Convert oscilloscope acquisition to de-embed, embed and simulate channel effects - S-parameter series

Introduction to Signal Acquisition and Theory

Accurately and reliably analyzing signal data from today's high-speed digital systems begins with a thorough understanding of data acquisition and analysis theory. With knowledge of theory and tools, designers can accurately and efficiently model device behavior. This knowledge enables engineers to develop the best design the first time, maximize efficiency, and optimize their value proposition.

This is the first of six articles that will guide high-speed digital system designers and verification engineers through detailed channel element measurements and modeling to manipulate oscilloscope acquisitions to find the signals that engineers want to see and measure. Additional processing is required if the real signal (for various reasons) cannot be probed or is probed in a different location than expected, or if the measurement element itself (such as the probe) affects the measurement result and needs to be removed from the reported measurement result.

About a decade ago, the electronics industry abandoned traditional parallel bus interfaces and began adopting serial topologies. At first glance, this may seem a little strange. Because to get the same effective throughput, the bus clock rate had to be multiplied by at least a factor of 8, and it also meant that digital designers needed to become experts in new building blocks, such as phase-locked loop technology; which was traditionally the domain of analog designers. The problem was that integrated circuits were limited by inputs and outputs; it was not a matter of internal functionality, but getting the signals in and out of the device. In addition, low-grade printed circuit boards made of FR-4 had become an expensive commodity in the sense that low-cost materials had to be used to maintain profit margins, and using an eight-bit parallel bus was a waste of routing volume. The move away from this technology was a move toward higher data rates and microwave principles used in design. We now call this field of engineering signal integrity.

Signal integrity practitioners solve the problem of countless problems when digital data is transmitted from a digital transmitter through a channel to a receiver. At rates of several gigabits per second (Gbs), any factor in the transmission path will affect the signal to some extent. Developers and designers must understand what the most important factors are and how to model and measure them. Only after understanding these factors can they use simulators or other measurement equipment to help understand and optimize system performance. The purpose of engineers in signal integrity research is related to the simulation of measurement results.

Engineers working in the high-speed digital field do not need to be signal integrity experts, but they must understand signal integrity issues. For example, verification and design engineers need to understand how to solve the problem of remotely specified signal characteristics, but they do not need to worry about the loss factor of FR-4 due to humidity. They also want to use measurement or simulation models to run certain system scenarios to see the impact of changing the characteristics of one element or changing multiple elements at the same time. These elements may be printed circuit board transmission lines, vias on the board, connectors, resistors, inductors, capacitors, or even the probes themselves. Sometimes, one of these elements may be another design whose only purpose is to be able to measure the transmitted signal at certain points. These are called "fixtures", and although they may have excellent qualities, they also have an impact on the measurement and sometimes must be considered.

When evaluating these systems, an oscilloscope is ultimately used to view the signal. Even if the signal location is difficult to access or is affected by system elements during acquisition, or is driven by added elements, the system can be modeled and an accurate simulation of the actual signal can be derived. Keysight has developed a range of tools that can be used to effectively measure these elements, derive models from simulations, more accurately filter measured data, and ultimately accurately characterize the signal of interest.

The Era of Hardware-Based Co-Simulation Has Arrived

Not all oscilloscope de-embedding applications generate the relevant transfer function from a complex circuit model. Some applications simply extract the S21 component from the S-parameter file and use it directly as the transfer function for the embedding application, or use its inverse as the transfer function for the de-embedding application.

Whether you use an oscilloscope probe or a test fixture to make measurements, the verification task inevitably becomes a co-simulation process. Co-simulation, the combination of simulation and measurement, can show problems that measurement alone cannot. It can show what the measured signal would look like if it were not affected by extraneous circuits that were not present when the physical measurement was made. It can also show the other side of the story - what the measured signal would look like if it were not affected by extraneous circuits (parasitics) that were present in the physical measurement path. It can even show what it would look like if it were at a different physical location than the actual measurement.

Co-simulation has been used for decades to extract measured waveforms from oscilloscopes and import them into EDA simulation tools. While it has been extremely impactful, it has also been tedious and time consuming. Modern high-performance oscilloscopes now have the ability to co-simulate real-time measured waveforms directly on the oscilloscope. These co-simulations simply transform the measured waveform. A linear filter, possibly with gain, is used to render different views of the measured waveform—that is, convert the oscilloscope's measured waveform to a filtered waveform that renders what the signal simulation would look like if the measured circuit was changed. If the circuit under test is to be changed by removing components, this process is often called de-embedding. If it is changed by adding components, it is called embedding. In any case, the key to performing these measured-to-simulated signal views is to create a voltage transfer function to transform the physical measurement results into the target measurement results. This is the first step to ultimately understand the measured results.

Transfer function derivation

Deriving the filter transfer function requires defining two circuits. The first circuit accurately reflects the existing measurement conditions on the bench, including the oscilloscope observation point (the oscilloscope's front panel input connector or probe). The second circuit reflects the target measurement conditions. For example, suppose there is a cable between the power supply device under test (DUT) and the oscilloscope. The goal is to remove the effects of the cable (de-embed). In this case, the measurement circuit will behave as if there is a cable between the power supply and the oscilloscope channel input.

Figure 1. Measurement and simulation circuit model for observing waveforms without cables.

As shown in Figure 1, the simulated circuit is identical to the measured circuit, except that the cables are removed (i.e., the simulated oscilloscope is connected directly to the source). By assuming that both circuits are linear and time-invariant, the simulation can be performed using basic nodal analysis. Analysis of the circuits will generate two transfer functions (in the frequency domain) from the common source to the observation nodes of each circuit. Assumptions:

The ratio of these transfer functions produces the desired correction transfer function H(f), which can be used to transform or convert the measured waveform into a simulated waveform.

It will produce filtered, simulated or expected results.

Transfer function derivation

Figure 2. Transfer functions Hm, Hs, and H for the cable de-embedding example.

Since the oscilloscope operates natively in the time domain, it applies the transfer function to the measured waveform, Vmeas (t), by convolving the impulse response h(t). This becomes the inverse of the Fourier transform of the frequency domain transfer function, H(f), which is:

The oscilloscope uses a finite impulse response (FIR) digital filter to perform the convolution, which can be implemented using digital signal processing (DSP) hardware (such as the Keysight Infiniium oscilloscope) or software. Both methods are accurate and effective, and the obvious advantage of the hardware implementation is speed—faster processing and updating the display. Figure 3 shows the impulse response h(t) and the filter that can be used to measure the signal, Vmeas (t).

Figure 3. Example of the pulse response of the correction filter (blue) and de-embed transfer function (red) for a lossy cable.

Figure 4 compares the frequency response of the correction filter to the de-embedded transfer function applied to the measured waveform. In this case, the target transfer function is a bandwidth-limited version of the calculation in Figure 2. The waveform in Figure 5 represents the effect of applying the correction transfer function in Figure 3 to the measured waveform.

Figure 4. The frequency response of the correction filter (blue) compared to the frequency response of the target de-embedding transfer function of the lossy cable.

Figure 5. Example of waveforms Vmeas and Vsim for a lossy cable

Creating a Transfer Function

Circuit Modeling

Calculating the transfer function requires a complete and accurate description of the measured and simulated circuits. The circuits shown above are a good example. These circuits are described using Y-parameter model elements. Y-parameter models are a type of N-port network model that describes the port current as a function of the port voltage. They are very convenient for performing nodal circuit analysis. However, any N-port network model can be used to describe these circuits, as all N-port model types (Z, Y, S, H, etc.) can be converted to other N-port model types.