Some simple calibration techniques applied to a vector network analyzer can aid in making accurate S-parameter measurements on a wide range of impedance transformers.
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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An unun transformer has two unbalanced terminals with an arbitrary impedance transformation. In order to measure transmission coefficients for the transformer, another identical transformer must be placed in cascade in order to transform the impedance back to that of the characteristic impedance of the test equipment. This procedure is called a back-to-back or front-to-front impedance transformation. In order to measure reflection coefficients, the VNA is connected to another device terminal with a load having reference to ground and with an impedance value that is N times that of the reference impedance of the test equipment. Figure 5 shows the connection arrangements for both cases.
A balun transformer has an unbalanced terminal and a balanced terminal, and can also have an arbitrary impedance transformation ratio. In order to measure its transmission coefficients, it must be put in cascade with another identical transformer in order to convert the impedance back to that of the characteristic impedance of the test equipment. In order to measure the reflection coefficients, the VNA test port is connected to another device terminal, with a load without reference to ground, and with an impedance value that is N times that of the reference impedance of the test equipment. Figure 6 shows the connection arrangements for both cases.
When it is desirable to make Sparameter measurements related to reflection coefficients, a calibration can be performed on both test ports of the VNA. However, the operating time will take longer compared to a calibration performed on only just one of the test ports. For S-parameter measurements related to the transmission coefficients, both test ports should be calibrated. It is a matter of choice for the user which type of calibration technique is used, since many methods are available based on different calibration standards, including thru-reflect-match (TRM) and thru-reflect-line (TRL) approaches. In some situations, it may be useful to simultaneously analyze transmission and reflection parameters, such as insertion and return loss, in order to better understand the behavior of a particular transformer design.
In the case of measurements with different device connectors, the described procedure is valid, but it must include the addition of accessory equipment, such as an adapter, in order to mate the DUT to the test equipment.12 Figures 7 and 8 show the experimental performance of a laboratory measurement for a 1:4 unun transformer device, and the measurement result through a S21 transmission parameter. The VNA was calibrated at both test ports, together with the cables, to minimize their effects on the measurements. Figure 8 shows that the cut-off frequencies are 30 and 450 MHz, indicating a bandwidth of 420 MHz for this device. Insertion loss remains flat across the bandwidth, at about 0.3 dB. These results were obtained with two devices in a back-to-back configuration. Since only one transformer would be used in most practical circuits, the loss can be reduced by one-half in the linear region of the measured response. Outside of the passband, the insertion loss increases significantly, reducing the performance of the impedance-matching transformers.
Expertise in calibration and measurement procedures is always a goal for communications systems research organizations.4,11,12 In this report, techniques were presented for making response measurements on unun and balun impedance transformers with an arbitrary transformation ratio. In addition to the basic measurement approaches, techniques were shown for minimizing measurement errors by means of careful calibration procedures. The calibration approaches presented, along with the measurement techniques, have been shown to produce repeatable and accurate results when compared to preduced or theoretical values for a wide range of impedance transformers.13
The measurement procedures work well with any number of commercial microwave VNAs. These techniques are valid for a variety of different impedance transformers, including narrowband and wideband types, with any range of impedance transformation ratios. The test method can also be applied to devices fabricated in a variety of different formats, including discrete planar, or microwave-integrated-circuit (MIC) technologies.
REFERENCES
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11. A. Rumiantsev, N. Ridler, "VNA Calibration," IEEE Microwave Magazine, Vol. 9, No. 3, pp. 86-99, June 2008.
12. H. Akel, "Characterization of Non-Uniform Devices Using Back-to-Back Measurement," RF Design, March 2007, pp. 66-68.
13. A. A. Ferreira Jr., J. A. J. Ribeiro e W. N. A. Pereira, "Designing Wideband RF Impedance Transformers," Microwaves & RF, Vol. 46, No. 3, March 2007, pp. 78-88.