SWAN/DWS micro-behavioral power/gnd plane modelling.


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SWAN/DWS micro-behavioral power/gnd plane modelling.

  1. 1. Piero Belforte 1993 – rev. 2009 MODELLING AND SIMULATION OF P.C.B. POWER AND GROUND DISTRIBUTION PLANES In circuits with very fast edges, power and ground planes cannot be considered ideal, zero-impedance elements. Current pulses injected by a switching driver at any point on the plane generate a voltage noise that propagates along the plane. The circular wave propagating from the injection point is reflected by both lumped component discontinuities (e.g. decoupling capacitors) and plane boundaries, which act like open terminations causing a total reflection of the incident wave. The result is a deterioration of signals which will impair data transmission. These effects can be taken into account only by including accurate models of the ground and power planes in the simulation. Normally it is very difficult to simulate these planes, not just from the standpoint of modeling, but more importantly because plane models generally have a great many inductors and/or transmission lines, and simulators such as Spice cannot handle these efficiently. DWS, however, simulates such models very quickly. Figure 1 shows a 2-layer metal plane under investigation and its crossection. If a TDR step (50 ps rise time or less) is injected into a metal layer using the other layer as reference, a response such as shown in Fig.2 is obtained. For slow edges, the plane acts as a two-plate capacitor of capacitance where A ( A = 0.05 m2 ) is the behavior of the two planes (DUT plane and reference plane). The detail of the waveforms shows a P y t hH t Y X = 250mm Y = 200mm P = 25mm t = 0.035 mm h = 1.3 mm TDR injection point 50 x X Fig. 1: Two-layer metal plane. A C  0 r h metal plane area, h ( h=1.3 mm ) the dielectric thickness and r (r= 4.7) the relative permittivity of the dielectric. The overall time constant is 50*C where 50 ohm is the value of TDR reference impedance. The overall curve shows the general capacitive significant noise due to TDR step reflections at the open boundaries of the plane. Changing the injection point alters this waveforms. Almost any injection point can be used as long as it corresponds to the point used in the simulation for model extraction by parameter optimization. 1.00 # #RHO 0.80 # 0.60 # 0.40 # 0.20 # 0.00 # -0.20# -0.40# -0.60# -0.80# -1.00# 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 TIME[nS] Fig. 2: TDR response of the 2-layer metal plane Copyright Piero Belforte 1993-2012
  2. 2. 0.0  -0.1  -0.2  METAL PLANE MODELING Two different approaches can be used to implement the model: an "unbalanced" or a "full-floating" model. The "unbalanced" model uses one of the two planes as an ideal reference plane. In this case, the propagation effects are assigned to the second plane, that is, quantized in both x and y directions using a constant pitch of approximately 25 mm. The latter is then replaced by an array of ideal transmission lines placed at the edges of the mesh. (Fig. 3a) This structure is useful for modeling packages or p.c. boards having only one metal plane. The ideal plane used for reference will consist of the p.c. board supporting the package or the metal shield of the enclosure containing the p.c. board. As shown in Fig. 1, TDR pulse is injected at an arbitrary point in the actual plane. In the "full- -0.3  Simulated Measured -0.4  -0.5  -0.6  -0.7  -0.8  -0.9  -1.0  0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 TIME[nS] Fig. 4: Lossless Plane Model Validation. maintaining the same impedance and propagation time values. The resulting model is shown in Fig. 3b. This model can be used to simulate coupling between two or more metal planes for multilayer structures. shown in fig.4.The overall behavior of the result approaches the measured waveform but the actual reflection noise is more damped than its simulated counterpart. This damping effect due to skin effect losses on copper planes has a good noise limitation effect so that ignoring it can be too conservative. LOSSY MODEL MODEL VALIDATION Starting from the preceding 2Z0, TD Z0, TD Td = 120 ps 50 ohm Z0 = 13.35 ohm a S11=0, S21=pwl, 2Z0 S11=0, S21=pwl, Z0 where pwl is: 50 ohm 1 2-port S-parameter B A = 0.97 t = 300ps B A tB t b Fig. 3: Discrete approximation of TL model for a metal plane a) Unbalanced model b) full-floating model floating" model, both planes are given a discrete representation and used to simulate the propagation effects. In this case the lines of the "unbalanced" model are replaced by balanced transmission lines, DWS is used to validate the array model simulating the TDR setup. Simulation runs very fast, even if 178 transmission lines are required to model the metal plane. The result of model simulation is considerations, a new version of the 2-D model is created replacing each ideal line with a lossy counterpart represented by a 2-port S-parameter block.
  3. 3. 0.0  during post-layout checks included in the POST-LAYOUT environment. In this case distribution plane model parameters are extracted from p.c. board crossection data while power pin and decoupling capacitors are automatically connected to the right nodes of the plane model. Obviously this process causes a quantization error that is negligible if the array pitch has been selected on the basis of bandwidth (time resolution) requirements. In case of more complicated physical structures like gridded planes a model optimization versus the -0.1  -0.2  -0.3  -0.4  -0.5  -0.6  -0.7  -0.8  -0.9  -1.0  0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 TIME[nS] Fig. 5: Measure and simulation of the lossy model. For an accurate model, it is necessary to adjust the model so that the simulation of the experimental setup fits the actual TDR curve. This is a simple parameter extraction process, adjusting the model parameters A and tB inside the PWL representation of the S21 transmission coefficient of the transmission lines of the mesh. After a few trials, the optimized parameter values are obtained as shown in Fig.5. Correspondence between measurement and simulation is very good, including damping effects. The addition of two parameters determines a slight slow down of simulation runs in comparison with the lossless model. Imax=50mA tr=tf=1ns 76 10nF 25mm 50mm 36 Cdec 10nF 125mm Fig. 6: Analyzed situation from simulations are shown in Fig.7. MODEL EXTENSIONS actual TDR measure is recommended to get best results. MULTILAYERED STRUCTURES More realistic situations can be investigated using accurate device and interconnect models connected to the 2-D plane model. This task can be carried out automatically An extension to multilayered structures can be obtained by creating a stack of the models 50mV BOUNCE NOISE EVALUATION The lossy model can be utilized to evaluate the amount of switching noise in actual operation. A simplified test situation is shown in Fig.6. The two-layer rectangular p.c. board, a set of decoupling capacitors and a noise source consisting of a trapezoidal current pulse are connected as shown in Fig.6 . The effect of decoupling capacitor placement on noise amplitude at various positions inside the p.c. board can be easily analyzed. Some results coming a) 0mV V(36) -50mV 50mV a) 0mV V(76) -50mV 50mV b) 0mV V(36) -50mV 50mV b) 0mV -50mV 40.00 V(76) 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00 130.00 140.00 TIME[nS] Fig. 7: Simulation of switching noise effects a) Cdec on node 76, b) Cdec on node 36
  4. 4. shown in Fig.3. The first layer can be modeled using both balanced and unbalanced transmission lines, while the upper layers are represented only by balanced models (Fig. 8a and 8b). In this way the coupling between superimposed metal planes is taken into account implementing a quasistatic approximation of planecoupling effects. Under steady state conditions, the multilayered structure acts as a capacitive divider. Depending on the fineness of the mesh, a ground plane model may consist of several hundreds or even thousands of transmission lines. However, since DWS handles transmission lines and BTM S-parameters blocks very efficiently, this does not result in overly long simulation times. For example, simulating a p.c.b. including interconnect models, IBIS models, and power distribution planes containing about 20,000 transmission lines takes few seconds on a current PC. Exploiting its unique performance DWS is able also to simulate conventional models, composed tens of thousands of inductances and resistances, generated by commercial 3D Field Solvers. Balanced transmission line t1 t2 t3 t4 h1 h2 H h3 Unbalanced transmission line a) Balanced transmission line t1 t2 t3 b) Fig. 8: Multilayered structures: a) mixed balanced and unbalanced model, b) full balanced model h1 h2 H