ADS 2009 Signal Integrity Eye Diagram Solutions

(Syndicated content from: http://signal-integrity.tm.agilent.com/2009/ads-2009-signal-integrity-eye-diagram-solutions/)

New Agilent ADS signal integrity video! ADS Transient-Convolution Simulator Solves Eye Closure Problems (15 minutes).

See also the story behind recent speed improvements via multithreading ("Agilent Technologies Introduces Industry’s Fastest Signal Integrity Circuit Simulator") and use of a GPU ("Agilent Technologies to Collaborate with NVIDIA to Accelerate Signal Integrity Simulations Using CUDA-Based GPUs")

We’ve Moved! Please Updated Your Bookmarks!

The overhead of syndicating the content here seems to outweigh the benefits, so this is the last post here. Please bookmark our new Signal Integrity site instead. Thanks!

GPU-Accelerated Time-Domain Circuit Simulation Paper at CICC

(Syndicated content from: http://signal-integrity-tips.com/2009/gpu-accelerated-time-domain-circuit-simulation-paper-at-cicc/)

Tired of waiting for your SPICE simulations to complete?

My colleague Rick Poore will be presenting IEEE Custom Integrated Circuits Conference (CICC) paper 20-3 about his work on “GPU-Accelerated Time-Domain Circuit Simulation” in San Jose at 11:05AM on Wednesday, September 16th.

Abstract

Time-domain circuit simulation is dominated by transistor model evaluation. A modern graphics processing unit (GPU) is a parallel, high performance computer suitable for non-graphics tasks. Simulation is sped up by 3-6x by moving transistor evaluation to a GPU. Implications for writing transistor models for good GPU performance are discussed.

Related posts

• GPU-Enabled Computers Speed Up Signal Integrity Simulations
• Straw Poll on Compute Power

Geometric Form Factor for Transmission Lines

(Syndicated content from: http://signal-integrity-tips.com/2009/geometric-form-factor-for-transmission-lines/)

The concept of a geometric form factor is very useful when thinking about transmission lines. It bundles up all the messy 2D geometry of cross-sections and field line patterns into one scalar quantity that is fixed for a particular configuration. Then you can think about the general concepts without getting bogged down in field integrals and field solvers.

To explore this idea, let’s start with a uniform relative dielectric constant ε_r like you’d have with stripline. (Later we’ll generalize to the case where the field lines “sees” a mixture of materials, for example dielectric and air for a microstrip.)

First define a unitless geometric form factor, F, such that capacitance per unit length, C, is:

…where ε₀ is the vacuum permittivity, 8.9pF/m (or 0.22pF/inch) and ε_r is the relative permittivity (relative dielectric constant), ~4.2 to 4.6 in FR4 glass/resin.

In general, we need a 2D electrostatic solver to determine F but let’s first look at a geometry for which there’s an exact, textbook, analytical solution: a rod of radius a, with its center a distance b above a ground plane like this:

The form factor is:

Couple of thing to note about F:
Unitless: F is a function of a geometric ratio, b/a.
Logarithm of a smallish ratio: In practical cases, the numerator and divisor are not of wildly different orders of magnitude. You wouldn’t create a transmission line with a = 1 mm and b = 1 km! No, for the realistic range of values of b/a, the natural logarithm of the function here is of order 1. For example if b=2a, then F is 0.21.

Let’s plot it and two other configurations (illustrated below) and you’ll see that (apart from the “short circuit” corner case at a = b) the blue curve varies slowly with b/a:

The neat thing about the form factor is that when you have it for capacitance, you get inductance and impedance “for free.” To see the first of these, consider the propagation velocity, v, which is both:

With a little algebra you can see that the inductance per unit length, L is given by:
L = Fμ₀
…where μ₀ is the vacuum permeability, 1.3 μH/m
Thus, you can think of F as “how inductive the geometry is versus the free space value of 1.”
If F < 1 the geometry is “more capacitive” than free space, if F > 1 it’s “more inductive.”
The second benefits is that once you have L and C, you also have impedance. Again a little algebra shows that:

…where Z₀ is the vacuum impedance, 377 Ω. The form factor and the relative dielectric constant determine how far the line impedance is from the “natural” value of Ω. A “capacitive” form factor < 1 lowers the impedance, as does a higher relative dielectric constant. If ε_r = 4.2, and you want Z = 50 Ω, then pick your geometry such that F is 0.27.

If you take the ground plane and wrap it around the rod, you get co-ax:

The form factor (magenta line above) is a bit lower (more capacitive) as you’d expect from bring the ground plane closer.

If instead you squash the rod into a ribbon and put a second ground plane on top, you get stripline:

The result is a bit less capactive, because the squashing increases the separation from ground.

You can generalize this idea to non-uniform dielectrics by using a blended or “effective” relative dielectric constant. In a future posting, I’ll also show how it’s useful for lumped elements like inductors from flat coils, and short and long solenoids.