Advanced Transmission Lines. Transmission Line 1

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1 Advanced Transmission Lines Transmission Line 1

2 Transmission Line 2 1. Transmission Line Theory :series resistance per unit length in. :series inductance per unit length in. :shunt conductance per unit length in. :shunt capacitance per unit length in. Let : complex propagation constant. We have the solutions : positive z-direction propagation wave. : negative z-direction propagation wave. : voltage or current amplitudes of positive or negative propagation waves. Also

3 Transmission Line 3 Define characteristic impedance Then and Characteristic impedance is the voltage to current ratio of the wave. For lossless line : attenuation constant. Power loss due to (conductor loss) and (dielectric loss). : propagation constant. : phase velocity. Decreases as or increases. : guided wavelength. Decreases as or increases. : increases as increases or decreases. Terminated Lossless Transmission Line Assume incident wave, reflected wave then

4 Transmission Line 4 At, Impedance Match For it is required that. That is, the load impedance must match the characteristic impedance of the transmission line. When to Consider Transmission Line Effect When the length of the transmission line is less than 1/20th of the wavelength of the highest frequency component of a signal, then transmission line effects can be safely ignored and the circuit can be modeled as a simple RLC circuit. The actual threshold used, 1/20th, 1/10th or 1/5th, is based on experience. For example, an interconnect on a silicon chip clocking at 3 GHz has an appreciable frequency component at 15 GHz. An interconnect reaches the 1/10th threshold when it is 0.6 mm long. This is less than the dimensions of most chips, which can be up to 2 cm on a side. Thus it takes a finite time for the variation of a voltage at one end of an interconnect to impact the voltage at the other end. When an Interconnect Should be Treated as a Transmission Line Rise time 90% of its final value. : the time required for the signal to change from 10% to

5 Transmission Line 5 Time of flight delay : the time required for the signal to pass through the line where is the line length.

6 Transmission Line 6 Transmission Line Structures Figure 5 Common transmission line structures suited to planar fabrication.

7 Transmission Line 7 Typical characteristic impedance range Typical Q range

8 Transmission Line 8 Substrate Property Property of typical substrate

9 Transmission Line 9 Property of organic substrate Skin Effect Skin effect: the concentration of charge and current near the surface of a conductor. Skin depth : the depth at which the magnitude of the current falls to of its value on the surface of the conductor. For planar metal trace, thickness should be at least to reduce resistance. Larger than that is less effective. Figure 11 (a) an electromagneticwave from the left incident at the interface of air and a conductor; and (b) profiles of the electric field magnitude (top) and current magnitude (bottom) as the wave travels into the conductor.

10 Transmission Line 10

11 Transmission Line Microstrip Line Formulas, Or

12 Transmission Line 12 where Loss Dielectric loss: where Conductor loss: is the surface resistance where is the conductivity.

13 Transmission Line 13 Correction for Surface Roughness where is the attenuation of the strip without roughness, is the r.m.s. surface roughness and is the skin depth. Surface roughness increases conductor loss. Example: consider a copper microstrip, where the skin depth at 4 GHz is 1 μm. Also assume that the r.m.s. surface roughness is of similar magnitude, that is, 1 μm (typical of 99% alumina). Then. that is to say, the loss is increased by approximately 60% when surface roughness is taken into account. Bends in Microstrip Right angle bends exhibit series inductance and shunt capacitance. Insertion loss cannot be ignored at higher frequency.

14 Transmission Line 14 Example: 0.75mm line width, 0.5mm thick substrate with relative permittivity is 9.9. Equivalent circuit capacitance and inductance are pf and nh, respectively. At 10 GHz,. Mitered (Chamfered) Microstrip Bends A mitered bend produces as good as, or better, performance than curved bends. This applies to a wide range of bend angles, from up to. At least 70% chamfer fraction ( ) is recommended for an acute-angled bend of Optimum right angle bends, 60% chamfer fraction. The mitered edge of the microstrip bend acts like a reflector to redirect the current flow. Figure 16 Mitered bend. Operating frequency limits The lower-order strong coupled TM mode:

15 Transmission Line 15 The lowest-order transverse microstrip resonance: Example:,,.

16 Transmission Line Strip Line Benefit: No dispersion. Shielded. Disadvantage: Difficult to attached lumped elements. Parallel waveguide modes Formulas where. Or

17 Transmission Line 17 where. Loss where

18 Transmission Line Coplanar Waveguide (CPW) Disadvantage of Microstrip Line Relative inaccessibility of the ground plane. Difficulty associated with making shunt connections between strip and ground. Sensitivity to substrate thickness. In integrated circuit technology lateral dimensions can be defined photolithographically with great accuracy, but the substrate thickness is often not controlled at all well. Increased radiation when thick substrates are used. CPW Benefit: Easier grounding of surface-mounted (or ball grid array (BGA)- mounted) components Lower fabrication costs. No via needed. Reduced dispersion Decreased radiation losses Photo-lithographically defined structures with relatively low dependence on substrate thickness. CPW Disadvantage: Difficult in routing. Can produce unwanted common mode if asymmetric. Air bridge needed to tie the two ground to the same potential.. Insensitive to substrate thickness.

19 Transmission Line 19

20 Coupled Transmission Lines Transmission Line Structure: symmetrical, two signal wire. Support differential (odd) and common (even) modes with different characteristic impedances and phase velocities. 2. Benefit: reduce interference. 3. Disadvantage: difficult to layout. When symmetry is broken due to bend or branch, common mode will be generated, contaminating differential signals. 4. Extra consideration needed to match both differential and common modes. Example: microstrip parallel coupled line

21 Transmission Line 21 Example: Coupling: 0.05 for a length of 1/4 wavelength.t

22 Transmission Line 22

23 Transmission Line 23 Moisture Effect on Dielectric PCB constructed with a dielectric that tends to absorb moisture (such as FR4) is exposed to a humid environment for a significant amount of time, both the loss tangent and the dielectric permittivity will increase. Fig. 25 shows an example of the insertion losses measured in a dry environment such as an Arizona winter (15% RH and 60 N F) and a humid environment such as Malaysia (95% RH and 95 N F). The dramatic increase in insertion losses corresponds to an increase in dissipated power. Fig. 26 depicts measured values of the same dielectric material for both low- and high-humidity environments. At about 7.5 GHz, the increase in the loss tangent is greater than 50%. Fig. 27 shows a relatively small increase of less than 5% in the dielectric permittivity. Fig. 28 shows the measured change in insertion loss (S 21 ) at 10 GHz for a microstrip transmission line built on FR4 that was dry at beginning and then exposed to humid conditions for 55 days. In this example, the dielectric transmission-line losses at 10 GHz were 6.3 db under dry conditions at t = 0. The dielectric became almost fully saturated within the first 7 days, increasing the loss to 8.9 db. Finally, the transmission-line loss stabilized to a value of 9.3 db of loss at t = 48 days.

24 Transmission Line 24 Figure 25 Figure 26 Figure 27

25 Figure 28 Transmission Line 25

26 Differential Signaling Single-ended signaling generally work well up to approximately 1 to 2 Gb/s. As data rates increase, it becomes increasingly difficult to maintain adequate signal integrity because of system noise due to switching, crosstalk and nonideal current return paths (Fig. 1). To reduce the effect of the system noise dramatically is to dedicate a pair of transmission lines for each bit on the bus. The two transmission lines are driven in the odd mode, and the differences between the voltages are used to recover the signal at the receiver using a differential amplifier (Fig. 2 and Fig. 3). Figure 1 How system noise can severely degrade signal integrity on single-ended buses. The ideal versus noisy receiver voltages compared to the reference voltage. 1

27 Figure 2 Differential signaling where each bit is transmitted from the driver to a receiver using a pair of transmission lines driven in the odd mode. The signal is recovered at the receiver with a differential amplifier. Figure 3 Example of how common-mode noise is eliminated with differential signaling: (a) single-ended waveforms at each leg of a differential receiver showing common mode noise; (b) differential waveform. Benefits of Differential Signaling 1. Reduce common mode noise. 2. Due to the cancellation effect of the positive and negative signal pair, crosstalk of differential line is lower than single-end line for the same separation. 3. For the same reason, radiation loss is also smaller, reducing EMI. 2

28 Note: crosstalk of single-end signal line might not be higher if the same area is used (Fig. 4 and 5). Figure 4 Cross sections used to compare differential versus single-ended crosstalk: (a) two single-ended signals; (b) two differential pairs with the same pair spacing as that of the single-ended signals in (a); (c) two widely spaced single-ended signals that occupy the same board area as the differential pairs (dimensions in mils). Figure 5 Crosstalk for the cross sections in Fig. 4 demonstrating that differential signaling does not reduce crosstalk compared to single-ended signaling if the same board area is used. However, if the spacing between differential pairs is similar to the spacing between single-ended signals, crosstalk in reduced (5-in. microstrip). 3

29 Figure 6 For an odd-mode (or differential) signal, the fields orient so that an ideal virtual reference plane existed between the conductors. When the physical plane is interrupted, the virtual plane provides a continuous reference for a differential signal and helps preserve signal integrity. 4. Virtual Ground. Helpful for signal integrity when not perfect ground exists. Drawback of Differential Signaling 1. Occupy larger area. 2. Due line routing is more difficult than single line. 3. AC common-mode conversion (ACCM conversion): if the phase difference of the two signals on a differential line is not, common mode signal will be generated. Possible causes (Fig. 7): a. Length differences between the line pair. b. Asymmetric lines. c. Coupling. d. Bends. e. Termination differences 4

30 Figure 7 Examples of asymmetry in a differential pair that can cause differential to common-mode conversion: (a) routing-length differences; (b) impedance differences due to etching variation; (c) crosstalk differences; (d) length differences due to bends. Figure 8 When asymmetry exists in the differential pair, part of the signal gets converted to common mode at the receiver. 5

31 Example (Fig. 9): Calculate the common mode voltage of the following circuit. Figure 9 Example circuit for computing ACCM conversion. Figure 10 Differential common-mode conversion plotted for Fig. 9 showing that a differential signal launched at the driver becomes common mode at the receiver when the frequency is about 12.5 GHz. Fiber-Weave Effect: for example, FR4 is made from a matrix of woven bundles of fiberglass ( ) embedded in an epoxy resin ( ) as shown in Fig. 11. The glass pitch shown is typical in the printed circuit board industry. It is possible for one leg of the differential signal to be routed between glass bundles and the other to be routed over a glass bundle that effectively gives each trace a unique propagation velocity causing an imbalance in the differential pair that causes ACCM conversion. To avoid, signal traces should align with fiber at an angle. 6

32 Figure 11 A typical FR4 substrate. Example (Fig. 12): calculate the ACCM conversion of a typical case of fiber-weave effect. Figure 12 A type fiber-weave effect of FR4 substrate on ACCM converion. 7

33 Effects of ACCM Conversion of Differential Line Bends and Compensation Techniques 1. Comparison of (a) right angle bend, (b) mitered bend, (c) round corner bend and (d) and rise time 100 ps (Fig. 14 and Fig. 15). bend. Length 25 mm, signal voltage 1 V The 45-degree-angle bend structure has the minimum common-mode noise and reflected differential-mode noise. 60% lower than the right-angle bend. For common mode noise, round corner bend is a little bit better than right angle bend and mitered bend. For reflected differential-mode noise, mitered bend is the worse while round corner bend and right angle bend is similar. The faster the rise-time, the higher both the common-mode noise and reflected differential-mode noise. 8

34 Figure 14 Figure Dual Back-to-Back Bends Can reduce common mode noise from 10s mv to 1s mv. The longer separation of the dual bends, the worse the performance. Saturate above 100 mm (Fig. 17). Figure 16 Dual back to back bends 9

35 Figure 17 Remnant common-mode noise of the dual back-to-back coupled bends observed at the probing point g for various length as depicted in Fig Compensation Capacitance for Common Mode Noise Reduction (Fig. 18) The bend of the outer line can be treated as an extra capacitor to ground. A capacitor can be added on the inner line to compensate. The 1.17 pf capacitance can reduce the maximum common-mode noise by 53.48% against the uncompensated right-angle bend. 4. Compensation Patch for Common Mode Noise Reduction (Fig. 19) Due to space limitation and cost, difficult to add lumped 10

36 capacitors to compensate. Instead, use patch metal on inner bend to achieve similar capacitive effect. For the right-angle bends, a square patch of the side lengths 5.8 mm achieves 58% improvement. For 45-degree bends with a fan-shaped patch, a of 4 mm achieves 46% improvement. Figure 18 Transient analyses at the receiver for right-angle bends with shunt various compensation capacitances. 11 Figure 19 Common-mode noise of coupled bends with the parallel patch capacitance. (a) Right-angle bends with a square patch. (b) 45-degree-angle bends with a fan-shaped patch.

37 5. Slow Wave Structure Use slow wave structure on the inner line to compensate the shorter path. Figure % reduction in common mode noise. Figure 22 About 5-dB reduction in common mode noise. 6. Parasitic Trace Figure db reduction of common mode noise. 12

38 Bandwidth of Digital Signal By Fourier transform, a time-domain waveform can be thought of equivalently as being composed of the sum of infinite sinusoidal frequency components., Example: 1-GHz clock signal waveform (period 1 ns) having rise and fall times ( ) of 100 ps, a 50% duty cycle, and an amplitude of 5 V. The spectrum components are Note that because of the 50% duty cycle, the even harmonics are zero. The DC component of the waveform, is the average value of the waveform which is 2.5 V. Observe that the ninth harmonic of 9 GHz has a wavelength of 3.33 cm. To use lumped-circuit approximation to analyze a circuit driven by this frequency would require that the largest dimension of the circuit be less that 3.33mm. Similarly, to analyze a circuit that is driven by the fundamental frequency of 1 GHz, whose wavelength is 30 cm would restrict the maximum circuit dimensions to being less than 3 cm. This shows clearly that use of lumped-circuit analysis methods to 13

39 analyze a circuit having a physical dimension of, say, 3 cm that is driven by this clockwaveform would result in erroneous results for all but perhaps the fundamental frequency of the waveform. Approximate the trapezoidal pulse by finite number of harmonics It shows that the result is pretty good when up to the ninth harmonic is applied. Therefore, the required bandwidth is at least 9 GHz which is close to. Therefore, Figure 25 Approximating the clock waveform with first and third harmonics. 14

40 Figure 26 Approximating the clock waveform with first, third and fifth harmonics. Figure 27 Approximating the clock waveform with up to the ninth harmonics 15

41 Meshed-ground Plane Figure 1 Rectangular Cell Benefit: 1. Improve flexibility of FPC. 2. Improve adhesion between different metallization layers 3. Reduce weight. Figure 2 Rhombus Cell Short coming: 1. Lower operation frequency due to stop band of EBG. 2. Generate radiation due to perturbation on ground. 3. Deteriorate isolation due to holes on ground plane. Effect: 1. Reduce capacitance per unit length due to the removal of metal under transmission lines. The larger the aperture, the smaller the capacitance. 2. Increase inductance per unit length due to the perturbation of current path on ground plane. The larger the aperture, the larger the inductance. 3. Increase characteristic impedance. 4. The periodic cells create stop band. 5. Transmission line characteristics are more frequency dependent. 1

42 Benefit of rhombus cell over rectangular cell 1. Characteristic impedance is less sensitive to alignment. 2. Higher operation frequency due to the less perturbation of ground current reducing the EBG effect. Case Study: Rectangular Cell Figure 3 1. Impact of Trace-to-Aperture Intersecting Angle (Fig. 4) a. When βwas small, the response changed fast. b. curve was flattened dramatically from to. c. from to. d. Inductance and Capacitance.Solid Ground:,.. 2

43 Figure 4 Figure 5 2. Impact of Trace-to-Baseline Offset (Fig. 5) a. For, change of the offset causes large change of the capacitance, thus the impedance changes a lot.. b. For, almost no change of impedance. c. For, small change of impedance.. d. Inductance and Capacitance. Solid Ground:,. 3. Impact of Aperture Dimension (Fig. 6) a. increases when the aperture dimension increased. b. When τapproaches 1/2, the trace moved closer to the top of a row of apertures. A slight change of aperture size will make the return current distribution drastically different, leading to 3

44 significant change of. c. Forsmaller τvalues, the per-unit-length parameters changed minimally with aperture dimension changes. d. did not change much as the trace shifted if aperture size was small, e.g.. e. changed more dramatically for larger aperture sizes. f. is independent of, if the aperture size to trace width ratio is smaller than 1/2. g. Inductance and Capacitance. Solid Ground:,. Figure 6 Figure 7 4

45 4. Impact of aperture-to-aperture separation (Fig. 7) a. decreased as b increased for different. b. As b increased, approaching solid reference conductor case. c. changed slightly faster for the no trace offset situation compared to the trace offset cases. d. Inductance and Capacitance. Solid Ground:,. Case Study: Rhombus Cell Line width: 0.36 mm. Substrate thickness: 0.2 mm. Substrate dielectric constant: Line offset effect (Fig. 8) a. The middle case provides the shortest return current path, thus the best transmitting performance b. The center and the edge cases have the longest return current 5

46 path, thus have poor characteristics. c. Cutoff at about 6 GHz due to EBG effect except the middle case. The cutoff of the middle case is about twice of the other case because the effective cell size is half. 2. Cell Size Effect (Fig. 9) a. As cell size increases, cutoff frequency decreases. Figure 8 Figure 9 Figure Improving performance by adding a trace on ground plan (Fig. 10) 6

47 a. A straight current path is generated on ground plane to reduce EBG effect. b. 10, 15 and 20 TG cases maintain -3-dB insertion loss over the 10 GHz, which show almost ideal characteristics of the general microstrip line. 7