Seminario d’Eccellenza “ITALO GORINI” Scuola di Dottorato

1. Seminario d’Eccellenza “ITALO GORINI”Scuola di Dottorato METODOLOGIE E DISPOSITIVI DI MISURA Linea di Ricerca A6: MISURE PER LA CARATTERIZZAZIONE DI COMPONENTI E SISTEMI Responsabile: Prof. Gregorio Andria, Politecnico di Bari Siena, 5-9 settembre 2011

2. MISURE PER LA CARATTERIZZAZIONE DI COMPONENTI E SISTEMI Seminario d’Eccellenza “ITALO GORINI” Le Misure ad Alta Frequenza per le Applicazionidi Signal Integrity Prof. Andrea Ferrero Dip. Elettronica- Politecnicodi Torino

3. Summary • Signal Integrity and Microwave • S-parameter: so what? • VNA Hardware Evolution • Error Models and Calibration Techniques • Interconnection and Fixture Design • Calibration design for the DUT

4. Signal Integrity and Microwave

5. Microwave Measurements • Power Measurements • Time Domain Signals • Frequency Domain Linear Parameters: • S parameters

6. Few Remainders

7. [M] [M]becomes a 4x4matrix Few Remainders • Linear Network: The ratio among voltages and currents on the n ports DOES NOT depend on signal levels thus the behaviour can be described as linear relationship ie: • Where M can be any relationship among any linear combination of voltages and currents ie: • V=Z * I • I = Y * V Here Y and Z are two examples of possible M matrix but anyone is acceptable 1 3 2 4

8. Scattering Paremeters Demystified • Let’s take the following combinations of I and V: • Where ZR is a parameter called Reference Impedance than the Ohm law equivalent becomes: G is called Reflection Coefficient

9. Scattering Paremeters Demystified • Let’s move to n-ports everything become vectors and matricies: S is called Scattering matrix

10. Signal Trasmission at High Frequency • A structure where the Electromagnetic field can propagate along an axis with a UNIFORM transversal section is called Trasmission Line E E E E Coax cable Waveguide Bifilar Line Microstrip We will assume MONOMODAL propagation IT’S ALL ABOUT FIELD CONFINEMENT

11. I(z) V(z) z So why S and not Z or Y? Let’s take a transmission line: l Plane A Plane B • V and I are complex function of the position while if: • Zr = Appropriate constant of the propagation called Line Characteristic impedance then: • a and b function along the line become simply: Reflected signal Incident signal

12. I(z) V(z) Some usefull properties a(z) Note that: b(z) Z

13. z The S-matrix of a transmission line a1 a2 b1 b2 l Port 1 Port 2 So tocompletelydescribe the propagationalong a trasmissionlinewewillneed: REFERENCE PLANES REFERENCE IMPEDANCE S-MATRIX

14. Differential S-parameters • Whatifinsteadof single endedvoltages and currentswewishtousedifferentialones and associate the information to a coupleofwires? I1 For Each Couple I3 V1 V3 I2 I4 V2 V4

15. WHY differential S-parameters? Ed • The differential mode Ed propagates mainly in the air thus it suffers much less of dielectric loss and anysotrtopy • FR4 is a must for Digital application but FR4 is lossy and anysotropic thus… • Differental propagation became a must for high speed digital systems Ec E

16. DifferentialS-parameters • What are the propagation properties and is it usefull to have an “S-parameter equivalent”? • Use a linear combination of V and I it’s just another convention but to link it to propagation became more tricky: • Which Reference impedance we need to take? • What if we wish to have some port left single ended, i.e. an Operational Amplifier? • Which are the properties of the new parameters?

17. Mixed Mode S-parameter • Traditional definitions are: BUT THESE ARE VALID ONLY IF

18. Generalized Mixed Mode • In general we may have BILINEAR MATRIX TRANSFORM

19. Impedance Measurements ? R Z | |,F

20. Impedance Measurements Z ? R | |,F

21. Let’s move to microwave DownConversion and Digitizing ADC ADC Directional Coupler aa bb Microwave Source a <-b G

22. 2 port Measurements

23. 2 port Measurements S11 S21 a1 a1 b1 b2

24. The oldquestionsofS-parameterMeasurements • How can we generate microwavesignals? • How can we sample microwavesignals? • Where’s the referenceplane ? • What’s the referenceimpedance?

25. Plus new problems… for digital Low cost application • How do I keep reasonable microwave signals on non microwave substrate ? • How can I make proper interconnections to measure these signals ? • How much accuracy can I accept ?

26. IF Digitizer FOUR-CHANNEL MICROWAVE RECEIVER am1 bm1 bm2 am2 DUT PORT 1 PORT 2 BIAS 1 BIAS 2 REFLECTOMETER MICROWAVESOURCE VNA BASIC SCHEME SIGNAL SEPARATION

27. VNA Source • Synthetised Source (PLL+DDS) • Very Broadband • Very Fast Sweeping • Power Leveled • Low Phase Noise Not really Necessary • High Repeatability Agilent PNA Source block

28. SignalSeparation • Provides a and b waves separation • Provides signal excitation at DUT ports • It may have also bias tee and attenuators Receiver Block am1 bm1 bm2 am2 MICROWAVESOURCE

29. Receiver Block • Typically two or three downconversion • Digital vectorial measurement of mag and phase • Phase lock of the internalsource through receiversignals

30. Phase Lock through its receiver Unlike the old VNA where thesource was autonomuos lockedand the receiver could be lock to any microwave signal, modernVNAs cannot work unlesstheir internal source is used.As example: You cannot use a VNA to measurethe signal coming out from a chipwhere it’s clock cannot be lock toan external refenrence

31. 4 Ports4 Ref 4 Rec Today VNA Hardware: 2-ports2 Ref2 Rec

32. Are 4 ports VNA enough? Ex. Package/Socket footprint Port 4 & Port 10 Port 6 & Port 12 Port 2 & Port 8 • Differential pairs are used so: • 12-port data is required for channel modeling • Data for a fully characterized 12-port DUT results in a completely filled 12x12 matrix GNDs Port 1 & Port 7 Port 5 & Port 11 Port 3 & Port 9 Ports 1-6 are on the socket bottom Ports 7-12 are on the socket top

33. RIGHTPORTS LEFTPORTS 12 ports VNA 2 Ref 2 Switched Rec

34. RIGHTPORTS LEFTPORTS 12 ports VNA 2 Ref 2 Switched Rec

35. Custom Fixtures Interfacing • Repeatibility • Standard Availability

36. On Wafer

37. Let’s summarize up to now • Directional Couplers have finite directivity and frequency depend behaviour • Switches are not ideal and frequency dependent • Reference Plane position depends on cable, adapter interconnections and so on • DownConversion and Digitizing problems like: • Source Phase Noise • Frequency accuracy and repeatibility • Non linearity of mixer/sampler • ADC Dynamic Range & Speed Accuracy ???

38. Cause ofUncertainty • SystematicErrors (85%) • MicrowaveComponents • Interconnections • Incorrect Standard Modeling • CalibrationAlgorithm • RandomError (10%) • Connection Repeatibility • FrequencyStability • Noise • Drift (5%) Lab Care Calibration

39. Is Calibration fundamental? • What if we would measure 30g of Ham with the scale plate of 1 ton? SO A GOOD CAL IS FUNDAMENTAL AND MANY TIMES VERY DIFFICULT TO ACHIEVE THIS IS THE SAME EFFECT OF 1m cable at 10GHz if we are looking for 1 degree of phase shift on S11

40. Raw vs. Corrected Data

41. How does the calibration work? Example TRL Thru Reflect Line

42. b0 a0 b4 a4 Error Model • Ipothesis • sampler (mixer),and all the other system components are linear and invariant parts • The two half are independent 4-port networks which “talk” only through the DUT am1 bm1 b3 a3 • Let the half • 8 unknowns:a0, b0, a1, b1,a3, b3, a4, b4 • The two acquire data are proportional to b3,b4 : • am1=k1b3 , bm1=k2b4 DUT a2 b1 b2 a1

43. 4 port equation Reflection Coefficients of the downconversion part and reading vs. wave Error Model Definition II 8 eq. with 10 unknowns. (a0, b0, a1, b1, a3, b3, a4, b4, Vm1, Vm2): Let use Vm1 e V m2 as independent variables and called them: am1=Vm1, bm1=Vm2, a1= a1DUT e b1= b1DUT we find the following model

44. Error Model Definition III

45. Error Model Definition IV If we call am1 and bm1

46. The famous error box Shuffle the last 2 Equations and rename as

47. ErrorBox E Ideal VNA DUT b1 bm1 The birth of the famous error box Since we are in the S-parameter world the LINEAR RELATIONSHIP WHICH LINKS THE MEASUREMENT TO THE ACTUAL WAVES WILL BE Linear relationshipgivenas a Linear FictiuosNetwork calledError Box a1 am1

48. Error Box Property • It’s not an actual network but only a linear system model • Every parameter is frequency dependent but time invariant • Since the E parameters are more or less link with some specifications of the coupler they are also called:

49. Two Port Error Model Two error boxes on the right and left To apply this model, 4 independent readings on each source position are required 2-ports Measured S-matrix NOT POSSIBLE

50. FULL 2-Ports Error Model 8 error terms, but 7 UNKNOWS TO GET Tdut TA, TB are the transmission matrix equivalent of the two E matrices of left and right side while Tmis the transmission matrix equivalent of Sm