CIRCUITSSYSTEMSSIGNAL PROCESS VOL. 19, NO. I, 2000, PP. 59-69 EXACT SOLUTION OF A BANDPASS MATCHING PROBLEM* S. C. Dutta Roy 1 Abstract. This paper discusses the exact design of a bandpass matching circuit for trans- mission of power from a source of internal resistance R 1 to a load of resistance R 2. The design is obtained in terms of an unknown Q factor, the value of which is to be determined by solving a cubic equation. Key words: Bandpass matching, matching network design, rf circuits. 1. Introduction Many radio frequency circuits require maximum available power to be transmitted at some frequency coo from a source of internal resistance R1 to a resistive load R2, with a specified half-power bandwidth W = 092 - COl.The matching network shown in Figure 1 was suggested for this purpose by Clarke and Hess [1], and an approximate design has been worked out for narrow bandwidths. The circuit was also discussed by Smith [2] later. However, the precise conditions under which the approximate design will work and the resulting deviations in performance characteristics from the specified ones do not appear to have been investigated in the literature. The purpose of this paper is to obtain an exact design of the matching network and examine its limitations. Our results show that, as expected, the approximate design of [1] closely matches the exact design for narrow band- widths, and that the network is also useful for much larger bandwidths than those envisaged in [1]. The design has been obtained using the method of Sun and Fidler [3] in terms of an unknown Q factor, the value of which is to be determined from the solutions of a cubic equation. * Received July 7, 1999;revised August 16, 1999. 1 Department of Electrical Engineering, Indian Institute of Technology,Hauz Khas, New Delhi- 110016, India. E-mail: scdroy@ee.iitd.ernet.in