Prerequisite reading - Chapter 4 Interconnect I – class 16 Prerequisite reading - Chapter 4 12/4/2002

Outline Transmission line losses DC losses in the conductor Frequency dependent conductor losses Frequency dependent dielectric losses Effect of surface roughness Differential line losses Incorporating frequency domain parameters into time domain waveforms Measuring Losses Variations in the dielectric constant Interconnect: Adv 12/4/2002

Focus This chapter focuses on subtle high speed transmission characteristics that have been ignored in most designs in the past These effects become critical in modern designs Older BKM assumptions break down Become more critical as speeds increase As speeds increase, new effects that did not matter become significant This increases the number of variables that must be comprehended Many of these new effects are very difficult to understand This chapter will outline several of the most prominent non-ideal transmission lines issues critical to modern design Interconnect: Adv 12/4/2002

Transmission Line Losses Key Topics: DC resistive losses in the conductor Frequency dependent resistive losses in the conductor Frequency dependent dielectric resistive losses Effect of surface roughness Differential line resistive losses Interconnect: Adv 12/4/2002

Transmission Line Losses (cont’d) These losses can be separated into two categories Metal losses Normal metals are not infinitely conductive Dielectric losses Classic model are derived from the alignment of Electric dipoles in the dielectric with the applied field Dipoles will tend oscillate with the applied time varying field – this takes energy Why do we care about losses? Losses degrade the signal amplitude, causing severe problems for long buses Losses degrade the signal edge rates, causing significant timing push-outs Losses will ultimately become a primary speed limiter of our current technology Interconnect: Adv 12/4/2002

Incorporation Losses Into The Circuit Model A series resistor, R, is included to account for conductor losses in both the power and ground plane A shunt resistor, G, is included to account for Dielectric Losses R L G C Interconnect: Adv 12/4/2002

DC Resistive Losses w t Reference Plane At low frequencies, the current flowing in a conductor will spread out as much as possible DC losses are dominated by the cross sectional area & the resistively (inverse of conductivity) of the signal conductor Current flows through entire cross section of signal conductor and ground plane w t Reference Plane The current in a typical ground plane will spread out so much that the DC plane resistance is negligible The DC losses of FR4 are very negligible Interconnect: Adv 12/4/2002

AC Resistive Losses As the frequency of a signal increases, the current will tend to migrate towards the periphery or “skin” of the conductor - This is known as the “skin effect”. This will cause the current to flow in a smaller area than the DC case Since the current will flow in a smaller area, the resistance will increase over DC Coaxial Cable Cross Section at High Frequency Outer (Ground) conductor Inner (signal) conductor Areas of high current density Interconnect: Adv 12/4/2002

The Skin Effect Why? When a field impinges upon a conductor, the field will penetrate the conductor and be attenuated remember the signal travels between the conductors The field amplitude decreases exponentially into the thickness of the conductor – skin depth is defined as the penetration depth at a given frequency where the amplitude is attenuated 63% (e-1) of initial value X Amplitude Penetration into conductor Electromagnetic Wave Interconnect: Adv 12/4/2002

The Skin Effect – Spatial View The fields will induce currents that flow in the metal Skin effect confines 63% (e-1) of the current to 1 skin depth – the current density will decease exponentially into the thickness of the conductor The total area of current flow can be approximated to be in one skin depth because the total area below the exponential curve can be equated to the area of a square 1 0.9 0.8 0.7 0.6 0.5 Current 0.4 0.3 0.2 0.1 1 2 3 4 5 6 Interconnect: Adv Skin Depths 12/4/2002

Microstrip Frequency Dependent Resistance Skin effect causes the current to flow in a smaller area Frequency dependent losses can be approximated by modifying DC equations to comprehend current flow Approximation assumes that the current is confined to on skin depth, and it ignores the current return path The current will be concentrated in the lower portion of the conductor due to local fields w t E-fields Interconnect: Adv 12/4/2002

Microstrip Frequency Dependent Resistance Estimates The total resistance curve will stay at approximately the DC value until the skin depth is less than the conductor thickness, then it will vary with Example of frequency dependent resistance 40 35 30 25 Resistance, Ohms 20 15 Tline parameter terms 10 5 0.E+00 1.E+09 2.E+09 3.E+09 4.E+09 5.E+09 6.E+09 Frequency, Hz R0 ~ resistance/unit length Rs ~ resistance/sqrt(freq)/unit length Interconnect: Adv 12/4/2002

Microstrip Return Path Resistance The return current in the reference plane also contributes to the frequency dependent losses w t H (Current Density in plane) D The area that the return current will flow in will allow an effective width to be estimated Interconnect: Adv 12/4/2002

Microstrip Return Path Resistance The current density formulae can be integrated to get the total current contained within chosen bounds This shows that 79.5% of the current is contained in a distance +/- 3H (W of 6H) from the conductor center Assuming a penetration of 1 skin depth, the ground return resistance can be approximated as follows Interconnect: Adv 12/4/2002

Total Microstrip AC Resistance The total resistance is approximately the sum of the signal and ground path resistance This is an excellent “back of the envelope” formula for microstrip AC resistance Interconnect: Adv 12/4/2002

More exact Formula – Microstrip (From Collins) This formula was derived using conformal mapping techniques The formula is not exact should only be used for estimates Interconnect: Adv 12/4/2002

Stripline Losses In a stripline, the fields are referenced to two planes The total current will be distributed in both planes, and in the upper and lower portion of the signal conductor 2 ) / ( 1 H D I + µ 2 ) / ( 1 H D I + µ d d d d For example: In a symmetrical stripline,the area in which current will travel increases by a factor of 2 and the resistance decreases by a factor of 2 This inspires the parallel microstrip model Interconnect: Adv 12/4/2002

Calculating Stripline Losses The skin effect resistance of a stripline can be approximated as follows: where the resistances are calculated from the microstrip formulae at the appropriate heights w H2 t H1 Interconnect: Adv 12/4/2002

Surface Resistance for Microstrip The surface resistance (Rs) is often used to evaluate the resistive properties of a metal Observation of AC loss equations show the resistance is proportional to the square root of Frequency Rs is a constant that scales the square root behavior Is caused by the skin loss phenomena Used in specialized T-line models (i.e.,W-Element) Interconnect: Adv 12/4/2002

Surface Roughness alters Rs The formulae presented assumes a perfectly smooth surface The copper must be rough so it will adhere to the laminate Surface roughness can increase the calculated resistance 10-50% as well as frequency dependence proportions Increase the effective path length and decreases the area Skin-Depth Plane Trace Tooth structure (4-7 microns) Interconnect: Adv 12/4/2002

Surface Roughness Effects Frequency Dependence Surface roughness is not a significant factor until skin depth approaches the tooth size (typically 100 MHz – 300 MHz) At high frequencies, the loss becomes unpredictable from regular geometric object because it is heavily dependent on a random tooth structure. No longer varies with the root of frequency – something else Interconnect: Adv 12/4/2002

Example of Surface Roughness Measurements indicate that the surface roughness may cause the AC resistance to deviate from F0.5 Tooth Structure Interconnect: Adv 12/4/2002

Dielectric Losses Classic model of dielectric losses derived from damped oscillations of electric dipoles in the material aligning with the applied fields Dipoles oscillate with the applied time varying field – this takes energy Dielectric constant becomes complex with losses PWB board manufacturers specify this was a parameter called “Loss Tangent” or Tan d The real portion is the typical dielectric constant, the imaginary portion represents the losses, or the conductivity of the dielectric Interconnect: Adv 12/4/2002

Glass Weave Effects High Speed Signals Resin Material Glass Material Data shows that Fiber Weave Effect cannot be ignored for High Speed signals Glass Weave Epoxy trough Weave Alignment Dielectric Constant Variation – from different sample board Trace Zo Interconnect: Adv 12/4/2002

Current Distribution and Differential Losses 4.5 Vary 5 2 Zdiff Varies 10 GHz 5 GHz Trace Separation (mils) Loss, 1-|S(2,1)| Differential Single Line Transitional 1 2 Zdiff Zodd Ports matched to diff. mode impedance Current distributions effect the loss Evidence of a “sweet spot” where the loss is smallest Interconnect: Adv 12/4/2002

Differential Microstrip Loss Trends - Tand Microstrip losses as a function of frequency and loss tangent assuming smooth conductor (5/5/5; Circuit on page x) y = -1E-09x - 1.1925 R 2 = 0.9992 y = -5E-10x - 1.2079 = 0.9953 -25 -20 -15 -10 -5 5 10 15 20 25 Frequency, GHz Loss, dB tand=0.01 tand=0.03 Model indicates linear behavior past 2.5 - 4 GHz Interconnect: Adv 12/4/2002

Low Freq. Differential Loss Trends - Spacing W/S/W=5/15/5 Curves Intersect W/S/W=5/5/5 Losses at low frequency are greater for narrow spaced diff. microstrip Model predicts that loss curves for wide and narrow spaces intersect at: 700MHz when Tand=0.03, 3 GHz when Tand=0.01 Interconnect: Adv 12/4/2002

High Freq. Microstrip Loss Trends - Spacing microstrip differential loss, w=5, er=4.2, h=4.5, tand=0.03, Zodd over spacing = 50 +/- 5 ohms -30 -25 -20 -15 -10 -5 2 4 6 8 10 12 14 16 18 20 Frequency, GHz Loss, dB 5-5 5-10 5-15 5-20 Model predicts losses at high frequencies are greater for wide spacing Phenomenon is exacerbated with high values of Tand (Don’t ask why yet … wait a few slides) Interconnect: Adv 12/4/2002

Conductor Loss Concepts – mS vs Spacing Conductor losses increase due to skin effect & proximity effect In absence of dielectric losses, narrow spacing will produce higher losses due to proximity effect – area of current flow determines losses (approx. root F behavior) Current Distributions Narrow Spacing Wide Spacing E-Fields Interconnect: Adv 12/4/2002

Dielectric Loss Concepts – mS vs Spacing Dielectric losses increase due to damped response of electric dipoles with frequency of applied oscillating electric field Tand losses increase linear w/ freq. (assuming homogeneous media) Why does narrow spacing have the highest losses at low frequencies but the lowest loss at high frequencies? At low frequencies, Tand losses are small and losses are dominated by skin and proximity effects; Narrow spacing = smaller area for current = high loss At high frequencies, Tand losses dominate; Smaller spacing leads to more E-fields fringing through the air and less through the lossy dielectric Interconnect: Adv 12/4/2002

Does Not Apply for Homogeneous Dielectric stripline differential loss, w=5, er=4.2, B=18, tand=0.03, Zodd over spacing = 51 +/- 5 ohms -40 -35 -30 -25 -20 -15 -10 -5 2 4 6 8 10 12 14 16 18 20 Frequency, GHz S=10 through 20 S=5 Narrow spacing remains the highest loss configuration in a stripline over freq. Since the dielectric media is homogeneous, all the fields are contained within the lossy material Since no fields fringe into a loss-free dielectric, the only conductor losses are affected by spacing Interconnect: Adv 12/4/2002

Assignment Use Ansoft 2 (or HSPICE) and create a family of plots of for different line widths of losses verses frequency for the following case. W=1, 2, 5, 10, 20 mils H2=10 mils T=1.5 mils H1=10 mils Er=4.0 Tand=.025 Metal sigma= 4.2e7 Interconnect: Adv 12/4/2002