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s-parameters (also called s-matrix or scattering parameters) represent the linear characteristics of rf electronic circuits and components. from the s-parameter matrix, you can calculate characteristics of linear networks such as gain, loss, impedance, phase group delay, and voltage standing wave ratio (vswr).

s-parameters can be easily imported, visualized, and analyzed in matlab^® using rf toolbox™.

the s-parameter matrix describes networks with an arbitrary number of ports. it provides a relationship between the incident wave and the reflected and transmitted waves at each port over a range of frequencies. for example, for a two-port device, a four-element matrix of s-parameter data represents the bidirectional behavior of the network as a function of frequency as shown in figure 1:

• s₁₁ = input port reflection
• s₁₂ = reverse gain
• s₂₁ = forward gain (linear gain/insertion loss)
• s₂₂ = output port reflection

in this example, s₁₁ is defined as the ratio of the reflected wave to the incident wave at port-1 while port-2 is terminated on the characteristic impedance. the value of s₁₁ provides a direct measure of the port matching condition, that is, s₁₁= 1 represents an open circuit; s₁₁= -1 represents a short circuit; and s₁₁= 0 represents a perfectly matched circuit.

benefits of using s-parameters

easier to measure than y or z matrices: the measurement of y or z parameters requires open- and short-circuit terminations that are challenging to maintain at rf and microwave frequencies, therefore their measurement is less reliable than s-parameters.

flexible: for circuit analysis or simulation, s-parameters can be easily converted to z-parameters, y-parameters, and other linear matrices.

portable: s-parameters are often stored in a standard file format called touchstone^®. most rf analysis tools and simulators can read and , thus making them a portable file format to exchange measurements and design information.

measuring and visualizing s-parameters with matlab

s-parameters are measured using vector network analyzers (vnas) over different operating conditions. as a result, rf test engineers must often process a large amount of s-parameter data. typical tasks include de-embedding, cascading, and visualizing s-parameters.

rf toolbox and instrument control toolbox™ allow you to combine s-parameter measurements and data analysis. automated workflows enable scale-up testing, validating scenarios, extracting statistical information on device performance, and easily sharing results with customers and colleagues.

s-parameter data can also be analytically calculated for a given component prior to its realization via behavioral models, circuit analysis, and electromagnetic simulation, as offered, for example, by antenna toolbox™ and rf pcb toolbox™.

visualization is the first step for inspecting s-parameter data. the elements of the s-parameter matrix are complex and can be visualized on a  in terms of magnitude and phase or on a polar plot. the  is a special polar plot format often used for the design of matching networks and for stability analysis.

fitting s-parameters with matlab

fitting s-parameters—and general frequency-domain data—with rational functions such as laplace transfer functions is often used for circuit analysis and for extracting equivalent pole-zero representations.

for example, using rational functions enables time-domain simulation of s-parameters to estimate step and impulse responses. the use of laplace transfer functions in place of s-parameters also aids in enforcing causality and creating reduced order models.

using the function , you can fit s-parameters and general frequency-domain data with an equivalent laplace transfer function, which can then be used for circuit analysis and time-domain simulation. this is particularly convenient for extracting equivalent circuit representations of rf components (28:54), the analysis of signal integrity problems, and the design of serdes equalizers.

using s-parameters for signal integrity analysis with matlab

s-parameter data can be used in signal integrity toolbox™ to describe n-port channels in high-speed digital interconnects to characterize the effects of impedance mismatches, reflections, losses, dispersion, and crosstalk.

signal integrity engineers use s-parameters to model the channel, including pcb traces and vias, connectors, and packages. typical tasks include changing the port order, converting single-ended data to mixed-mode s-parameters, and checking passivity.

the analysis and simulation of s-parameters is required for the design of high-speed digital interconnects to identify issues and develop equalization algorithms in serdes toolbox™.

using s-parameters for rf budget analysis and system design in matlab and simulink

system design of rf transmitters and receivers begins with a of gain, power, noise, and nonlinearity. in the early stages of the design, system engineers use s-parameter data to anticipate the frequency dependent behavior of selected components and to predict the impact of impedance mismatches.

as the wireless system design is elaborated, rf transceiver models and s-parameter data are simulated in rf blockset™ together with baseband algorithms to estimate the system performance in terms of bit error rate (ber), adjacent channel leakage ratio (aclr), or error vector magnitude (evm).

using s-parameters for matching network design in matlab

s-parameter data is used for to improve the rf system performance. often the design of matching networks is combined with an optimization routine to determine the best possible trade-off between different requirements.

with rf toolbox, you can design matching networks for antennas and minimize mismatch losses. similarly, you can use s-parameter data to design input and output matching networks of low noise amplifiers (lna) and improve the tradeoff between maximizing gain and minimizing the noise figure using optimization toolbox™.

matching networks can be implemented using lumped components, such as rlc, or planar distributed elements, like microstrips, stubs, and tapers designed on pcbs.