Basics on High Frequency Circuit Analysis

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1 Basics on High Frequency Circuit Anaysis Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from Agient Technoogies Educator s Corner: 999 RF Design and Measurement Seminar, David Bao, Joe Civeo, Ed Henice, Sara Meszaros, Andy Potter, Boyd Shaw, My e Truong Eectrica Size + - ow frequencies waveengths >> wire ength current () traves down wires easiy for efficient power transmission measured votage and current not dependent on position aong wire High frequencies Waveength or < ength of transmission medium need transmission ines for efficient power transmission matching to characteristic impedance ( ) is very important for ow refection and maximum power transfer measured enveope votage dependent on position aong ine

2 The Need of Transmission ine Theory For anaog circuits: f the physica ength of the transmission media is arger % of the waveength of the highest frequency of interest For digita circuits: f the propagation time in the ongest transmission path is arger than % of the fastest transition time 3 Common Transmission Media Uniform nterconnects twisted-pair copanar a b coaxia r w w h waveguide r w microstrip h w (Hewett-Packard's RF Design and Measurement Seminar, ) 4

Common Transmission Media (cont) Practica interconnects can be decomposed in segments of uniform interconnects (usuay necessary) PCB (add-in card) Components (Chip + Pkg) PCB (Motherboard) Connector

3 Common Transmission Media (cont) Practica interconnects can be decomposed in segments of uniform interconnects (usuay necessary) PCB (add-in card) Components (Chip + Pkg) PCB (Motherboard) Connector (H. Heck, 5) 5 Common Transmission Media (cont) High-speed BGA (Ba Grid Array) packages Fip chip interconnect (bump) Chip Compete signa path (chip to board) Signa ayer Power/ground pane Through via Burried via Chip carrier (substrate) Power/ground pane Bind via Signa ayer BGA ba Board 6 3

4 From umped Circuits to Distributed Circuits (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) 7 Transmission ine Mode The interconnect is modeed using an infinite number of RCG sections (R. udwig and P. Bretchko, RF Circuit Design, Prentice Ha, ) 8 4

5 Transmission ine Mode The interconnect is modeed using an infinite number of RCG sections (R. udwig and P. Bretchko, RF Circuit Design, Prentice Ha, ) 9 Transmission ine Mode Generic equivaent circuit for each section (R,, C and G are per unit ength) The interconnect is modeed using an infinite number of these sections, making z (R. udwig and P. Bretchko, RF Circuit Design, Prentice Ha, ) 5

6 Transmission ine Equations Time-Domain (Teegrapher Equations) v( z, t) i( z, t Ri( z, t) ) z t i( z, t) v( z, t Gv( z, t) C ) z t Teegrapher Equations in Frequency-Domain d ( z) ( R j) ( z) dz d( z) ( G jc) ( z) dz Transmission ine Equations (cont) Wave equation (frequency-domain) d ( z) d ( z) ( z) ( z) dz dz where ( R j)( G jc) is the compex propagation constant Soutions to the wave equation are ( z) z z e e ( z) incident waves refected waves j z z e e 6

7 Transmission ine Equations (cont) Soutions in the frequency domain v ( z) z z e e ( z) ( R j)( G jc) Soutions in the time domain z z e e j z ( z, t) cos( t z ) e cos( t z ) e z Waveength v p f Phase veocity, wave veocity or propagation speed dz v p dt (speed at which a constant phase point traves down the ine) 3 Transmission ine Symbo (ossy) Transmission ine, ength aong the ine, z 4 7

8 8 5 Characteristic mpedance Characteristic impedance of the T C j G j R 6 Refection Coefficient Refection coefficient aong the ine, Refection coefficient at the oad, e e e ) ( ) ( e e e ) (,

9 nput mpedance nput impedance aong the ine in, in ( ) ( ) ( ) tanh( ) tanh( ) 7 Modeing Uniform nterconnects (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) 8 9

Modeing Uniform nterconnects (cont) Parasitic effects associated to each transmission media Capacitance between conductors, C Resistance of conductors (conductor osses), R nductance of conductor

10 Modeing Uniform nterconnects (cont) Parasitic effects associated to each transmission media Capacitance between conductors, C Resistance of conductors (conductor osses), R nductance of conductor oops, Dieectric conductivity (dieectric osses), G R, C,, and G must be determined per unit ength 9 nterconnect Shunt Capacitance ( F/m) (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX)

11 Fringing Capacitance Effect (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) nterconnect Series nductance ( 4 7 H/m) (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX)

12 nterconnect Series DC Resistance (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) 3 Skin Effect (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) 4

13 EM-Simuation of Conductor Current Distribution (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) 5 Proximity Effect (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) 6 3

14 Proximity and Skin Effects E. Bogatin, Essentia principes of signa integrity, EEE Microwave Magazine, vo., pp. 34-4, Aug.. 7 Edge and ndy Effects Exampe W EM simuation using Sonnet At MHz: r H W W = mi = 4 mi H = 5 mi r = 4. dieectric oss tan =.7 PC-FR-6 Poycad aminates 8 4

15 Edge and ndy Effects Exampe (cont) W EM simuation using Sonnet At MHz: r H W W = mi = 4 mi H = 5 mi r = 4. dieectric oss tan =.7 PC-FR-6 Poycad aminates 9 Edge and ndy Effects Exampe (cont) W EM simuation using Sonnet At MHz: r H W W = mi = 4 mi H = 5 mi r = 4. dieectric oss tan =.7 PC-FR-6 Poycad aminates 3 5

16 Edge and ndy Effects Exampe (cont) W EM simuation using Sonnet At GHz: r H W W = mi = 4 mi H = 5 mi r = 4. dieectric oss tan =.7 PC-FR-6 Poycad aminates 3 nterconnect Shunt Conductance (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) 3 6

17 oss Tangent of Typica Materias (A. Weisshaar, Tutoria on High-Speed nterconnects, MS June 4, Fort Worth, TX) 33 Power Transfer Efficiency RS R oad Power (normaized) R / RS Maximum power is transferred when R = RS (Hewett-Packard's RF Design and Measurement Seminar, ) 34 7

18 Power Transfer Efficiency (cont) For compex impedances, maximum power transfer occurs when = S* (conjugate match) Rs +jx s = R +jx -jx R = s* = R - jx At high frequencies, maximum power transfer occurs when RS = R = o o o (Hewett-Packard's RF Design and Measurement Seminar, ) 35 The Smith Chart +jx +R Poar pane 9 o + 8 o o -jx Rectiinear impedance pane -9 o Smith Chart maps rectiinear impedance pane onto poar pane = o = = (short) = ±8 O Constant X Constant R = (open) = O Smith Chart (Hewett-Packard's RF Design and Measurement Seminar, ) 36 8

19 The Smith Chart nterpretation (matched) +. 8 (short circuit) j (pure capacitive) j (pure inductive) Circes of constant X Circes of constant R (open circuit) 37 ightwave Anaogy to RF Energy ncident Transmitted Refected ightwave RF (Hewett-Packard's RF Design and Measurement Seminar, ) 38 9

20 Transmission ine Terminated with o s = o o = characteristic impedance of transmission ine o inc ref = (a the incident power is absorbed in the oad) For refection, a transmission ine terminated in o behaves ike an infinitey ong transmission ine (Hewett-Packard's RF Design and Measurement Seminar, ) 39 Transmission ine Terminated with Short, Open s = o inc ref n phase ( ) for open Out of phase (8 ) for short For refection, a transmission ine terminated in a short or open refects a power back to source (Hewett-Packard's RF Design and Measurement Seminar, ) 4

21 Transmission ine Terminated with 5 s = o = 5 inc ref Standing wave pattern does not go to zero as with short or open (Hewett-Packard's RF Design and Measurement Seminar, ) 4 Refection Parameters Refection Coefficient = refected incident = = - O + O Return oss = - og(), = E max E min Standing Wave Ratio SWR = E max = + E min No refection ( = o) Fu refection ( = open, short) db R db SWR (Hewett-Packard's RF Design and Measurement Seminar, ) 4

22 Standing Wave Ratio EM Simuation Microstrip ine aminate: Rogers RO33 H = 5 mi r = 3 tan() =.3 at GHz ossy metas: Cu = S/m t =.6 mi (haf-once copper) W =.5 mi = 87.5 mi 43 Standing Wave Ratio EM Simuation (cont) Using port = port = 5 f =. GHz f = 3 GHz 44

Transmission Coefficient = = Transmitted ncident = nsertion oss (db) = -

23 Standing Wave Ratio EM Simuation (cont) Using port = 5, port = K f =. GHz f = 3 GHz 45 Transmission Parameters ncident DUT Transmitted Transmission Coefficient = = Transmitted ncident = nsertion oss (db) = - og Trans nc = - og Gain (db) = og Trans nc = og nsertion Phase (deg) = Trans nc = 46 3

24 N-Ports Networks (inear Circuits) (R. udwig and P. Bretchko, RF Circuit Design, Prentice Ha, ) 47 mpedance Matrix Representation () N N N N N N NN Each eement of matrix is given by ij i j for k j k 48 4

25 5 49 Admittance Matrix Representation (Y) Each eement of matrix Y is given by N N Y NN N N N N Y Y Y Y Y Y Y Y Y Y j k j i ij k Y for 5 -Parameters for -Port Networks Equivaent circuit:

26 Y-Parameters for -Port Networks Y Equivaent circuit: Y Y Y Y Y 5 H-Parameters (Hybrid) for -Port Networks H H H H H H Equivaent circuit: 5 6

27 The Scattering Matrix (S) + + o + + o N + N + on N S ij N N N N-port inear Network k + ok k k + k i j k for k j N S S S S S S SN SN N k+ = if we terminate port k with a matched oad ( K = ok ) k k S S S N N NN 53 The Scattering Matrix Representation (S) They can be more easiy obtained at high frequencies: ncident and refected waves can be measured using a ector Network Anayzer (NA) They do not require shorts or opens (active devices might osciate or sef-destroy) They are more directy reated to high-frequency effects (, T,, R, SWR, etc.) We can convert back and forth between S, Y and parameters 54 7

28 Measuring S-Parameters ncident S Transmitted Forward b a S Refected DUT oad b a = S Refected = ncident S = Transmitted ncident = b a a = = b a a = S Refected = ncident S = Transmitted ncident = b a a = = b a a = oad a = b DUT Transmitted S S Refected ncident b a Reverse 55 Meaning of the S-parameters (cont) S : forward refection coefficient (input match) S : reverse refection coefficient (output match) S : forward transmission coefficient (gain or oss) S : reverse transmission coefficient (isoation) Sii i S ii i i for ki k i for ki k Sij T ji S ij i j k for k j T ji k for k j 56 8

29 An RF Prototype 57 Hybrid Microwave ntegrated Circuits (cont) M. Pozar (998), Microwave Engineering. Amherst, MA: John Wiey and Sons. 58 9

30 Monoithic Microwave ntegrated Circuits (MMC) M. Pozar (998), Microwave Engineering. Amherst, MA: John Wiey and Sons. 59 High Speed nterconnects J.C. Rautio, Rigorous Evauation of Worst Case Tota Crosstak in the Time Domain Using Frequency Domain Scattering Parameters, High-Performance System Design Conference 6 3

31 High Speed nterconnects (cont) J.C. Rautio, Rigorous Evauation of Worst Case Tota Crosstak in the Time Domain Using Frequency Domain Scattering Parameters, High-Performance System Design Conference 6 3

(Refer Slide Time: 2:34) L C V

(Refer Slide Time: 2:34) L C V Microwave Integrated Circuits Professor Jayanta Mukherjee Department of Eectrica Engineering Indian Intitute of Technoogy Bombay Modue 1 Lecture No 2 Refection Coefficient, SWR, Smith Chart. Heo wecome