{"id":889,"date":"2010-11-01T12:31:14","date_gmt":"2010-11-01T12:31:14","guid":{"rendered":"http:\/\/zukenblog.wpengine.com\/?p=889"},"modified":"2025-02-21T10:48:07","modified_gmt":"2025-02-21T10:48:07","slug":"s-parameters-microwave-goes-mainstream-for-high-speed-pcb-design-part-1","status":"publish","type":"post","link":"https:\/\/www.zuken.com\/en\/blog\/s-parameters-microwave-goes-mainstream-for-high-speed-pcb-design-part-1\/","title":{"rendered":"S-Parameters: Microwave goes Mainstream for High-Speed PCB Design Part 1"},"content":{"rendered":"

I\u2019m going to be talking about S-Parameters, but before I dive into the details let me gently introduce you and put it all in a bit of context.<\/p>\n

So here goes. Mainstream high-speed PCB design has generally followed in the slipstream of RF and microwave engineering. This is often out of necessity, as techniques have been simplified and made applicable to wider use. For example IBIS<\/a> models that describe input\/output behaviour without revealing internal design details are published for most high-speed integrated circuits.<\/p>\n

And we all know double data rate memory has become the de facto<\/em> standard for PC-based designs. This has turned the design of every board that uses it into a high-speed electronic engineering exercise – often involving system-level and multi-board interconnect.<\/p>\n

For high-speed differential channels, such as USB, signal-enhancing components such as common-mode filters are often involved. At today\u2019s 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 frequencies into the multi-Gigahertz range.<\/p>\n

Luckily, such a technique is ready and waiting: S-Parameters.<\/p>\n

I\u2019d like to explain to you in straightforward terms what S-Parameters are and why they\u2019re so useful. When I say \u201cstraightforward\u201d, \u00a0I mean that in a technical sense, but this is a specialised area. If you\u2019re not designing high-speed PCBs, or you don\u2019t know much about signal integrity, you might want to tune out now.<\/p>\n

For the purpose of simplicity, I\u2019ll limit all the discussion to two-port networks.<\/p>\n

What S-Parameters Represent<\/h2>\n

Let\u2019s start with a definition.<\/p>\n

S-Parameters are Scattering Parameters: <\/em> they describe how derivatives of a wave arriving at a circuit network port are scattered<\/em> 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. S<\/em>21<\/sub>, therefore, is the S-Parameter for the wave scattered to<\/em> Port 2 from<\/em> Port 1, representing the transformation in terms of both magnitude and phase.<\/p>\n

Let me show you an example to illustrate what I mean. S-Parameters are used in high-frequency electronics circuits, but first imagine that you wanted to describe the behaviour of a lens as shown in Figure 1.\u00a0 This is useful because in the lens, as in high-speed circuits, we are concerned with both transmission and reflection, and the lens is easier to visualise.<\/p>\n

Figure 1: Lens Analogy<\/p>\n

At high frequencies, the behaviour of a lens is analogous to that of a high-speed circuit such as a filter<\/p>\n

You could analyse the physical properties in detail to predict the transmission and reflection of light at various frequencies. But this a complex task, and if you failed to take account of more subtle effects, your result might not be accurate.<\/p>\n

An alternative approach would be to treat the lens as a black box, and merely measure its behaviour at various frequencies.<\/p>\n

Let a<\/em>1<\/sub> and a<\/em>2<\/sub> be the incident waves on the left-hand (Port 1) and right-hand (Port 2) sides of the lens respectively.<\/p>\n

At each individual frequency, we need to know:<\/p>\n

    \n
  1. The amplitude and phase shift of light transmitted from<\/em> Port 1 to<\/em> Port 2.\u00a0 Let S<\/em>21<\/sub> represent this transformation, so that the output at Port 2 given input a1 at Port 1 is S<\/em>21<\/sub>a<\/em>1<\/sub>.<\/li>\n
  2. The amplitude and phase of light reflected from Port 1 for input a<\/em>1<\/sub>.\u00a0 Let S11 <\/sub><\/em>represent this transformation, so that the reflection at Port 1 is S11<\/sub>a1<\/sub><\/em>.<\/li>\n
  3. The same information as in 1), but for light transmitted from<\/em> port 2 to<\/em> port 1 (S<\/em>12<\/sub>a<\/em>2<\/sub>).<\/li>\n
  4. The same information as in 2), but for light reflected from<\/em> port 2 (S22<\/sub>a2<\/sub><\/em>).<\/li>\n<\/ol>\n

    OK, time for a short video clip. This is a two-port network \u2013 it could be a connector or a filter \u2013 and this is what happens to a sine wave at just one frequency, described as S-Parameters. An S-Parameter model contains a set of parameters for a large number of frequencies that cover the frequency content of a fast digital signal.<\/p>\n

    <\/div>\n
    <\/div>\n

    At Port 1 and Port 2, the final results (b1 and b2 respectively) are the sum of the transmitted and reflected waves, so that, expressed in matrix form:<\/p>\n

    The items in the matrices include magnitude and phase, and can be expressed either as complex numbers or as magnitude and phase angle.<\/p>\n

    Like visible light, digital electronic signals contain a range of frequencies at various amplitudes and phase angles.\u00a0 If we know S<\/em>11<\/sub>, S<\/em>12<\/sub>, S<\/em>21<\/sub> and S<\/em>22<\/sub> for a range of frequencies within the limits of operation, we have the means to simulate a circuit such as a filter without the need to know the internal structure, and making no assumptions that might affect simulation accuracy.<\/p>\n

    S<\/em>21 <\/sub>is the forward voltage transmission coefficient<\/em>, because if you multiply the incident AC voltage at Port 1 by S<\/em>21<\/sub>, you get the voltage transmitted to Port 2.<\/p>\n

    S<\/em>11<\/sub> is the input voltage reflection coefficient<\/em>, because if you multiply the incident AC voltage at Port 1 by S<\/em>11,<\/sub> you get the voltage reflected from Port 1.<\/p>\n