ME 458: Electronic Packaging and Materials Electromagnetic part Lecture note

Transcription

1 ME 458: Electrnic Packaging and Materials Electrmagnetic part ecture nte I. What is Signal Integrity (SI) - Timing and quality f the signal - Higher signal bandwidth and small sie f packaging leads t increasingly difficulties in maintaining gd signal. SI prblems ) Reflectin Nise Impedance discntinuity alng the signal transmissin path is the rt cause f reflectin nise. When a signal reaches the end f an imprperly terminated transmissin line, sme f the energy within the signal will return alng the same line. Reflectins als ccur when signals jump ruting layers and impedance values are discntinuus at the bundary. This culd be the result f manufacturing variatins, design cnsideratins, etc. When a trace is ruted ver planes with via hles, stubs, gaps at different lcatins r within the prximity f ther traces, impedance discntinuity will ccur and reflectin can be bserved. In high-speed systems, reflectin nise increases time delay and prduces versht, undersht and ringing. Reflectin nise can be minimied by cntrlling trace characteristic impedance, eliminating stubs and by using apprpriate terminatin. ) Crsstalk Nise Crsstalk is caused by electrmagnetic cupling between multiple parallel transmissin lines. A quiet line (victim) when cupled t an active signal line (aggressr) can pick up nise causing

2 false lgic switching. In larger packages where multiple active lines switch simultaneusly, crsstalk can induce pwer/grund nise. When tw lines switch in the same directin, either frm high t lw r lw t high, extra delay is intrduced. This delay can significantly increase r decrease the sampling windw. Crsstalk can be cntrlled by line spacing, placement f grund pins between signal pins and keeping reference planes clse t signal pins (by reducing the lp inductance which is a functin f area f the return current lp). 3) Pwer/Grund Nise This nise is due t parasitics f the pwer/grund delivery system during drivers simultaneus switching utput (SSO). It is smetimes als called Grund Bunce, Delta-I Nise r Simultaneus Switching Nise (SSN). The di/dt when the input t a gate is changed frm lw t high r vice versa multiplied by the package inductance () causes fluctuatins, r simultaneus switching nise (SSN: v.di/dt) between pwer and grund planes. The I/O supply current always travels in a lp, and in the breakut regin f large packages, multiple I/Os can share a cmmn return lp. The lcatin f pwer/grund and I/O pins determine the sie f the lp. Via crsstalk cuples the lps frmed by the I/O and the cmmn return path exacerbating the prblem. SSN can impact system timing, cause false lgic switching, intrduce nise in the pwer rail and create utput jitter and increase radiatin at resnant frequencies. wering cre vltage t reduce SSN reduces nise margin and makes the package mre susceptible t signal integrity prblems. SSN can be reduced by prviding prper return paths t signals. The return current will travel n a reference plane, either pwer r grund that is in clse prximity t the signal. 4) Electrmagnetic interference (EMI) EMI is the interference frm electrmagnetic radiatin frm nearby surce. In general, EMI will get wrse at higher frequencies.

3 5) SI Testing: eye diagram 6. SI Terms Term Bit Errr Rate Crsstalk Dispersin Definitin A measurement f the number f errrs detected at a receiver in a given length f time, smetimes specified as a percentage f received bits; smetimes specified in expnential frm (E-8 t indicate bit errr in E-8 bits). Undesirable signal cupling frm nisy aggressr nets t victim nets. May be eliminated by increasing the spacing between the nets r reducing signal amplitude f the aggressr net. "Smearing" f a signal r wavefrm as a result f transmissin thrugh a

4 Equaliatin Eye Diagram Fall time Impedance (Characteristic Impedance) Inter-Symbl Interference Jitter Oversht Ringing Risetime Skin Effect/ss Electrmagnetic Interference (EMI) Mutual Capacitance Mutual Inductance nn-ideal transmissin line. Thrugh a nn-ideal medium, signals travel at different velcities accrding t their frequency. Dispersin f the signal is the result. All cables and PCB transmissin lines are nn-ideal. Amplificatin r attenuatin f certain frequency cmpnents f a signal. Used t cunteract the effects f a nn-ideal transmissin medium. An eye diagram f a signal verlays the signal wavefrm ver many cycles. Each cycle wavefrm is aligned t a cmmn timing reference, typically a clck. An eye diagram prvides a visual indicatin f the vltage and timing uncertainty assciated with the signal. It can be generated by synchrniing an scillscpe t a timing reference. The time it takes fr a wavefrm t transitin frm the high lgic state t the lw lgic state. Falltime is usually measured frm 9% f the ttal signal swing t % f the signal swing. Electrical characteristic f a transmissin line, derived frm the capacitance and inductance per unit length. A frm f data crruptin r nise due t the effect that data has n datadependent channel characteristics. The jitter f a peridic signal is the delay between the expected transitin f the signal and the actual transitin. Jitter is a er mean randm variable. When wrst case analysis is undertaken the maximum value f this randm variable is used. Phenmenn where a signal rises t a level greater than its steady-state vltage befre settling t its steady-state vltage. Cmmn name fr the wavefrm that is seen when a transmissin line ends at a high impedance discntinuity. The signal first vershts, then dips dwn belw the target value, and cntinues this with decreasing amplitude until it cnverges n the target vltage. The time it takes fr a signal t rise frm % f its ttal lgic swing t 9% f its ttal lgic swing. Electrical lss in a nn-ideal medium due t skin effect. Skin effect is the tendancy fr high-frequency signal cmpnents t travel clse t the surface f the medium. Electrmagnetic interference (EMI) is any electrmagnetic disturbance that degrades r limits the perfrmance f the cnsidered electrnic system. It can be induced by the system being cnsidered r its envirnment. The amunt f interference an equipment can emit is regulated. The capacitance between tw cnductrs (ne cnsidered aggressr, the ther victim) when all ther cnductrs are cnnected tgether and then regarded as an ignred grund. It describes the amunt f cupling due t the electric field. The mutual capacitance will inject an ften undesired current int the victim line prprtinal t the rate f change f vltage n the aggressr line. Mutual Capacitance it a cause f crsstalk. The inductance between tw cnductrs (ne cnsidered aggressr, the ther victim) placed clse enugh that the magnetic field induced by a

5 Reflectin Skew SSO (Simultaneus switching utputs) current flwing int the aggressr line encmpasses the victim. The mutual inductance will inject an ften undesired vltage nise nt the victim prprtinal t the rate f change f the current n the aggressr line. A prcess that ccurs when a prpagating electrmagnetic wave impinges upn a change in its supprting media prperties. In the case f an abrupt change the incident wave will "bunce" ff f the barrier in the ppsite directin it came frm. In ther cases, sme f the wave reflects while the rest cntinues n. The difference in arrival time f bits transmitted at the same time. Bits can be elements f a parallel bus r members f a differential pair. Defines a mment in time when multiple device utputs switch t the same level. Such simultaneus switching may induce rapid current changes which cmbined with the inductance f grund pins, bnd wires, and grup metaliatin can be surce f grund bunce. II. Imprtant Mathematical Backgrund Furier Transfrm Frequency dmain <> Time dmain F ( ω) f ( t)exp ( jωt ) dt f ( t) F( ω)exp( jωt ) dω π Example: Square wave signal > dd harmnics x 4 ( t ) sin ( π ft ) sin ( π 3 ) sin ( 5 )... 3 ft π π 5 ft + + +

6 Phasr Phasr is a tl fr help slving linear system. It relies n amplitude and phase functin withut the time dependent. ( t) Re[ Ze ɶ jωt ] > Z ɶ is the phasr f the instantaneus functin ( t ) Kirchff s vltage law: The directed sum f the electrical ptential differences arund a clsed circuit must be er. Kirchff s current law: At any pint in an electrical circuit, the sum f currents flwing twards that pint is equal t the sum f currents flwing away frm that pint. RC circuit example: Given vltage surce vs ( t ), find the current i( t ) The vltage surce is v ( t) V sin ( ωt φ ) +. Applying Kirchhff s vltage law (KV), we get s Ri( t) + i( t) dt vs ( t) C Step : Adpt a csine reference π π vs ( t) V sin ( ωt + φ ) V cs ωt φ V cs ωt + φ Step : Express time-dependent variables as phasrs π j( ωt+ φ π / ) jωt vs ( t) V cs ωt + φ Re V e Re Vɶ j se where Vɶ s Ve φ π i( t) Re[ Ie ɶ jωt ] jωt jωt Iɶ jωt i dt Re[ Ie ɶ ] dt Re Ie ɶ dt Re e jω Step 3: Recast the equatin in phasr frm jωt Iɶ j t j t Ri( t) + i( t) dt vs ( t) C becmes R Re[ Ie ɶ ω ω ] + Re e Re[ Vɶ se ] C jω r RIɶ + Iɶ Vɶ s jωc Step 4: Slve equatin in phasr dmain RIɶ + Iɶ Vɶ s R + Iɶ Vɶ s jωc jωc ( / )

7 Vɶ s j C j( / ) j C Iɶ ω φ π ω Vɶ s Ve + jωcr + jωcr R + j ω C Then, we can write it in magnitude and phase frmat jπ / ( / ) j C ( / ) Ce V C Iɶ ω ω ω Ve Ve e jωcr jφ + ( ωcr) e + + ( ωcr) where φ tan ( ωrc ) φ π φ π ( φ φ ) j j j Step 5: Find the instantaneus value jωt VωC j( φ φ ) jωt VωC i( t) Re Ie ɶ Re e e cs t + ( ωcr) + + ( ωcr) Vectr analysis - Vectr additin and subtractin C A + B ( ω φ φ ) - Dt prduct A B AB csθ AB if A A xˆ + A yˆ + A ˆ and B B xˆ + B yˆ + B ˆ x y x y A B A B + A B + A B x x y y - Crss prduct A B n ˆABsinθ AB xˆ yˆ ˆ ( ) ( ) ( ) A B A A A A B A B xˆ A B A B yˆ + A B A B ˆ x y y y x x x y y x B B B x y

8 - Crdinate systems - Cartisian Crdinates - Cylindrical Crdinates - Spherical Crdinates Gradient f a scalar field (del r gradient peratr) xˆ + yˆ + ˆ x y T T T Fr example T xˆ + yˆ + ˆ x y > directinal derivative Divergence f a vectr field E E E x y x y E + + Divergence therem Edv E ds v S Outgingness f vectr field Curl f a vectr field B By B B x B y B x B xˆ yˆ + ˆ Or y x x y xˆ yˆ ˆ B x y B B B x y Stke s therem ( ) Rtatin f the vectr field s B ds B dl aplacian Operatr V V V scalar > V ( V ) + + x y vectr > c + + ˆ ˆ ˆ + + x y E E x Ex y Ey E

9 III. Physical basic fr transmissin line Transmissin line is used t transprt a signal frm ne pint t anther Imprtant parameters - characteristic impedance - wave speed in transmissin line - capacitance - inductance - lss Physical basic fr resistance - Apprximatin fr the resistance f intercnnects ρd R A R the resistance (Ohm) A ρ d the crss-sectin area (m ) the bulk resisitivity f the cnductr (Ohm-m) the distance between the ends f the intercnnect (m) - Bulk resistivity ρ σ is the cnductivity (Siemens/meter) σ

10 It is intrinsic material prperty - Resistance per length R ρ R d A - Sheet resistance ρd R tw Current distributin and skin depth - skin depth δ σπµ µ where δ σ r f skin depth (m) cnductivity f cnductr (Siemens/m) µ permeability f free space µ relative permeability f cnductr r f frequency f the wave (H) > Current crwding prblem Physical basic fr capacitance dv i C dt Cmplex permittivity ε ε jε ε Dielectric cnstant ε r, Dielectric lss ε > lss tangent ε ε ε - Parallel plate apprximatin A C ε h C capacitance (Farad) ε permittivity f free space (Farad/m) A area f the plate h separatin between the plates

11 - Capacitance per length f micrstrip line ( + ε ).67.4 r C 5.98h ln.8 w + t where C capacitance per length (pf/inch) ε relative dielectric cnstant f the insulatin r h dielectric thickness (mils), w line width (mils), t thickness f cnductr (mils) mil / inches.54 mm - Capacitance per length f strip line.4ε r C.9b ln.8 w + t where C capacitance per length (pf/inch) ε relative dielectric cnstant f the insulatin r b h + h + t ttal dielectric thickness (mils) w line width (mils), t thickness f cnductr (mils) Physical basic fr inductance - What is inductance? V di dt - There are circular magnetic-field line lps arund all current - Inductance is the number f Webers f field line lps arund a cnductr per ampere f current thrugh it. N I is inductance (Henry) N is the number f magnetic-field line lps (Webers) - Self inductance and mutual inductance V nise di M dt

12 V nise the vltage nise induced t the quite wire M the mutual inductance between the tw wire I the current in the secnd wire > lead t crss talk, grund bunce Partial inductance: cnsider nly a sectin f wire Apprximatin f partial self inductance f a rund rd d 3 5d ln r 4 partial self-inductance (nh) r radius f the wire (inches) d length f wire (inches) Apprximatin f partial mutual inductance between tw cnductr segments M d s s 5d ln + s d d M partial mutual inductance (nh) s center-t-center separatin (inches) d length f the tw wire (inches) Electrical Impedance Electrical Impedance r simply impedance, describes a measure f ppsitin t a sinusidal alternating current (AC). Electrical impedance extends the cncept f resistance t AC circuits, describing nt nly the relative amplitudes f the vltage and current, but als the relative phases. In general impedance is a cmplex quantity and the term cmplex impedance may be used interchangeably; the plar frm cnveniently captures bth magnitude and phase characteristics, Z R + jx where Z impedance; R resistance; X reactance Resistr > Z R Capacitr > Z jωc Inductr > Z jω

13 ump element mdel IV. Transmissin line mdel R : the cmbined resistance f bth cnductrs per unit length (Ω/m) : the cmbined inductance f bth cnductr per unit length (H/m) G : the cnductance f the insulatin medium per unit length (S/m) C : the capacitance f the tw cnductrs per unit length (F/m) Transmissin line equatin KV: vltage law i(, t) v(, t) R i(, t) v( +, t) t i(, t) [ v( +, t) v(, t) ] R i(, t) + t [ v( +, t) v(, t) ] i(, t) R i(, t) + t v(, t) i(, t) R i(, t) + t KC: Current law v( +, t) i(, t) G v( +, t) C i( +, t) t v( +, t) [ i( +, t) i(, t) ] G v( +, t) + C t [ i( +, t) i(, t) ] v( +, t) G v( +, t) + C t

14 i(, t) v(, t) G v(, t) + C t Time dependent frm v(, t) i(, t) R i(, t) + t i(, t) v(, t) G v(, t) + C t d Vɶ diɶ ( R + jω ) d d d Vɶ ( R + jω )( G + jωc ) Vɶ d d Vɶ γ Vɶ d d Iɶ γ Iɶ d γ R + jω G + jωc where ( )( ) γ is the cmplex prpagatin cnstant. It can be written as γ α + jβ ( R j )( G j C ) ( R j )( G j C ) Phasr frm dvɶ ( R + jω ) Iɶ d diɶ ( G + jωc ) Vɶ d α Re + ω + ω ; β Im + ω + ω α is the attenuatin cnstant, β is the phase cnstant Wave prpagatin in transmissin line Wave equatins d Vɶ γ Vɶ d d Iɶ γ Iɶ d Slutin t the wave equatin Vɶ + γ γ V e + V e ; Iɶ + γ I e + I e crrespnds t wave prpagatin in + directin + crrespnds t wave prpagatin in directin e γ e γ Because dvɶ ( R + jω ) Iɶ and Vɶ + γ V e + V e d γ γ

15 d V + e γ V e γ + ( R + j ω ) I ɶ( ) d + γ γ γ V e V e ( R + jω ) Iɶ γ + γ γ Iɶ V e V e ( R + jω ) Characteristic Impedance + V V R + jω R + jω Z ( Ω) + I I γ G + jωc R + jω ssless transmissin line R G > Z ( Ω) G + jωc C Wavelength and wave velcity in the lssless transmissin line π π ω λ (m); u p (m/s) β ω C β C Characteristic impedance f micrstrip line and strip line Micrstrip line Z h ln ε w + t r w.< < 3.; < ε r < 5 h Strip line 87.9( h + t) h Z ln ε.8w t 4h r + w h < h ;. < <.; h t h <.5; < ε < 5 r Reflectin Frm Vɶ + γ V e + V e V V ( ) Z Z + Iɶ γ γ e e γ

16 Fr lssless line γ jβ j j Vɶ + β β V e + V e V V Iɶ e e Z Z Z V ɶ Iɶ + jβ jβ > frm Slving fr V gives V Z Z V + Z + Z ( ) Vɶ Vɶ V + V + V V Iɶ Iɶ ( ) Z Z + + V + V, we have Z Z + V V Reflectin cefficient V Z Z Γ + V Z + Z Vltage reflectin cefficient Γ is the rati f the amplitude f the reflected vltage wave t the amplitude f the incident vltage wave at the lad Γ is a cmplex number Γ means perfectly matched line > n reflectin Γ means ttal reflectin Example: A 5 Ω transmissin line is cnnected t a lad as shwn n the right. What is the reflectin cefficient when we send a MH signal? Given that lad is a) R 5 Ω, C b) R 5 Ω, C pf c) R Ω, C pf Slutins: Z Z a) Γ > matched line Z + Z π b) Z R 5 j ( 5 - j59) j ωc 8

17 j9 ( j ) ( ) Z Z j59 Γ Z Z 5 j j59 59e j e j Z R j j59 ωc π c) 8 j34.9 e 34.9 j3.7.85e Z Z j e Γ Z + Z j e j7.46 j7.54 Input impedance f the lssless line Frm Vɶ + γ V e + V e V V ( ) Z Z + Iɶ γ γ e e γ Fr lssless line γ and V Γ V + jβ jβ jβ ( ) Vɶ V e + Γe V Z + + Iɶ e Γe V Z ɶ Iɶ jβ jβ ( ) Z ( l) Z Z cs βl + jz sin βl in Z cs βl + jz sin βl Z Z + jz tan βl Z + jz tan βl Derivatin f the input impedance ( ) jβ jβ ( e Γe ) ( ) ( jβ Γ jβ ) Vɶ V e + Γ e e + Γe Z Iɶ V e e Z + jβ jβ jβ jβ Z +

18 jβl jβl ( e + Γe ) β β ( Γ ) Z ( l) Z e e in j j l Frm jβl jβl e cs βl + j sin βl, and e cs βl j sin βl We get Z ( l) Z in Frm Z Z ( l) Z in ( cs βl + j sin βl + Γ( cs βl j sin βl) ) ( cs βl + j sin βl Γ( cs βl j sin βl) ) (( + Γ ) cs βl + ( Γ) j sin βl) ( Γ ) cs βl + ( + Γ) j sin βl ( ) Z Z Z + Z + Z Z Z Γ + Γ Z + Z Z + Z Z + Z Z + Z Z + Z Z Γ Z + Z Z + Z Z (( + Γ ) cs βl + ( Γ) j sin βl) ( Γ ) cs βl + ( + Γ) j sin βl ( ) Z Z cs βl + j sin βl Z + Z Z + Z Z Z cs βl + j sin βl Z + Z Z + Z ( Z cs βl + Z j sin βl) ( cs β + sin β ) Z Z l Z j l Example Find the length l f the shrted 5 Ω lssless transmissin line (see figure belw) such that its input impedance at GH is equivalent t impedance f a capacitr with capacitance 8 C ) 5 pf. Assume that the phase velcity f the wave n the line is m/s. ( eq Zl cs βl + jz sin βl Frm Zin Z Z cs βl + jzl sin βl, in this case, Z l. Then, we have

19 jz sin βl Zin Z jz tan βl Z cs βl We want Zc Zin jz tan βl r jωc eq tan βl Z ωc 9 ( ) π v p π f π β and frm λ β π 8 λ f v S we have t slve fr tan βl Z ωc 5 π 5 eq ( )( ) There are several slutins fr tan β l βl.8334 l.45 m r 45 mm β π Other slutins satisfy βl nπ where n is any integer p eq V. Crsstalk in transmissin line Capacitive crsstalk KC: v v b f dv + cm x Z Z dt s v f vb Zcm x dt s dv - Far-end nise dvs vfe Zcmd dt fr the line length d, c m is the mutual capacitance per-unit-length - Near-end nise dv vne Zcm x dt s

20 dvs v v is the peak vltage > (assuming triangular edge) dt t x c is the capacitance per unit length, vp is the phase velcity, t is the rise time, t TOF time f flight distance/phase velcity v t v v Z c Z c v v t 4 p NE m m p Because Z C and v p C Z v C C s p c v Z c v v v 4 4 C m NE m p Inductive crsstalk KV: dis vb m x + v f dt m is the mutual inductance Current is cntinuus v b v f vs and is Z Z Z dis m x dvs v m x + v v v dt Z dt m dvs vb x Z dt m dvs v f x Z dt b f b b - Far-end nise m dv vfe d Z dt s - Near-end nise

21 v NE m dv x Z dt s dvs v v is the peak vltage > (assuming triangular edge) dt t x c is the capacitance per unit length, vp is the phase velcity, t is the rise time, t TOF time f flight distance/phase velcity m vp t v vp vne m v Z t 4 Z Because Z v NE 4 m v C and v p C vp C s Z C is the inductance per unit length Ttal crsstalk capacitive + inductive m dvs cm m vfe d Zcm ; vne + v Z dt 4 C Graphical explanatin

22 Equivalent circuit mdel fr crsstalk analysis in multiple traces Inductance matrix M M M M MM is the self-inductance f line M per unit length MM NM is the mutual inductance between line M and line N per unit length Capacitance matrix C C CM C C C M C CM CM CMM C is the self capacitance f line N per unit length where NN C is the mutual capacitance between lines M and N MN Example: Calculate near and far end crsstalk-induced nise magnitudes and sketch the wavefrms f circuit shwn belw: Vinput.V, Trise ps. ength f line is inches. Assume the fllwing capacitance and inductance matrix: 9.869nH.3nH.3nH 9.869nH (per inch).5pf.39 pf C.39 pf.5pf (per inch)

23 m dvs - Far end crss talk > vfe d Zcm Z dt 9.869nH The characteristic impedance is Z O 69.4 C.5pF Ω. dvs Because the input signal is assume t be triangle ramp dt In this case, cm C, and m, therefre m dv s v vfe d Zcm d ZC Z dt Z T in rise ( ) ( ) vin vlt/psec T.3 nh/inch ( inches) ( 64.9 Ω)(.39 pf/inch ) vlt/psec.37 vlts 64.9 Ω rise cm m - Near end crss talk > vne + v 4 C In this case, cm C, m, C C, and, c m C v + v + v m NE 4 C 4 C (.5pF/inch ) ( ) (.3 nh/inch) ( ) pf/inch nh/inch.8 vlts vlt Prpagatin delay f the inch line is d d d C inch 9.869nH.5pF v C p.8454 nsec ( ) ( )( ) m V/ ps/div Useful references: - Digital Signal Integrity: Mdeling and Simulatin with Intercnnects and Packages by Brian Yung - Signal Integrity Simplified by Eric Bgatin - Fundamentals f Applied Electrmagnetics by Fawwa Ulaby