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can realize frequency doublers (x2), triplers (x3), quadruplers (x4), quintuplers (x5), and so on [15, 16]. A frequency multiplier helps in generating signals at high frequencies where it is otherwise difficult or impossible. Also a signal generated by a multiplier may have a more accurate frequency than a signal produced directly with an oscillator.

The nonlinear element may be either a diode (either resistive or capacitive diode, i.e., a varistor or a varactor, respectively) or a transistor. The multiplication efficiency h is defined as

In order to optimize the frequency multiplication efficiency, the nonlinear element must be conjugate matched to the embedding network at the input and output frequencies and terminated with proper, pure reactive loads at other harmonic frequencies. Especially important are the proper reactive terminations at the idler frequencies (intermediate harmonics between the fundamental and output frequency) in higher-order multipliers. The efficiency h of a multiplier based on a nonlinear reactive element is at maximum unity at any multiplication factor n , if both the nonlinear element and the embedding network are lossless (Manley–Rowe equations; see [17]). In practice the efficiency decreases rapidly versus an increasing multiplication factor. A positive, monotonically voltage-dependent nonlinear resistance can produce a multiplication efficiency of 1/n 2 at maximum. The efficiency of a transistor multiplier may be greater than unity.

8.6 Detectors

Detecting a signal requires transforming it into a useful or observable form. In a diode detector an RF signal is transformed into a voltage proportional to the signal power. Operation of a detector is based on the nonlinearity of a diode, such as a Schottky or p-n diode. When a sinusoidal voltage is applied over the diode, the current contains, besides a component at the signal frequency, harmonic components and a dc component that is proportional to the signal power. Diode detectors are used for power measurement, automatic level control, AM demodulation, and so on.

Let us consider a Schottky diode, where the series resistance R s and the junction capacitance Cj are assumed negligible. When a bias voltage VB

and a small sinusoidal signal Vs cos v t are applied over the junction resistance (see Figure 8.24), the diode current can be presented as a series:

+ a2(Is + IB ) V4s 2 cos 2v t + . . .

Further terms are negligible if a Vs << 1 [see a in (8.2)] or at room temperature Vs << 25 mV. IB is the direct current caused by the bias voltage, I (VB ). The second term is the dc component proportional to the signal power; that is, it is the useful component. According to (8.38), the junction can be considered as a voltage source with a voltage

and with an internal resistance R j . The diode is said to follow the square law, because the useful signal is directly proportional to the RF power, that is, to the square of the signal voltage (Vo ~ Vs 2 ). The voltage sensitivity is the ratio of the detector output voltage Vo and the applied signal power Ps in an impedance-matched case, as in

Figure 8.24 Current in a diode with an exponential I–V characteristic, when a dc bias and a sinusoidal signal are applied to the diode.

Figure 8.26 Response of a diode detector.

1 mW), the response no longer follows the square law. Finally, the output voltage will saturate. On the other hand, at very low power levels noise is the limiting factor.

8.7 Monolithic Microwave Circuits

Circuits consisting of microstrip lines, lumped passive elements (resistors, inductors, and capacitors), and semiconductor diodes and transistors may be integrated (connected without connectors) and be made very small. If components are soldered or bonded on a microstrip circuit, we call it a hybrid circuit. If a circuit is integrated directly on the surface of a semiconductor substrate, it is called a monolithic integrated circuit.

Up to about 2 GHz the monolithic circuits are made on Si; at higher frequencies the substrate is usually GaAs and these circuits are called monolithic microwave integrated circuits (MMICs). The advantages of the MMICs are their extremely small size, suitability to mass production, good repeatability, and high reliability. For example, a whole microwave amplifier can easily be fabricated on a GaAs chip with an area of 1 mm2 and a thickness of 100 m m. Design and fabrication of a single MMIC becomes very expensive, but in mass production its price becomes reasonable. Microwave applications

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gaining from mass production of integrated circuits include mobile phones, satellite TV receivers, GPS receivers, and WLAN terminals.

From diodes the Schottky diode and from transistors both MESFET and HEMT are easily suited to GaAs-MMICs. The transmission lines are either microstrip lines or coplanar waveguides. Resistors are either ion-planted directly in GaAs or are thin metal films in the transmission lines. Inductors (coils) may be narrow microstrip lines in the form of a loop or a spiral; capacitors have either an interdigital or metal-insulator-metal (MIM) structure (see Figure 4.7). Grounding is realized by a metallized via in the substrate. Figure 8.27 presents a GaAs-MMIC with typical elements. Digital microwave circuits have been made using MMIC technology up to tens of gigahertz, analog circuits up to 200 GHz. Integrated optoelectronic circuits are made using similar technology. In designing MMICs, commercially available software packages are used for both electrical and layout design.

Figure 8.27 Monolithic microwave integrated circuit on gallium arsenide (GaAs-MMIC).

References

[1]Sze, S. M., Semiconductor Devices, Physics, and Technology, New York: John Wiley & Sons, 1985.

[2]Howes, M. J., and D. V. Morgan, Gallium Arsenide Materials, Devices, and Circuits,

Chichester, England: John Wiley & Sons, 1986.

[3]Yngvesson, S., Microwave Semiconductor Devices, Boston, MA: Kluwer Academic Publishers, 1991.

[4]Zhang, J., and A. V. Ra¨isa¨nen, ‘‘Computer-Aided Design of Step Recovery Diode Frequency Multipliers,’’ IEEE Trans. on Microwave Theory and Techniques, Vol. 44, No. 12, 1996, pp. 2612–2616.

[5]Gentili, C., Microwave Amplifiers and Oscillators, New York: McGraw-Hill, 1987.

[6]Rogers, R. G., Low Phase Noise Microwave Oscillator Design, Norwood, MA: Artech House, 1991.

[7]Liao, S. Y., Microwave Circuit Analysis and Amplifier Design, Englewood Cliffs, NJ: Prentice Hall, 1987.

[8]Abrie, P. L. D., Design of RF and Microwave Amplifiers and Oscillators, Norwood, MA: Artech House, 1999.

[9]Ha, T., Solid-State Microwave Amplifier Design, New York: John Wiley & Sons, 1981.

[10]Pozar, D. M., Microwave Engineering, 2nd ed., New York: John Wiley & Sons, 1998.

[11]Lange, J., ‘‘Noise Characterization of Linear Two-Ports in Terms of Invariant Parameters,’’ IEEE J. of Solid-State Circuits, Vol. 2, No. 2, 1967, pp. 37–40.

[12]Hoffmann, R. K., Handbook of Microwave Integrated Circuits, Norwood, MA: Artech House, 1987.

[13]Held, D. N., and A. R. Kerr, ‘‘Conversion Loss and Noise of Microwave and Millime- ter-Wave Mixers: Part I—Theory,’’ IEEE Trans. on Microwave Theory and Techniques,

Vol. 26, No. 2, 1978, pp. 49–55.

[14]Maas, S. A., Microwave Mixers, 2nd ed., Norwood, MA: Artech House, 1993.

[15]Ra¨isa¨nen, A. V., ‘‘Frequency Multipliers for Millimeter and Submillimeter Wavelengths,’’ Proc. IEEE, Vol. 80, No. 11, 1992, pp. 1842–1852.

[16]Faber, M. T., J. Chramiec, and M. E. Adamski, Microwave and Millimeter-Wave Diode Frequency Multipliers, Norwood, MA: Artech House, 1995.

[17]Collin, R. E., Foundations for Microwave Engineering, 2nd ed., New York: IEEE Press, 2001.

[18]Bahl, I., and P. Bhartia, Microwave Solid State Circuit Design, New York: John Wiley & Sons, 1988.