L-C Transformer Cuts Cost And Size, Adds Low-Pass Filtering

L-C equivalents of microwave quarter-wave transformers provide cost savings, miniaturization, and supplementary low-pass filtering. Typically, these transformers have been synthesized directly with published design tables.^{1, 2} But the circuit shown here is attained by using the pi equivalents of microwave quarter-wave sections. The benefit of this approach is design simplicity. Many years ago, this author used it to realize an L-C version of the 3/2-wavelength hybrid ring.³

Impedance levels for a double quarter-wave transformer are available in a classic reference.⁴ For an impedance transformation ratio of 1.5 (applicable to a 50- to 75-Ω transformer) and normalized bandwidth of 0.6, the quarter-wave sections have normalized impedances of Z1 = 1.1197 and Z2 = 1.3396 (see the figure, a). An L-C equivalent is realized by replacing the quarter-wave sections with reactive pi sections and combining central capacitors (see the figure, b). Note that the schematic shows the normalized circuit g's. Upon denormalizing, circuit-element values and their actual realization are shown for a center frequency of 10 MHz in Table 1.

This L-C transformer was constructed as a test piece, with through-lead components and point-to-point wiring in a Hammond 1590H die-cast aluminum enclosure with BNC panel jacks. The transformer was cascaded with a 75- to 50-Ω minimum-loss pad and tested in a 50-Ω setup. Table 2 shows the measured transformer insertion loss after subtracting the nominal 5.7 dB contributed by the minimum-loss pad.

Unlike conventional transformers, the L-C transformer requires no expensive bifilar magnet wire. With surface-mount components and automated manufacture, it can offer low-cost miniaturization at frequencies well into the microwave region. Also, replacing transmission-line transformers with quarter-wave sections of artificial-line L-C transformers adds supplementary low-pass filtering that provides useful selectivity. Additional stop-band rejection can be obtained using the L-C equivalent of transformers with three or more quarter-wave sections. When properly applied, the technique described here can enhance the integration of many subsystems and systems.

References:

1. Matthaei, G.L., "Tables of Chebychev Impedance Transforming Networks of Low-Pass Filter Form," Proc. IEEE, Vol. 52, p. 939-963, August 1964.
2. Cristal, E.C., "Tables of Maximally Flat Impedance Transforming Networks of Low-Pass Filter Form," IEEE Trans. MTT, Vol. MTT-13, p. 693-695, Sept. 1965.
3. Kurzrok, R.M., "Design Technique for Lumped-Circuit Hybrid Ring," Electronics, May 18, 1962.
4. Matthaei, G.L., Young, L., and Jones, E.M.T., "Microwave Filters, Impedance Matching Networks, and Coupling Structures," McGraw-Hill, Chapter 6, 1964.

L-C equivalents of microwave quarter-wave transformers provide cost savings, miniaturization, and supplementary low-pass filtering. Typically, these transformers have been synthesized directly with published design tables.^{1, 2} But the circuit shown here is attained by using the pi equivalents of microwave quarter-wave sections. The benefit of this approach is design simplicity. Many years ago, this author used it to realize an L-C version of the 3/2-wavelength hybrid ring.³

Impedance levels for a double quarter-wave transformer are available in a classic reference.⁴ For an impedance transformation ratio of 1.5 (applicable to a 50- to 75-Ω transformer) and normalized bandwidth of 0.6, the quarter-wave sections have normalized impedances of Z1 = 1.1197 and Z2 = 1.3396 (see the figure, a). An L-C equivalent is realized by replacing the quarter-wave sections with reactive pi sections and combining central capacitors (see the figure, b). Note that the schematic shows the normalized circuit g's. Upon denormalizing, circuit-element values and their actual realization are shown for a center frequency of 10 MHz in Table 1.

This L-C transformer was constructed as a test piece, with through-lead components and point-to-point wiring in a Hammond 1590H die-cast aluminum enclosure with BNC panel jacks. The transformer was cascaded with a 75- to 50-Ω minimum-loss pad and tested in a 50-Ω setup. Table 2 shows the measured transformer insertion loss after subtracting the nominal 5.7 dB contributed by the minimum-loss pad.

Unlike conventional transformers, the L-C transformer requires no expensive bifilar magnet wire. With surface-mount components and automated manufacture, it can offer low-cost miniaturization at frequencies well into the microwave region. Also, replacing transmission-line transformers with quarter-wave sections of artificial-line L-C transformers adds supplementary low-pass filtering that provides useful selectivity. Additional stop-band rejection can be obtained using the L-C equivalent of transformers with three or more quarter-wave sections. When properly applied, the technique described here can enhance the integration of many subsystems and systems.

References:

1. Matthaei, G.L., "Tables of Chebychev Impedance Transforming Networks of Low-Pass Filter Form," Proc. IEEE, Vol. 52, p. 939-963, August 1964.
2. Cristal, E.C., "Tables of Maximally Flat Impedance Transforming Networks of Low-Pass Filter Form," IEEE Trans. MTT, Vol. MTT-13, p. 693-695, Sept. 1965.
3. Kurzrok, R.M., "Design Technique for Lumped-Circuit Hybrid Ring," Electronics, May 18, 1962.
4. Matthaei, G.L., Young, L., and Jones, E.M.T., "Microwave Filters, Impedance Matching Networks, and Coupling Structures," McGraw-Hill, Chapter 6, 1964.