The t parameters are related to the s parameters as follows. Sparameter techniques hp application note 951 hp memory. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. At high rf and microwave frequencies direct measurement of y, z, or h parameters is difficult due to. You can describe any network in terms of either, and if you have one set of parameters, you can derive another. Scattering parameters or sparameters describe the electrical behavior of linear electrical. For 50ohm s parameters, and with the twoport element terminated with 50 ohms at each port, the s 21 parameter represents the voltage gain of the element from port 1 to port 2. Hybrid parameters also known as h parameters are known as hybrid parameters as they use z parameters, y parameters, voltage ratio, and current ratios to represent the relationship between voltage and current in a two port network h parameters are useful in describing the inputoutput characteristics of circuits where it is hard to measure z or y parameters such as a transistor. Another parameter which may be required in the future would be nameddestdestination. Pdf this paper provides tables which contain the conversion between the various common twoport parameters, z, y, h, abcd, s, and t. Part ii to appear in the next issue of in compliance magazine explains the s parameters use in emc measurements and testing the background needed for the study of s parameters consists of two fundamental topics.
Suppose one has a network of which s21 0, one faces a similar problem. Networks which include nonreciprocal materials in the transmission medium such as those containing magnetically. For microwave integrated circuits mics planar transmission lines such as the microstrip line have. The matrix elements s11,s12,s21,s22 are referred to as the scattering parameters or the sparameters. Define the reference plane as the point where the transmission line terminates onto the n port. In their most basic sense, s parameters refer to the ratio of voltage out versus voltage in. Conversion from sparameters to other parameter sets is a matter of routine algebra. The measurement is direct and only involves measurement of relative quantities such as the swr or the location of the. This report develops the scattering parameter concept and defines the s parameters of a generalized linear two port network.
Here, for example, is s 11 in terms of the z parameters. There s certain devices that can t be represented in. Conversions between s, z, y, h, abcd, and t parameters. Abcd parameters can be used to describe the behavior of a linear network, just as s parameters can. When two or more twoport networks are connected, the twoport parameters of the combined network can be found by performing matrix algebra on the matrices of parameters for the component twoports. This white paper will create a strong foundation of test and measurement science related to sparameter measurements and analysis. This is an example of why we need different two port representations s parameters, y parameters, z parameters, h parameters. Note that s parameters are not independent of z parameters. Most microwave engineers are very familiar with s parameters, we. Sparameters are important in microwave design because they. For microwave integrated circuits mics planar transmission lines such as the microstrip line have become very important.
For a more detailed defi nition, please refer to the textbooks 1 to 5. The s parameters are converted to mixedmode, and the. Following a demonstration of the strategy used to convert s parameters to conventional two port parameters, it addresses the utility of s parameters. When measuring the sparameter of an nport, all n ports must be terminated. For example, the abcd and t matrices are adept at cascaded networks. However, s parameters are easily converted to t parameters, see main article for details. For each possible selection of p, there is exactly one x f term.
The notation, s c z, indicates the conversion from s parameters to 2 parameters and z parameters to s parameters. More accurate network design, application note an 951, keysight technologies, pdf slides plus quicktime. When opening a pdf document from a command shell, you can pass the parameters to the open command using the a switch with the following syntax. When z11z22, the twoport circuit is said to be symmetrical. Derivation of a 4port directional coupler duration. Numerical data that represents inputoutput characteristics. To develop models of transmission lines, we first need to determine the tl parameters.
Part i discusses the fundamental background needed to understand the concept of s parameters. S parameters are defined with respect to a reference impedance that is typically 50 ohms. A transmission line is an example of a symmetrical 2port network. When z12z21, the twoport circuit is called a reciprocal circuit. Useful matrix operations certain simple matrix operations are useful in manipulating and evaluating sparameter matrices. For high frequencies, it is convenient to describe a given network in terms of wavesrather than voltages or currents. Click response, then measure, then device parameters, then xf parameter. So, in this case, t parameters are the desired parameters and y parameters are the given parameters. The 2port network shown to the left is representative of that implied in the application of these equations. Scattering parameters rf and microwave circuits university of. Simple model precise model dc superimposition model.
Sparameter measurements basics for high speed digital engineers frequency dependent effects are becoming more prominent with the increasing data rates of digital systems. So, just by doing the inverse of y parameters matrix, we will get the z parameters matrix. S scattering, and t chain scattering or chain transfer. To convert from s parameters to t parameters the following formulas apply. S parameters depend upon the network and the characteristic impedances of the source and load used to measure it, and the frequency measured at. Forward s parameters can be measured by driving the input and terminating the output. So in total there are x parameters for each possible. The parameters marked with an asterisk are the minimum set required for a complete low. It is the component of the output due to the large signal input a11, so is indexed only to the receive port tone x f p. Z parameters are not unique to lowfrequency circuits, and s parameters are not unique to microwave networks. Pdf the concept of describing rf circuits in terms of waves is discussed and the smatrix and related matrices are defined.
X parameters are the mathematically correct superset of s parameters, applicable to both largesignal and smallsignal conditions, for linear and nonlinear components. The t parameter matrix can then be converted back to the desired s parameter matrix using the equations in appendix a. How to convert s parameter of package to rlgc model in ads duration. Since s and t parameters are defined in terms of a s and b s, they will contain the source and load normalizing imped ances zol and 202. The s parameters can be measured by embedding the twoport network the deviceundertest, or, dut in a transmission line whose ends are connected to a network analyzer. The measurement is direct and only involves measurement of relative quantities such as the swr or the. Differential circuit topology is commonlyused as an implementation method, with the goal of enhancing the data carrying capable of the physical layer. Conversions between s, z, y, h, abcd, and t parameters which are. The t s parameters are technical specifications of subwoofers that are often used in box building by the more advanced user. Figure 3 shows examples of typical forward s parameter plots. Each part of the puzzle has been created the pieces now fit together seamlessly. Unlike s parameters, a t parameter file has no agreed format for the storage of noise figure data. Simple equivalent circuit that models only the inductance, the resistance at dc, and the self. S zl t parameters will result in ill conditioned t matrix.
To convert from t parameters to s parameters the following formulas apply. We can adapt these singleended s parameters to describe differential networks to report differential and common modes of operation which are commonly known as mixedmode s parameters ref1, ref2. However, unlike s parameters, there is no simple physical means to measure the t parameters in a system, sometimes referred to as youla waves. The complex measurement can be displayed as a real value by specifying the magnitude, angle, real or imaginary component in. For the s parameter subscripts ij, j is the port that is excited the input port, and i is the output port. Eee 194 rf sparameter matrices 5 we find that it is simply s. The scattering transfer parameters or t parameters of a 2port network are expressed by the t parameter matrix and are closely related to the corresponding s parameter matrix. A11 the s parameter is a ratio, so it is basically a nondimensional parameter. S parameters sddij in the upper left quadrant of the s parameter matrix, commontocommon sccij in the lower right quadrant, and mode conversion parameters sdcij and scdij in the upperright and lowerleft quadrants, respectively. Understanding what these parameters mean can help you choose the best subwoofer for your current enclosure, or they can help you build a.
S 11 is the input reflection coefficient with the output port terminated by a matched load. Following a demonstration of the strategy used to convert s parameters to conventional two port parameters, it addresses the utility of s parameters in the analysis of active networks. When these s parameters are aligned in a matrix form a11, it is referred to as an s matrix scattering matrix. The parameters s11, s22 have the meaning of reflection coefficients, and s21, s12, the meaning of transmission coefficients. The sparameter scattering parameter expresses device characteristics using the. S parameters come in a matrix, with the number of rows and columns equal to the number of ports. It s important to realize that although we associate s parameters with high. Sparameters are a useful method for representing a circuit as a black box. Ts thielesmall parameters sonic electronix learning. The following paragraphs will describe the conversion of singleended s parameters to mixedmode s parameters and uses a 3port network as an example. Sparameter that is incident at port jdetected at port i is described as sij.