Column Control DTX

S-Parameters and Two-port Measurements

Application Notes

Introduction 

Network analyzers are the fundamental instrument for the characterization of the devices and components used in RF and microwave systems. Network analyzers were briefly introduced in the previous laboratory for their use in impedance matching; they now will be examined in more detail within the context of component measurement. Transfer functions are more naturally expressed in the Laplace or frequency domain, and swept frequency instruments, like network analyzers, can provide a direct measurement of these transfer functions by sweeping a signal source and a tuned receiver across a range of frequencies. Two-port measurements provide an explicit characterization of linear system blocks with a single input and a single output, by far the most common type of element. A two-port network could be as simple as a section of cable, or as complex as a complete transmitter-receiver link. In its simplest format, a reference excitation is applied to one port, and the response from the other port is recorded as a function of the sweep frequency. More complex elements with more than two ports can be characterized by extension, and the measurement techniques extend easily by simple multiplexing of the stimulus and response ports. Scattering parameters, or S-parameters for short, are the working language of network analyzers (NA). They provide a complete description of any linear, time-invariant element which then fully represents the behavior of that element within any system that it may be connected to. Scattering parameters involve phase information, and they are thus complex phasor quantities, and they are also frequency-dependent. Once known, they can be transformed into other network parameters for circuit design, optimization, or tuning.

A quick overview 

An electrical port is a pair of terminals across which a unique voltage and current can be defined, and through which an electrical signal or power can flow. A two-terminal element such as a resistor, capacitor, or inductor is a one-port device. The characteristics of that element define a relationship between the port voltage and the port current, for example, V = IR, or V = L dI/dt. One of these variables say voltage, can be considered as a stimulus to the element, and the other variable, say current, can be considered as the response. The characteristics of the two-terminal element thus describe an electrical stimulus-response relationship.  

A two-port device or network is the simplest electrical element with a unique input and output. A generic two-port network is illustrated in figure 1 below where the port variables of voltage and current are denoted in their more conventional circuit theory manner.

Because of the larger number of variables (now four), a two-port network requires a more elaborate method of characterization, and several matrix approaches exist for organizing this process. One such method is the impedance matrix, or Z-matrix. The Z-matrix representation of a two-port network can be thought of as having the two port currents, I1 and I 2 , be the independent stimuli, and the two port voltages, V1 and V2 , be the responses that arise from those stimuli.

Reversing the roles of the stimuli and responses gives an alternative representation, the admittance matrix, or Y-matrix.

Simple matrix algebra shows that the impedance and admittance matrices are inverses of each other, Y = Z−1. Numerous other representations are possible, each with different choices for the stimuli and responses. The more common ones are the G-, H-, and T- or ABCD-matrices, which are developed in other courses on linear network theory.  

When dealing with high-frequency systems where the propagation of signals is better described by traveling waves, the choice of stimuli and responses needs to be modified. The stimuli are best described by waves that are incident upon the ports, and the responses are best described by waves that are reflected back from those same ports. Figure 2 illustrates the same two-port network as in figure 1, but with the port variables now labeled as an incident (in-going, +) and reflected (out-going, −) voltage waves.

×

Please have a salesperson contact me.

*Indicates required field

Preferred method of communication? *Required Field
Preferred method of communication? Change email?
Preferred method of communication?

By clicking the button, you are providing Keysight with your personal data. See the Keysight Privacy Statement for information on how we use this data.

Thank you.

A sales representative will contact you soon.

Column Control DTX