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Measurements and analytical model prediction for the input reflection of the used ENVIROFLEX 316 D transmission line.
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In this paper, an extended transmission line theory is derived and utilized in order to generate simple broadband models for ferrite transmission line transformers in the kilo- and megahertz range. Using the extended description of a transmission line leads to a compact element which can easily be inserted into the circuit of a device. The resultin...
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... components in ferrite transmission line transformers, the used lines are discussed first. Individual measurements of several 3.5 m long copies of the same ENVIROFLEX 316 D coaxial transmission line [18] (used throughout this work) were conducted using a calibrated Rohde & Schwarz ZNC3 [19] vector network analyzer (VNA). The results are shown in Fig. 1. Additionally, as one option to analytically obtain a frequency-dependent characterization, Tesche's model for coaxial lines [20] is included. The used parameters were determined based on datasheet values of the geometric and electrical properties and are listed in Table I. Note that due to the through-open-short-match (TOSM) ...
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... (S-parameter) results refer to a strictly real and constant reference impedance of 50 Ω [21], [22]. Hence, no extension for complex-valued reference impedances using pseudo-waves or power waves [21]- [25] is required. This is done to achieve general applicability so that the results actually characterize the used type of transmission line. Fig. 1 shows the measured and expected result of reflections being observable solely caused by the frequency-dependent line impedance not exactly matching the specified 50 Ω in our frequency range of interest (100 kHz -50 MHz). As the diagram shows, a purely analytical but satisfactory approximation of a coaxial cable's characteristic ...
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... of the line act akin to the primary and secondary side of a classical transformer. Once more the BNC-to-Banana adapters used in order to realize these connections were included in the analytical model as additional LC-elements. Furthermore, supplementary measurements in which the connections are realized with a circuit board were performed. Fig. 10 compares the model with the respective measurements on the basis of |S 11 | for various numbers of windings. Due to the inner conductor (primary side) representing a short circuit for low frequencies, no power is transmitted though the transformer. This unbalanced short circuit current observes the inductance of the windings on the ...
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... core, leading to the initial drop in |S 11 | as the reactance rises with frequency. Again, the predictions of the broadband model including the low frequency behavior are highly accurate for a large number of windings. Minor disturbances can again be observed at high frequencies. This measurement was conducted for all N for which data is given in Fig. 11. The shown diagrams in Fig. 10 are selected to exemplify the impact of changing the number of windings on the behavior of the transformer and the accuracy of the model. All other measurements follow the same mentioned observations. Fig. 11 shows the cutoff frequency f −3dB at which |S 11 (f −3dB )| reaches −3 dB as well as the ...
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... in |S 11 | as the reactance rises with frequency. Again, the predictions of the broadband model including the low frequency behavior are highly accurate for a large number of windings. Minor disturbances can again be observed at high frequencies. This measurement was conducted for all N for which data is given in Fig. 11. The shown diagrams in Fig. 10 are selected to exemplify the impact of changing the number of windings on the behavior of the transformer and the accuracy of the model. All other measurements follow the same mentioned observations. Fig. 11 shows the cutoff frequency f −3dB at which |S 11 (f −3dB )| reaches −3 dB as well as the frequency and magnitude at the initial ...
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... again be observed at high frequencies. This measurement was conducted for all N for which data is given in Fig. 11. The shown diagrams in Fig. 10 are selected to exemplify the impact of changing the number of windings on the behavior of the transformer and the accuracy of the model. All other measurements follow the same mentioned observations. Fig. 11 shows the cutoff frequency f −3dB at which |S 11 (f −3dB )| reaches −3 dB as well as the frequency and magnitude at the initial minimum. As with the simple transmission line transformer configuration with polarity reversal, with an increasing number of windings the analytical predictions converge towards the measurement ...
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... order to verify the extended transmission line model from the perspective of full-wave electromagnetics, the classical transformer configuration shown in Fig. 9 is also analyzed with CST Studio Suite (CST) [12]. Fig. 12 shows the generated model. It consists of a 50 Ω parallel-plate transmission line of length l ≈ 1.58 m with ideal conductors fed by transverse electromagnetic (TEM) excitation through 50 Ω coaxial ports. Hence, the simulation study offers another independent example of verifying the extended transmission line theory. Due to the ...
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... of verifying the extended transmission line theory. Due to the agreement between simulation and theory, this is an indication that such changes do not detract from the applicability of the generated models. Of course, choosing a parallel-plate line instead of a coaxial line also offers the advantage of easier modeling and meshing. As shown in Fig. 13, the obtained scattering parameters accurately match the analytical predictions over the entire considered frequency ...
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... currents carried by them were evaluated through integration of the fields along curves lying in the perpendicular cross sections of the transmission line. The magnitude of the hereby extracted current through the primary side of the transformer as well as the difference between the currents carried by the individual conductors are displayed in Fig. 14 over the length of the transmission line and while varying the frequency. Notably, as can be expected for the short circuited primary side of the transformer the current I p strongly increases for lower frequencies. For larger frequencies, the coupling between the primary and secondary side of the transformer induced by the ...
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... the magnitude of the currents over the length of the transmission line leads to the diagram shown in Fig. 15 comparing the frequency dependence of the two currents and their difference. Again, it can be seen that for low frequencies the assumption of equal but opposite currents does not hold and that instead an unsymmetrical current is present which has to be suppressed before the typical transmission line behavior can be ascribed. Only for ...
