94 Radio Engineering for Wireless Communication and Sensor Applications
ance coaxial line are matched to each other using a three-section l /4 transformer. Different impedances are realized by changing the inner conductor diameter. Abrupt changes in line dimensions cause not only reflections but also reactive fields and reactive energy storages. In an equivalent circuit these can be modeled using shunt susceptances. In an accurate analysis and design these reactive components must be taken into account.
Instead of using a multisection transformer, we can use a tapered section at least l g /2 long, as shown in Figure 4.21(b). The tapering may be linear or follow other mathematical functions leading to different frequency responses.
4.3.4 Resistive Matching
Matching of a load can be improved simply by introducing an attenuator in front of the load, as shown in Figure 4.22. This may be a useful solution, for example, in a measurement application when a wide measurement bandwidth is required but the power loss is not a problem.
Let us assume that the load reflection coefficient is r L and the insertion loss of an attenuator matched to the line is L [see (5.32)]. If the incident power to the attenuator is P, power after the attenuator is P /L . From this power, a part X1 − | rL |2 C × P /L is absorbed to the load and a part | r L |2 × P /L is reflected. The reflected power is further attenuated in the attenuator to a value of | rL |2 × P /L 2. When compared to a situation without an attenuator, the power reflection coefficient decreases from a value of | r L |2 to a value of | rL |2/L 2. The drawback of this method is that the power absorbed to the load is at maximum P /L . The attenuator is realized in integrated circuits using resistors shown in Figure 4.23. Two applications of resistive matching are illustrated in Figure 4.24.
A better solution than the attenuator is an isolator (see Section 6.2.3) placed in front of the load. An ideal isolator is lossless in the forward direction but absorbs the backward reflected wave fully. The reflected power is also lost in this case but more power is available to the load, although in practice
Figure 4.22 Resistive matching with an attenuator.
Impedance Matching |
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Figure 4.23 Resistive lumped elements for integrated circuits: (a) planar resistor; and (b) chip resistor.
Figure 4.24 Applications of resistive matching: (a) a diode detector; and (b) an amplifier chain.
an isolator also has some attenuation in the forward direction. Furthermore, it does not fully block the backward reflected wave and its ports are not fully matched to the line.
References
[1]Bryant, G. H., Principles of Microwave Measurements, London, England: Peter Peregrinus, 1988.
[2]Smith, P. H., ‘‘Transmission Line Calculator,’’ Electronics, Vol. 12, No. 1, 1939, pp. 29–31.
[3]Collin, R. E., Foundations for Microwave Engineering, 2nd ed., New York: IEEE Press, 2001.
[4]Matthaei, G. L., L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures, Dedham, MA: Artech House, 1980.