Application Note 1432
J rmsj RJ pp J pp t, P σ J rms RJ t
(t) 1
ϕ (t) S (t) = P(2π f d t + ϕ (t)) S P f d ϕ (t) J ϕ 1 1 J [s] = ϕ [rad] J [UI] = ϕ [rad] 2π f d 2π Φ(t) 2π f d t ϕ (t) 1 d 1 d ƒ (t) = Φ(t) = ƒ d + ϕ (t). 2π dt 2π dt 1 d ƒ (t) = ƒ (t) ƒ d = ϕ (t) 2π dt 2
J pp J rms µσ J rms RJ σ J pp RJ RJ J pp J rms RJ J pp J rms RJ J pp J rms RJ J pp RJ J pp σ J pp RJ J pp RJ RJ σ J rms J RJ rms J pp pp J 3
J pp J RJ pp J TJ = n σ J TJ = n J r R m J s + J P D P J + J P D P J J pp J pp J ppj rms J rms RJ J pp J pp σ J RJ rms σ σ σ σ σ σ ϕ(t) A Appl sin(2π f J t) A out (f J ) X Tfer (f J ) A out (f J )/A Appl (f J ) ϕ (t) A Appl sin(2π f J t) A Tol (f J ) 4
5 J pp σ J pp σ
A Appl A Appl sin(2π f J t) X Tfer f J A Appl f J J TJ J RJ pp n J rms (t) 6
7 Σ
J NF R W J truth J meas R J truth J meas (1 100 R) J 9J N 2 F J > R 1+ R R 2 3J NF J > 1 (100 R) 2 R J min R J NF J R 8
J CR 3J NF J m 2 eas = J D 2 UT + J C 2R + ρ J DUT J CR ρ ρ ρ J CR /J DUT 1 J DUT J meas R f d f d J applied (t) A sin(2π f J t) J DUT (t) A' sin(2π f J t) J g (t) J g (t) 9
ϕ (t) V ref (t) A ref sin (2π f d t π/2) V DUT (t) A DUT sin(2π f d t ϕ (t)) π V(t) K ϕ sin (ϕ (t)) ϕ K ϕ sin(ϕ (t)) K ϕ ϕ (t) K ϕ 2 2 1 V rms ( f ) ϕ rms ( f ) S ϕ (f) = = --------[ rad2 / Hz ] 2 K ϕ f f f S ϕ (f) f ϕ 2 rms (f) ϕπ L(f) V DUT (t) A DUT sin(2π f d t ϕ (t)) L(f) 1 P ( f ) L( f ) = = 2P C f sin(2 f c t + (t)) sin(2 f c t + 0 ) sin(2 f c t + /2) K sin (t) K (t) 10
L ( f )[ 1 / Hz ] = 1 2 S ϕ ( f )[ rad2 / Hz ] J rms = f 2 ϕ 2 ( f ) rms df f 1 f ϕ rms(f)/ f L(f) J rms = f 2 f 1 S ϕ ( f )df = f 2 f 1 2L( f )df L(f) 11
L(f) L Random ( f ) = n = h n f n h n nn n n f 1 f 2 X Tfer ( f J ) A out (f J )/A Appl (f J ) µ 12
ϕ (t) sin(2π ft)/2π ft 13
J rms J pp X Tfer (f J ) A out (f J )/A Appl (f J ) 14
A Appl (f J ) 15
ϕ (t) J rms J pp 16
J pp J rms 17
t n T FS T n =, for n = 0, 1, 2,..., N 1, N n T FS N N t, P P t N N (t, P) J rms J rms RJ J rms J pp 18
N(t, P) (t µ) 2 Aexp [ ], 2σ 2 µ L, σ L µ R σ R A σ L σ R J µ R µ L N(t, P)/ t 0 2 N(t, P)/ t 2 0 N (t, P) 19
µ L σ L µ R σ R 20
(t) 1 2 (t T L ) 2 L BER RJ (t) = N L 2 σ L π t 2σ L L t T L BER RJ (t) = N L erfc ( ) 2σ L exp [ ] dt t 0 t T b 1 2T b t T L t T R T L T R J pp T L (T B T R ) (t) A sinusoidal t 1 2 π t A BER(t) = BER D LJ (t), 0 < t < T L {BER RJ (t), T L < t < T R R BER D J (t), T R < t < T B N L T L T R (t) T L T L σ R N L T R σ L N R (t) N L N R t T L t T R t T L T R t BER RJ (t) = N L erfc( ) + N Lerfc( ), 2σ L 2σ R 21
erf 1 (x) 1.192 0.6681 log(x) 0.0162 (log(x)) 2 t y A 0 A 1 t σ L σ R T L T R J r R m J s = 1 2 (σ L + σ R ) J P D P J = T L + (T B T R ). J TJ 14.1 J rms RJ J pp J TJ σ R σ L t T R t T L (t) (t) (t) (t) (t) (t) (t) (t) 22
J pp J rms J pp www.agilent.com/find/jitter µ 23
L(f) V noise tan( ϕ (t)) V noise /V carrier ϕ (t) ϕ (t) V noise /V carrier 1 2 2 1 2 V Noise rms / R 1 V Noise rms L(f) = ---- = 2 2 f V Carrier / R 2 f V Carrier 2 ϕ rms L(f) = 2 f L(f) = 1 2 S ϕ ( f ) L(f) S ϕ (f) L( f ) [ 1 / Hz ] = 1 2 S ϕ ( f )[ rad2 / Hz ] (L(f) 1 2 S ϕ (f)) V carrier V noise V noise V noise ϕ (t) S ϕ (f) T R t T L t 0 t' t' dt 1 2 (t T L ) 2 ρ (t ) dt = N L σ exp[ ] dt 2 L π 2σ L T L σ J RMS RJ N J pp t exp[ 1 2 (t T L ) ] 2 ΒΕR R LJ (t) = N L dt 2 σ L π t 2σ L Im (V) V(t) = (V Carrier + V(t)) expj(2 f c t + (t)) V Noise V Carrier 2 f c t Re (V) 24
µ (t T L )/( 2 σ) L 2 ΒΕR RJ (t) = N L e -u2 du π t T L 2 σ L 2 erf(t) = e -u2 du π 0 t 2 erfc(t) = 1 erf(t) = e -u2 du π t L t T L ΒΕR RJ (t) = N L erfc( ) 2σ L N L N R t T L t T R (t) T R T L ΒΕR R L J (T L ) = N L + N R erfc[ ] 2σ R T R T L ΒΕR R R J (T R ) = N L erfc[ ] + N R 2σ L ξ L/R erfc[(t R T L )/( 2σ L/R )] N L N R ΒΕR D L J (T L ) ξ R ΒΕR D R J (T R ) N L = 1 ξ R ξ L ΒΕR D R J (T R ) ξ L ΒΕR D L J (T L ) N R = 1 ξ R ξ L T R R T R t ΒΕR R J (t) = N R [ ] t T L erfc 2σ R T R T L ΒΕR D LJ (TL ) erfc[ ] ΒΕR R (TL )erfc( ) 2σ R t T L ΒΕR RJ (t) = ( T ) R T L T R T L 2σ L 1 erfc[ ] erfc [ ] 2σ R 2σ L T R T L ΒΕR D RJ (TR ) erfc[ ] ΒΕR L (TL ))erfc( 2σ L T R t ΒΕR RJ (t) = ( T ) R T L T R T L 2σ R 1 erfc[ ] erfc [ ] 2σ R 2σ L 25
(t) (t) r i t i r i t i t T ΒΕR RJ (t) = N erfc( ) 2σ ΒΕR RJ (t) t T 1 = erfc( ) N 2σ erf 1-1( (x) ΒΕR RJ (t) T 1 2erf ) 1 = + t N σ σ y A 0 A 1 tt A 0 /A 1 σ 1/A 1 r i -1( y i = 2erf ) 1 η = [y i (A 0 + A 1 N t)]2 i η χ dη/da 0 0 dη/da 1 0η y t 26
www.agilent.com/find/53310a www.agilent.com/find/jitter www.itu.int www.telcordia.com standards.ieee.org/getieee802 www.agilent.com/find/jitter www.agilent.com www.agilent.com/find/10ge www.agilent.com/find/10ge www.agilent.com/comms/bitalyzer www.boulder.nist.gov/timefreq/phase/properties/twelve.htm 27
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www.agilent.com/find/emailupdates-japan www.agilent.com/find/connectivity April 28, 2003 5988-8425JA 0000-00DEP