Impedance transformers are widely used in radio communications applications to match the impedance of different devices and components to the 50- characteristic impedance of a high-frequency system. To evaluate the performance of an impedance transformer, a microwave vector network analyzer (VNA) can be used in such a way that measurement errors are minimized. Calibration procedures will be presented for making measurements on impedance transformers, along with a brief background on scattering (S) parameters used for characterizing transformer performance.

Knowledge of impedance transformer behavior is important to the design of circuits and devices at RF and microwave frequencies as well as at optical wavelengths in modern communications systems. The current work presents a useful measurement procedure for obtaining the transformer’s frequency response and additional information needed to design interstage coupling networks for amplifiers, power dividers and combiners, instrumentation, optical receivers as the interface between a photodiode and the input amplifier circuits, and wideband microwave impedance matching circuits.^1-3

By using a microwave VNA, calibration techniques can be applied to remove the influences of undesired electrical effects, and to minimize the parasitic contributions of a device under test (DUT) during measurements. Measurements will be applied to devices that convert unbalanced-to-unbalanced (unun) and balanced-to-unbalanced (balun) impedance matching circuits. The techniques were validated by laboratory experiments in which different measurements were performed. Good results comparing theoretical and measured values were obtained. The procedure can be used for characterizing a variety of different impedance transformers, and with arbitrary transformation ratios.

A VNA generally has two test terminals for making two-port measurements, with unbalanced reference impedances of 50 . A number of different connectors, including SMA and Type N connectors, are used at RF and microwave frequencies as the interface between a DUT and the test equipment. In addition, VNAs with four and more test ports are available for measurements on more complex assemblies. In a VNA, swept-frequency signals are applied to a DUT and the S-parameters between ports measured and displayed in different formats, including on log magnitude plots and Smith charts. The test capabilities vary somewhat for VNAs from different manufacturers, including Agilent Technologies, Anritsu Company, and Rohde & Schwarz.⁴

Signals at desired frequencies for evaluation are applied to a DUT for swept-frequency measurements, but an analysis can also be performed at a single frequency. Several device characteristics can be evaluated, depending on each design need. Transmission characteristics are quoted, determined by S₂₁ and S₁₂ parameters, passband, insertion loss, phase, and electrical length. There is also interest in the reflection characteristics, as represented by the S₁₁ and S₂₂ parameters, the voltage standing wave ratio (VSWR), and the return loss, among other parameters.

A VNA performs measurements on a DUT such as an impedance transformer by means of an S-parameter matrix (S). These parameters tend to be more accurate at higher frequencies than at lower frequencies, so they are specified at a predetermined reference impedance. S-parameters relate the electromagnetic (EM) wave power with the same interpretation at all frequency bands. From S-parameter measurements, current and voltage descriptions can be obtained for twoand four-port networks (Fig. 1). The incident, reflected, and transmitted signals are identified by signals ai and bi, with i = 1, 2.^5-10

A circuit or a linear passive device that can be modeled by a two-access structure has signals related by a system of linear equations and matrix as shown in Eq. 1:

where

S₁₁ = (b₁/a₁)a₂=0

the reflection coefficient at the input with the matched output;

S₁₂ = (b₁/a₂)a₁=0 is the reverse transmission coefficient with the matched input;

S₂₁ = (b₂/a₁)a₂=0 is the forward transmission coefficient with the matched output; and

S₂₂ = (b₂/a₂)a₁=0 is the reflection coefficient at the output with the matched input.

In a reciprocal system, the S₂₁ and S₁₂ parameters are equal, i.e., the result at port 2 by incidence at access point 1 (or port 1) equals the result at port 1 with incident signals at access point 2 (or port 2). A system without loss follows the energy conservation principle, however, since the sum of the power entering the system equals the sum of the power leaving the system. These are fundamentally important S-parameter properties.⁵

Before making measurements with a VNA, it is necessary to calibrate the test equipment at the desired frequencies of interest to minimize measurement errors. Calibrations involve the use of precision standards with known values and employing standard connectors, such as an open circuit, a short circuit, and a reference load. Calibration can be performed at one of the VNA’s test terminals (ports) or at both in a two-port system. In the first approach, analysis is by means of only the S₁₁ or S₂₂ parameter, as shown in Fig. 2. The type of calibration will depend upon the equipment test terminal that will be used and access to the port of the DUT. In the second case, using both ports, in addition to the connector-based standards, a reference through-cable is also used in order to analyze the full set of S₁₁, S₁₂, S₂₁, and S₂₂ parameters (Fig. 3). In both cases, when it is necessary to connect the measurement equipment to a DUT using some kind of accessory (cables, adaptors, connectors, attenuators, etc.), it is possible to reduce the respective influences calibrating them together with the equipment (Fig. 4). When one or more accessories used in a calibration is not used during the actual measurements, errors can be introduced into the measurements. Specialized texts show the importance of a system calibration for a greater measurement accuracy and repeatability.¹¹

The measurement techniques developed here can be applied to impedance transformers in some situations. It will be described for a measurement configuration with two test terminals using 50- unbalanced reference impedances. Measurements will be considered for DUTs at the unbalanced-unbalanced (unun) and balanced-unbalanced (balun) configurations, with an impedance transformation ratio of 1:N and the same connectors used for the measurements. Measurements will be made for the transmission and reflection S-parameters.

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