Reading S-parameters: Sharp Dips

Figure 1. A resonant cavity composed of two interior layers
on a four-layer printed circuit board.  The return current from
the signal path couples into the plane cavity and excites its
resonance modes.

The last pattern we'll cover in this series on reading S-parameters is sharp dips. These dips result from coupling to high-Q resonant structures and represent very narrowband absorption in S21 or S11.

Where do you see resonant coupling? Resonant structures can include coupling to an interconnect that is floating and not terminated. The structure does not have to be a uniform transmission line, it can also be a cavity made up of two or more adjacent plates as shown in Figure 1. Commonly, when a signal goes through a cavity and we hit the resonances of the cavity, it absorbs energy and results in narrow dips in the S-parameters.

Reading S-parameters: Broad Dips

Figure 1. Quarter wave stubs exhibit resonance which
impacts S21 as broad dips.  The resonant frequency
can be computed based on the characteristics
of the transmission lines and its length.

Besides ripples and monotonic drop offs, the third pattern commonly seen in plots of S-parameters are broad dips due to stub resonances. Figure 1 shows an interconnect which includes a stub.  The interconnect is composed of 50 ohm uniform transmission lines which incorporate a branch point with an open at the end. 

Not surprisingly, the open stub is a discontinuity. What's going to happen? At the open, it's going to reflect and head back. At the junction, it's going to branch. Some of it's going to go back toward the source and some of it's going to go forward toward the receiver.

Reading S-parameters: Monotonic Drop Offs

Figure 1. As a signal propagates, the amplitude drops off
exponentially with distance due to signal losses.

Last week, we showed how ripple in S-parameters relates to the length of the interconnect. The second common pattern we see when reading plots of S-parameters is the monotonic drop off in the amplitude of the transmission coefficient (S21), commonly referred to as the insertion loss. If we apply a sine wave and look at its amplitude as it moves through that interconnect, we see that it drops off exponentially as shown in Figure 1.

V_Out is shown as V_In times a decaying exponential. (Note that attenuation is usually described using base 10 rather than base e).

Reading S-parameters: Ripples

Figure 1. Ripple patterns commonly seen in S11 and S21.

When we look at plots of S-parameters, we can observe four classic patterns that affect the S11 reflection coefficient (aka. return loss) and the S21 transmission coefficient (aka. insertion loss): ripples, monotonic drop offs, broad dips and sharp dips. In this post, we’ll look into how the characteristics of the interconnect affect the ripple pattern, which will help you better understand your own measurements. 

The ripples in S11 and sometimes in S21 in Figure 1 are due to reflections in the interconnect caused by impedance discontinuities. This phenomenon has been investigated in an earlier post, What S-parameters Reveal About Interconnects (Part III)

Six Ways Not to be Confused by S-parameters (Part II)

In Part I, we discussed three causes of confusion when working with S-parameters and what you can do to avoid them.  In this post, we’ll discuss three more ways not to be confused by S-parameters.

4. Know the difference between return loss and reflection coefficient

Figure 1. A 2-port device has two distinctly interesting
S-parameters, S11 and S21.  S11 is the reflection
coefficient of Port 1 (also called return loss), and
S21 is the transmission coefficient of Port 2
(also called insertion loss).

Let’s start by looking at a 2-port device illustrated in Figure 1.

There are two S-parameters of interest in a 2-port device.  The first is the reflection coefficient, S11, that measures the ratio of the reflection from Port 1 to the drive signal at that port.  The second is the transmission coefficient, S21, that is the ratio of the output of Port 2 to the drive signal into Port 1.  Confusion arises because historical measurements of return loss and insertion loss are often used interchangeably with reflection coefficient and transmission coefficient, respectively.

Six Ways Not to be Confused by S-parameters (Part I)

S-parameters describe the electrical properties of electronic interconnects, which can include connectors, printed circuit traces and vias, cables, and oscilloscope probes. Given that instruments such as Teledyne LeCroy’s WavePulser 40iX make measuring S-parameters relatively simple, there are still some aspects of S-parameters that can cause confusion, especially to new users. Here are six things you can do to avoid confusion when working with S-parameters.

1. Know where the fixture ends and the DUT begins

Figure 1. Characterizing a  microstrip line requires
two connectors, one at each end of the line. 
These connectors add their own characteristics to
the measurement. A TDR measurement can
determine the boundary between the connectors
and the microstrip PC line. 

Measuring S-parameters involves connecting a test instrument to the Device Under Test (DUT), placing the DUT in series with a number of other interconnect elements, as in Figure 1. The DUT is not isolated, and confusion can arise as to where you want the cables and fixtures to end and where the DUT begins. Do you want the DUT to include just the cable of the DUT? What about the connectors on its ends? What about the matching fixture or lead in in the circuit board?

Serial-Data Channel Emulation and S Parameters

Figure 1: Higher data rates + "same old" channel media
= degraded signal quality at receiver

Serial data rates have risen but propagation media for the channel remain unchanged, and that results in greater attenuation to the frequencies of interest. We could ignore these losses at lower frequencies, but now that rise times are so much faster, that's not an option. Channel effects now intrude into design margins to the point where eyes deteriorate and bit-error rates become unacceptable.

How Much Transmission-Line Loss is Too Much?

Figure 1: This plot represents the differential insertion-loss
profile for a 20" FR-4 microstrip trace

One of the fundamental facts of transmission lines is losses. Any effort to debug the performance of a high-speed serial data link begins there. But it begs an equally fundamental question: How much loss in a transmission line is too much? How do we quantify losses, and what is the connection between attenuation at the Nyquist frequency and the eye diagram? Is there a rule of thumb one might apply, some sort of rough estimate of how much loss might be too much for your channel to bear at a given data rate?

What S-parameters Reveal About Interconnects (Part III)

Figure 1: How ripple is introduced into S11 and S21

S-parameters are a great tool for understanding exactly what happens to a signal as it traverses an interconnect such as a transmission line. How much of it propagates through, and how much reflects off of impedance mismatches? From plotting return loss against insertion loss, we've weighed how much return loss may be tolerable before it significantly impacts insertion loss. Now we'll turn our attention to some common patterns exhibited by S11 and S21 and what they mean to the performance of an interconnect.

What S-parameters Reveal About Interconnects (Part II)

Figure 1: Measuring S-parameters
of a two-port interconnect

Having previously covered some of the fundamentals of S-parameters, it's now time to dig a little deeper into what they can show us about an interconnect; say, for example, a two-port microstrip line on a PC board. Unlike the one-port DUT in our earlier post, this configuration gives us the opportunity to look at not only S11 (return loss or reflected signal), but also S21 (insertion loss or transmitted signal).