# Modeling Physical Interconnects (Part 3)

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1 Modeling Physical Interconnects (Part 3) Dr. José Ernesto Rayas Sánchez 1 Outline Vias Vias in PCBs Types of vias in PCBs Pad and antipad Nonfunctional pads Modeling vias Calculating circuit element values with formulas Obtaining circuit element values from EM simulations 2

2 Vias They implement the vertical connections (conductive columns to connect traces on different layers) Vias exist at many physical levels: (R. Mellitz, 2003) 3 Vias in PCBs They are formed by drilling a hole (either mechanically or with a laser) Blind via: a via not passing through the complete PCB Through hole via: a via passing through the entire PCB stackup Buried via: a via connecting internal layers Conducting vias are plated with copper Plated through hole (PTH): conductive via passing through the entire PCB stackup 4

3 Types of Vias in PCBs (R. Mellitz, 2003) 5 PCB Stackup Example showing a 6-layer stackup (S. C. Thierauf, High-Speed Circuit Board Signal Integrity, Artech, 2004) 6

4 Vias in the PCB Stackup (S. C. Thierauf, High-Speed Circuit Board Signal Integrity, Artech, 2004) 7 Pad or Land A ring of copper that surrounds a plated via (to ensure electrical contact to traces even if there is some misalignment) (S. C. Thierauf, High-Speed Circuit Board Signal Integrity, Artech, 2004) 8

5 Antipad A hole in the power/ground plane to avoid electrical contact (S. C. Thierauf, High-Speed Circuit Board Signal Integrity, Artech, 2004) 9 Vias Connecting to Power/Ground Planes Small copper fingers are used for thermal isolation (S. C. Thierauf, High-Speed Circuit Board Signal Integrity, Artech, 2004) 10

6 Nonfunctional Pads They are used to anchor the via to the laminate They increase unwanted capacitive coupling to ground/power planes Increasing the antipad decreases the coupling (S. C. Thierauf, High-Speed Circuit Board Signal Integrity, Artech, 2004) 11 Modeling Vias If the via is electrically small (if t d(via) > 0.1t t ), it can be modeled with a lumped circuit (R. Mellitz, 2003) 12

7 Modeling Vias (cont) If the via is electrically small (if t d(via) > 0.1t t ), it can be modeled with a lumped circuit L barrel L barrel = 5.08h[ln(4h / d) + 1] (nh) C pad C pad C pad 1.41ε rdt 1 = D D 2 1 (pf) D 1 : pad diameter (in) D 2 : antipad diameter (in) T : thickness of PCB (in) ε r : relative permeability of the PCB h: via length (in) d: via diameter (in) (H. Johnson and M. Graham, High-Speed Digital Design, Prentice Hall, 1993) 13 Alternative Formula for the Via Inductance If the via is electrically small (if t d(via) > 0.1t t ), it can be modeled with a lumped circuit L barrel C pad C pad L barrel 2 µ 0 h + r + h = hln 2 π r r r + h h: via length (m) r: via radius (m) (M.E. Goldfarb and R.A. Pucel, 1991) 14

8 Modeling Vias Example (R. Mellitz, 2003) 15 Modeling a Plated Through Hole Via (PTH) (R. Mellitz, 2003) 16

9 Via Modeling though EM Simulation Some electromagnetic simulators have the capability of automatically synthesizing a lumped circuit model using inductors, capacitors, resistors and mutual inductors The equivalent circuit is usually provided in SPICE format This method is intended for any electrically small circuit (small with respect to the wavelength at the highest frequency of excitation) By using this approach, we can develop very accurate models of vias (with arbitrary geometries), without relying on empirical formulas 17 Modeling a Squared Grounded Via Using Sonnet (top layer) 18

10 (bottom layer, ground) 19 w D D FR4 h w = 50mil D = 80mil H = 100mil ε r = 4.3 loss tan =

11 21 22

12 23 24

13 200MHz GHz 26

14 20GHz 27 28

15 29 30

16 0.9 Lumped Circuit Model of a Squared Via L C R L (nh) L 808 µh (circuit model above 5GHz is useless) frequency (GHz) Lumped Circuit Model of a Squared Via L 2 C R 1.5 C (pf) 1 C 0.11 pf (circuit model above 5GHz is useless) frequency (GHz) 32

17 4 Lumped Circuit Model of a Squared Via L 3 2 C R 0 Ω R (circuit model above 5GHz is useless) R (ohms) frequency (GHz) 33 Estimating L with Formulas Taking h = 100mil, d = 50mil Using Johnson s formula: L barrel = 5.08h[ln(4h / d) + 1] = nh Using Goldfarb s formula: (r = d/2) L barrel 2 2 µ 0 h + r + h 2 2 = ln = nh 2 h + r r + h π r 34

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Single Transistor FM Transmitter Design In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency. FM is commonly used at VHF radio frequencies for