Efficiency and Bandwidth Considerations

In most cases, transmission line transformers use magnetic cores to improve their low frequency capabilities. Generally ferrite cores are the popular choices. Ferrites can achieve much higher permeabilities than their counterparts, powdered-irons. But powdered-irons are used in some cases where hazardous conditions (considerable flux in the core) can exist. Also toroids are more popular than rod cores because of their closed magnetic path and hence more inductance for the same number of turns. Figure 9 shows how the low frequency response can vary with a Ruthroff 4:1 unun design using ferrite toroidal cores with permeability from 100 to 1400.

Another consideration is the efficiency of the transformer as a function of the permeability of the ferrite core. Since the transmission line transformer has virtually no flux in the core (the currents cancel the flux) in the pass band, the loss is mainly due to the voltage drop along the length of the coiled transmission lines. In other words, the loss is mainly a dielectric loss. As noted in the basic building block, the voltage drop can be zero as in the delay line or the full input voltage as in the bootstrap and phase inverter connections. Also, the higher the impedance levels, the higher the voltage drops.

Figure 10 shows the loss as a function of the permeability of the core. Material E, a powdered-iron has a permeability of only 10. K5, Q1 and Q2 have permeabilities of 350, 125 and 40 respectively. Another loss characteristic is shown in Figure 11. 3C8 material has a permeability of 2700 while the other two ferrites have permeabilities of about 800. It should be noted that 3C8 material is a manganese-zinc ferrite while the others are nickel-zincs. It has a much lower bulk-resistivity than the other ferrites. In fact, there appears to be an inverse relationship between bulk-resistivity and permeability and loss. The exception is the CMD5005-R-107-8 ferrite from Ceramic Magnetics. It has both high permeability and bulk-resistivity and hence low loss.

And finally some words about transmission lines and the use of beads. Regular enameled-type wire held close together by twisting or with insulating tape have characteristic impedances in the 40 to 50 ohm range. The characteristic impedance can be lower when using low-impedance coax or stripline1. When the enameled-type wire is covered with Teflon sleeving, then 100 ohms is easily achieved. covering only one wire results in a characteristic impedance close to 75 ohms. By using extra spacing, about 150 ohms is the maximum practical characteristic impedance achievable.

Ferrite beads are generally used at frequencies high enough to meet the low frequency requirement because of the very low inductance of a beaded line. Beaded lines don't have the distributed capacitance which cause a self-resonance, and hence an upper frequency limit, in the coiled transmission line. But again, the losses with a beaded line are dielectric in nature and hence the proper ferrite should be used.