[degree]

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0.1 0.15 0.2 0.25 0.3 0.35 0.4 49.79

49.795 49.8 49.805

Group delay

群遅延特性(非対称)

0.1 0.15 0.2 0.25 0.3 0.35 0.4 49.79

49.795 49.8 49.805

Group delay

群遅延特性(対称)

Group Delay Characteristics of Delay Filter after Applying Window

Delay 0.3 samples Filter Tap 100 taps

Window Han

Pass band (0.1～0.4)・Fs

(28)

0 0.1 0.2 0.3 0.4 0.5 -100

-50 0

Power [dB]

マルチレート・フィルタの周波数特性(非対称)

0 0.1 0.2 0.3 0.4 0.5

-100 -50 0

Phase [rad]

0 0.1 0.2 0.3 0.4 0.5

-100 -50 0

Power [dB]

マルチレート・フィルタの周波数特性(対称)

0 0.1 0.2 0.3 0.4 0.5

-100 -50 0

Phase [rad]

Frequency Characteristics of Delay Filter after Applying Window

gain[dB]Phase[degree]

Delay 0.3 samples Filter Tap 100 taps

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0.05 0.1 0.15 0.2 0.25 0.3 49.79

49.795 49.8 49.805

Group delay

群遅延特性(非対称)

0.05 0.1 0.15 0.2 0.25 0.3

49.79 49.795 49.8 49.805

Group delay

Group Delay Characteristics of Delay Filter after Applying Window

Delay 0.3 samples Filter Tap 100 taps

Window Han

Pass band (0.05～0.3)・Fs

Window centered at impulse response Window centered at origin

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0.05 0.1 0.15 0.2 0.25 0.3 49.79

49.795 49.8 49.805

Group delay

群遅延特性(非対称)

0.05 0.1 0.15 0.2 0.25 0.3

49.79 49.795 49.8 49.805

Group delay

Group Delay Characteristics of Delay Filter after Applying Window

Delay 0.3 samples Filter Tap 100 taps

Window centered at impulse response Window centered at origin

Applying window centered at impulse response

Constant group delay over entire passband

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Proposed Filter DC Gain Adjustment

Digital filter DC gain :

1 2 3 4 5 -5 -4 -3 -2 -1

t Ts

Δt Ts



^aⁿ

a⁰ a¹

a² a³

a⁴ a⁵

a⁶

a⁷ a⁸

a⁹

a¹⁰

DC gain adjustment due to finite tap truncation is required

● Original filter

● Delay filter



^N

(33)

0 0.1 0.2 0.3 0.4 0.5 -100

-50 0

Normalized Frequency

Power [dB]

ゲイン未調整

0 0.1 0.2 0.3 0.4 0.5

-150 -100 -50 0

Frequency

Phase [degree]

0 0.1 0.2 0.3 0.4 0.5

-100 -50 0

Power [dB]

ゲイン未調整

0 0.1 0.2 0.3 0.4 0.5

-150 -100 -50 0

Frequency

Phase [degree]

Frequency Characteristics of Proposed Delay Filter

With DC gain adjustment WithoutDC gain adjustment

Delay 0.3 samples

Filter Tap 101 taps

Window Han

Cut-off Freq. 0.4・Fs

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0 0.1 0.2 0.3 0.4 0

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

gain [dB]

マルチレート・フィルタの周波数特性

0 0.1 0.2 0.3 0.4

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

gain [dB]

マルチレート・フィルタの周波数特性

Gain Characteristics of Proposed Delay Filter

Delay 0.1samples

Filter Tap 101 taps

Delay 0.3 samples Filter Tap 101 taps

0.005dB 0.0006dB

With DC gain adjustment WithoutDC gain adjustment

gain[dB]

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0 0.1 0.2 0.3 0.4 0

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

gain [dB]

マルチレート・フィルタの周波数特性

Original FIR filter

Gain Characteristics of Proposed Delay Filter

0 0.1 0.2 0.3 0.4

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

gain [dB]

Delay 0.1samples

Filter Tap 101 taps

Window Han

Cutoff Freq. 0.4・Fs

Delay 0.3 samples Filter Tap 101 taps

Window Han

Cutoff Freq. 0.4・Fs

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0 0.1 0.2 0.3 0.4 0

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

gain [dB]

Original FIR filter

Gain Characteristics of Proposed Delay Filter

0 0.1 0.2 0.3 0.4

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

gain [dB]

Delay 0.1samples

Filter Tap 101 taps

Delay 0.3 samples Filter Tap 101 taps

DC gain adjustment

Delay filter gain

Original FIR filter gain

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I/Q Delay Mismatch in Quadrature Modulator

s(t) t

p/2 fc

DAC

DAC I(t) = cos (2pf₀t)

Q(t) = sin(2pf₀t) SSB signal input

f_c I(t)+jQ(t)

0 f_c- f₀ f_c+f₀

f f

delay

in analog domain

Image rejection ratio

(39)

I/Q Delay Mismatch Compensation in Quadrature Modulator

s(t) t

p/2 fc

DAC

DAC I(t) = cos (2pf₀t)

Q(t) = sin(2pf₀t) SSB signal

DAC ： digital-to-analog converter SSB ： single side band

f_c I(t)+jQ(t)

0 f_c- f₀ f_c+f₀

f f

Delay

in analog domain

digital timing compensation τ

(40)

Matlab Simulation Results

(b) Timing skew case

Delay 0.3 samples Filter tap # 61 taps

-0.5 0 0.5

-140 -120 -100 -80 -60 -40 -20 0

Magnitude [dB]

タイミング・スキューのある信号image signal

-0.5 0 0.5

-140 -120 -100 -80 -60 -40 -20 0

Magnitude [dB]

理想信号

(a) Ideal case

signal

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Matlab Simulation Results

-0.5 0 0.5

-140 -120 -100 -80 -60 -40 -20 0

Magnitude [dB]

ゲイン無調整

(c) Compensation using delay filter

Without adjustment of window, gain

signal image

-0.5 0 0.5

-140 -120 -100 -80 -60 -40 -20 0

Magnitude [dB]

ゲイン改善signal image

Delay 0.3 samples Filter tap 61 taps

Window Han

FFT points 1024 points

(d) Compensation using delay filter With adjustment of window, gain

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M channel ADCs M-times sampling rate

Interleaved ADC System

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ADC ：analog-to-digital converter

ADC1 M

U X

CLK1

CLK2

ADC2

T_s

t CLK 1

CLK 2

Timing Skew in Interleaved ADC System

f_in Fs- f_inF^s f

f_in f 0

0

Analog Input

F^s=1/T^s F^s

f_in

Digital output Dout

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ADC1 M U

X

CLK1

CLK2

ADC2

T_s

t CLK 1

CLK 2

Timing Skew Compensation in Interleaved ADC System

f f Analog input

f_in Clock skew effect

compensation

Digital output Dout

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Matlab Simulation Results

0 0.1 0.2 0.3 0.4 0.5

-120 -100 -80 -60 -40 -20 0

Magnitude [dB]

スキューのある信号

0 0.1 0.2 0.3 0.4 0.5

-120 -100 -80 -60 -40 -20 0

Magnitude [dB]

スキューのある信号

Signal Signal Spurious

Delay 0.3 samples Filter tap 61 taps

Window Han

FFTpoints 1024 points

(a) Ideal case (b) Timing skew case

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0 0.1 0.2 0.3 0.4 0.5 -120

-100 -80 -60 -40 -20 0

Magnitude [dB]

補正後のスペクトラム

0 0.1 0.2 0.3 0.4 0.5

-120 -100 -80 -60 -40 -20 0

Magnitude [dB]

補正後のスペクトラム

Matlab Simulation Results

Delay 0.3 samples Filter tap 61 taps

Signal Spurious Signal Spurious

(c) Compensation using delay filter

Without adjustment of window, gain

(d) Compensation using delay filter With adjustment of window, gain

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Conclusion

● Linear phase digital filter

with fine time resolution of group delay

● Design consideration - How to apply window - DC gain adjustment

● Application Examples

- I/Q delay mismatch compensation in quadrature modulator

- Timing skew compensation in interleaved ADC system Future work

● Implementation issues

– Finite word length, finite tap effects – LSI implementation

Digitally-Assisted Compensationfor Timing Skew in ATE Systems