Portions of this DDR memory stick can be modeled as a multiport network by de-embedding S parameters
S parameters, Z-parameters, T-parameters, and plenty of other parameters are the primary ways to examine how high speed signals and high frequency waves interact with a receiver in an interconnect, particularly when the signal passes through some other network or connector on the way to a load component. Whether you are measuring a device under test or you are simulating the behavior of cascaded networks in an interconnect, you’ll need to determine accurate S parameters for each component in the network, either from simulations or measurements.
Interconnect designs, multiport networks, and individual devices will need to be subjected to measurements or simulations at some point, and the effects of impedance mismatch need to be considered in many devices to ensure signal integrity. De-embedding S parameters from circuit designs and devices under test allows you to drill down to the behavior of signals in your board in a specific circuit or component.
De-Embedding S parameters
If you’re examining a device under test that is equivalent to a 2-port network, the primary goal is to gather accurate measurements that show how signals interact with the input and output of a device. The S parameters nicely summarize how a device reflects and transmits input signals at each input port. If you’re measuring or simulating the effect of a device’s input impedance during circuit design, such as in load-pull analysis, you’ll need to know the S parameters of the device at various frequencies. The S parameters at each frequency can then be used to calculate the input and output impedances on each side of the network as functions of frequencies.
De-embedding S parameters refers to removing the effects of a test fixture, filter, or amplifier when gathering measurements for a device under test. In a test situation, you would measure the reflection and transmission from a device under test using a vector network analyzer. As part of this process, you need to measure the reflection and transmission coefficients from the device’s test fixture.
Subcircuit S parameters
The same ideas apply to subcircuits within a larger circuit as part of a simulation. If you are designing a particular subcircuit as part of a larger system, de-embedding S parameters for other subcircuits allows you to accurately and quickly examine how a particular subcircuit performs within a larger system and determine its own S parameters.
Relationship between S parameters, input signals, and output signals
You can then convert the simulated reflection and transmission coefficient at each frequency to S parameters using the standard formulas relating to the incident and reflected voltage. The S parameters for the particular subcircuit can be calculated directly from results in a SPICE-based simulation. Note that the same ideas are used in vector network analyzer frequency sweeps for measuring the S parameters of a device under test; the S parameters of the test fixtures and any filters, amplifiers, or other components need to be eliminated from the measurements.
Relationship to T-parameters
Mathematically, the S parameters can be easily de-embedded by considering the T-parameters (called the scattering transfer parameters) for a set of cascaded networks. The image below shows the relationship between the S parameters and T-parameters for a pair of networks in series.
Using T-parameters for de-embedding S parameters
If you want to determine the T-parameters (and thus the S parameters) for Network B, and you know the T and S parameters for Network A, you can calculate the T and S parameters for Network B using the T and S parameters for the pair of networks in series. You can easily extend this process to a larger number of cascaded networks, as well as networks with more than two ports. Note that T and S parameters are functions of frequency. Once you do extract the S parameters for a particular network, this information is normally stored (again, as a function of frequency) in an S parameter file. It can then be easily used for de-embedding S parameters in a later simulation.
Why Use De-embedding S parameters?
In terms of comparing measurements with simulations, the benefits of de-embedding S parameters is obvious: you can eliminate the S parameters for your fixtures from your measurements and your simulations, allowing you to easily compare simulations and experiments.
Similarly, if you know the S parameters for a particular fixture or component from measurements, you can then use these S parameters in simulations for a system to examine signal integrity. As part of circuit analysis and signal integrity simulations, this can be more complicated as the need for de-embedding S parameters depend on the circuit being designed.
When running large-scale models of a complete layout for signal integrity analysis, models for each subcircuit in a network are usually extracted S parameter files with a large number of ports. If you want to reduce the computation time in time-domain simulation, you can use de-embedding to remove many simpler components from your board-level circuit. This reduces your simulation to a smaller number of cascaded networks, ultimately reducing the simulation time.
You can extract S parameters and de-embed them using the right simulation package
On the other hand, if you are designing a more complicated circuit that can be broken into multiple networks, and you know the specific S parameters you need for the entire circuit, you can eliminate drill down to the S parameters for one network while by de-embedding S parameters for the remaining networks. You can then use parameter optimization with a frequency sweep or a series of time-domain simulations while varying component values to tailor the S parameters for one of your networks to the desired values.
De-embedding S parameters provides plenty of uses that were not covered here, and you can incorporate de-embedding S parameters into your design process with the right PCB design and analysis software. Allegro PCB Designer and Cadence’s full suite of analysis tools make it easy to perform many simulations with your designs and get a comprehensive view of the behavior of your circuits.
If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.