Timing Skew Compensaion Technique Using Digial Filer wih Novel Linear Phase Condiion Koji Asami Advanes Corporaion Hiroyuki Miyajima, uyoshi Kurosawa, Takenori Taeiwa, Haruo Kobayashi Gunma Universiy 1
Purpose Fine skew adjusmen using a digial filer while mainaining a linear phase condiion in ATE Timing accuracy is imporan o ATE Various digial filers are used for esing analog LSIs Linear phase condiion is required of he digial filer o preserve he analog waveform 2
Ouline Convenional linear phase FIR filer Time-shifed ideal filer Consrucion of linear phase filer Applicaion examples Conclusion 3
4 Types of Generalized Linear-Phase FIR Sysems 3 6 3 4 7 (1)Type I symmeric even-order (2)Type II symmeric odd-order 3 6 3 4 7 (3)Type III anisymmeric even-order (4)Type IV anisymmeric odd-order 4
Frequency Characerisics of 4 Types h(nt) Type I Type II Type III Type IV H(e jωt ) (N1)/2 jω(n1)t /2 e s akcos[ ωk ] k N/2 jω(n1)t /2 e s bkcos[ ω (k 1/2)T s ] k1 (N1)/2 j(ω(n1)t /2 /2) e s aksin[ω k ] k N/2 j(ω(n1)t /2 /2) e s bksin[ω (k 1/2)T s ] k1 Phase : 1s order funcion of frequency Delay : depends on number of Taps 5
Ouline Convenional linear phase FIR filer Time-shifed ideal filer Consrucion of linear phase filer Applicaion examples Conclusion 6
Ideal Filer Response Frequency Response Impulse Response 1. H(jω ) ωs - 2 ω S 2 ω Fourier Transform H(jω ) -5-4 -3-2 -1 1 2 3 4 5 T s ωs - 2 ω S 2 ω h() 1 sinc π T s ω s 2 T s : Sampling Rae 7
Discree-Time Expression k H(j ω-k ω ) s -2ω s -ω s ωs 2ωs ω Fourier Transform FIR is formed All zero h() k T s sinc π k k T s -5-4 -3-2 -1 1 2 3 4 5 8
Time Shifed Impulse Response G(jω ) - π π - π G(jω ) π ω ω -5-4 -3-2 -1 g 1 2 3 4 5 G(jω ) ω Δ Only phase changed Impulse response shifed 9
Influence o Coefficiens by Time Shif FIR h() k T s sinc π k k Time shif -5-4 -3-2 -1 1 2 3 4 5 IIR -5-4 -3-2 -1 h() 1 2 3 4 5 k T s Δ sinc π k k 1
Ouline Convenional linear phase FIR filer Time-shifed ideal filer Consrucion of linear phase filer Applicaion examples Conclusion 11
2 Tap FIR Model T s a a 1 a a 1 1 H(jω ) H(jω ) ωt s /2 a a 1 T s ω -5-4 -3-2 -1 1 2 3 4 5 12
2 Tap Delayed FIR Model T s a a 1 a a 1 1 H(jω ) ω a a 1 H(jω ) T s ωt s /2ω -5-4 -3-2 -1 1 2 3 4 5 13
2 Tap Delayed FIR Model T s a a 1 a a 1 1 H(jω ) IIR ω H(jω ) T s ωt s /2ω -5-4 -3-2 -1 1 2 3 4 5 14
Phase [radian] Gain [db] Comparison of Freq. Characerisic -1 2 Tap FIR Delayed -2 -.5.5 2-2 -.5.5 Normalized Frequency (Fs=1.) 2 Tap FIR Delayed Only slope of phase characerisic is changed 15
Frequency Characerisic of Proposed Filer g(nt) Type I Type II Type III Type IV j ω(n1)t /2ω e s G(e jωt ) j ω(n1)t /2ω e s (N1)/2 akcos[ ωk ] k N/2 bkcos[ ω (k 1/2)T s ] 1 k (N1)/2 j(ω(n1)t /2 /2ω ) e s aksin[ω k ] k N/2 j(ω(n1)t /2 /2ω ) e s bksin[ω (k 1/2)T s ] k1 Phase : 1s order funcion of frequency Delay : conrollable wih 16
Proposed Design Technique FIR wih Desired Characerisic Delayed Ideal Filer Delayed FIR Filer wih Desired Characerisic 17
Example of Raised Cosine Filer 61 ap Raised Cosine Filer.4.2 -.2 1 2 3 4 5 6 Delayed Filer (.3 samples delay).4.2 -.2 1 2 3 4 5 6 18
Group Delay [samples] Gain [db] Effec of Window Funcion -5-1.5.1.15.2.25 3.31 Rec 3.3 3.299.5.1.15.2.25 Normalized Frequency (Fs=1.) Hann Window funcion can reduce Gibbs phenomenon 19
Novel Linear Phase Condiion of D.F. Original FIR filer has complee linear phase Original FIR filer is band-limied Bandwidh of signal is below Nyquis rae Fine delay can be conrolled using Ideal filer Delayed filer has infinie impulse response Window funcion can consruc FIR effecively 2
Ouline Convenional linear phase FIR filer Time-shifed ideal filer Consrucion of linear phase filer Applicaion examples Conclusion 21
Applicaion o Quadraure Modulaor cos2 f I DAC s() sin 2 f Q DAC I jq fc 2 Image rejecion raio f fc f c f fc f f 22
Adjusmen of I/Q Skew cos2 f I DAC sin 2 f Q adjus DAC s() fc 2 I jq f fc f c f fc f f 23
Magniude [db] Magniude [db] Simulaion Resuls Image Signal -2-2 -4-4 -6-6 -8-8 -1 -.5.5 Normalized frequency (Fs=1.) (a) SSB signal wih I/Q skew -1 -.5.5 Normalized frequency (Fs=1.) (b) SSB signal wih compensaion Delay Compensaion Filer delay Taps Window.1 sampling poins 61 Taps Hann 24
Applicaion o Time-Inerleaved ADCs 1 2T S 1 2T S f CLK 1 ADC1 1 2T S 2 1 T S f h 1 1 T S f ADC2 2 h 2 CLK 2 f CLK 1 CLK 2 T s Compensae his componen Timing skew causes spurious componens 25
Magniude [db] Magniude [db] Simulaion Resuls Spurious QPSK signal -5-5 -1-1 -15.1.2.3.4.5 Normalized frequency (Fs=1.) -15.1.2.3.4.5 Normalized frequency (Fs=1.) (a) 2ch inerleaved ADC wih.1 samples skew (b) Compensae he skew using 91 aps delay filer 26
Conclusion Fine delay conrollable digial filer which mainains desired characerisics is proposed I is applicable no only o Low Pass Filers bu also o Band Pass Filers I can compensae he iming skew of analog modules in ATE 27