# Simulation solution:

Mainstream high speed pcb design has long followed in the slipstream of rf and microwave engineering. Of necessity, techniques have been simplified and made applicable to wider use: for example, IBIS models that describe input/output behaviour without revealing internal design details are published for most high speed ics.

Double data rate memory has become the de facto standard for pc based designs, turning every board that uses it into a high speed design exercise, often involving system level, multiboard interconnect. For high speed differential channels – such as USB – common mode filters and baluns are often employed. At today's bit rates, simple RLC models of such components do not fit the bill, but neither do models that require deep analysis of the physical structures.

What is needed is a technique that, as in IBIS, reveals the minimum amount of information about the internal structure, while describing the interface sufficiently to simulate it accurately at multigigahertz frequencies. Luckily, such a technique is ready and waiting: S-Parameters.

What are S-Parameters? S-Parameters – or scattering parameters – describe how derivatives of a wave arriving at a circuit network port are scattered to all of the ports, including the one at which the wave arrived. Each S-Parameter names the port to which the wave is scattered first, followed by the port from which it has been scattered: S21, therefore, is the S-Parameter for the wave scattered to Port 2 from Port 1, representing the transformation in terms of both magnitude and phase.

Imagine that you wanted to describe the behaviour of a lens (see figure 1). This is useful, because just as in high speed circuits, we are concerned with transmission and reflection and a lens is easier to visualise. You could analyse the physical properties in detail to predict the transmission and reflection of light at various frequencies. But that's a complex task. An alternative approach would be to treat the lens as a 'black box' and measure its behaviour at various frequencies.

Let a1 and a2 be the incident waves on the left hand (Port 1) and right hand (Port 2) sides of the lens respectively.

At each frequency, we need to know: • The amplitude and phase shift of light transmitted from Port 1 to Port 2. Let S21 represent this transformation, so the output at Port 2, given input a1 at Port 1, is S21a1. • The amplitude and phase of light reflected from Port 1 for input a1. Let S11 represent this transformation, so the reflection at Port 1 is S11a1. • The light transmitted from port 2 to port 1 (S12a2). • The light reflected from port 2 (S22a2). At Port 1 and Port 2, the final results (b1 and b2 respectively) are the sum of the transmitted and reflected waves.

The items in the matrices, which include magnitude and phase, can be expressed either as complex numbers or as magnitude and phase angle.
Like visible light, digital electronic signals contain a range of frequencies at various amplitudes and phase angles.

If we know S11, S12, S21 and S22 for a range of frequencies within the limits of operation, we can simulate a circuit such as a filter without needing to know the internal structure and without making assumptions that might affect accuracy.

S21 is the forward voltage transmission coefficient; if you multiply the incident ac voltage at Port 1 by S21, you get the voltage transmitted to Port 2. Meanwhile, S11 is the input voltage reflection coefficient; if you multiply the incident ac voltage at Port 1 by S11, you get the voltage reflected from Port 1.

Measuring S-Parameters S-Parameters represent the transmission and reflection of waves at a specific frequency, when the network is embedded within long transmission lines with a specific load. These models are adapted automatically for use with different loads and state the load at which the parameters were measured. S21 and S11 can be measured by embedding the component to be modelled within a test circuit, where the load impedance matches characteristic transmission line impedance. In this way, there is no reflection from the far end and no input signal a2 at Port 2. To find S12 and S22, the connections are reversed.

Two requirements commonly apply to S-Parameter models used in high-speed pcb design: Passivity: the model must not generate more energy that is supplied to it. A passive filter or a connector cannot exhibit gain.

Causality: determination of causality is more complex but, basically, the response of the model must depend only on its current and previous inputs. This will always be the case with a correctly constructed passive filter or connector model.

Simulation Most simulation of high speed digital circuits is performed by time domain simulators that work in conjunction with design capture and physical layout. S-Parameter models describe the response at a range of frequencies, rather than in the time domain, so they are first transformed into compatible macro models by importing them into the simulation library via IdEM.
A typical application is simulation of a USB port including a common mode filter.

A common mode filter is somteimes employed in high-speed differential buses such as USB to reduce off-board conducted emi. Differential signals comprise two complementary parts that, ideally, are always exactly opposite in phase.

Signals that are in-phase, therefore can be assumed to be unwanted noise. It is essential to simulate the complete circuit to make sure signal integrity is maintained after the physical printed circuit board connections are routed, since it is all too easy to accidentally break electrical symmetry at high frequencies.

Since differential pcb traces are usually routed nearby and in parallel, in-phase noise is often picked up on both sides of the differential pair. A common mode filter is used to suppress this noise, while allowing the differential signal to pass.

Summary With each large increment in bit rate comes a new set of high speed issues, so simulation techniques previously only required for rf and microwave applications have to be incorporated into mainstream pcb design flows.

S-Parameters allow accurate modelling of component behaviour without revealing the internal structure and can be derived by measurement alone. The ability to simulate S-Parameter models enhances the accuracy of eda software for high speed digital pcb design.

The requirements of fast turnaround and use by non specialists means designers must employ a combination of known good templates, embedded constraint management and simulation to achieve right first time results.

21089\S_Parameters.pdf

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