Stagger Tuning

The term "stagger tuning" refers to an amplifier comprising several stages in cascade, in which the stages are not tuned identically to the same frequency but are "staggered" at frequencies above and below the desired center frequency of the complete amplifier. Not only are the tunings of the individual stages nonidentical, but their bandwidths are also different.

The objectives of stagger tuning are twofold: (1) a greater gain-bandwidth factor is generally achieved than with a cascade of identical stages, and (2) a prescribed amplitude response, such as maximally fiat or equal ripple, can be synthesized, either of which is more desirable for filtering than is the response of identical stages.

Historically, the advantages and possibilities of stagger tuning were apparent to a few persons several years before it became a widely used technique. The desirability of synthesizing a complicated gain function from simple networks in a multistage amplifier was first advocated by Butter-worth in 1930,1 although the gain-bandwidth advantage did not become apparent until Schienemann's paper in 1939.2 The latter paper was apparently not utilized by anyone in this country until about 1943, although Landon in the meantime had published a paper having to do with the maximally flat response function.3 To Henry Wallman belongs the credit

1 S. Butterworth, On the Theory of Filter Amplifiers, Wireless Engr., vol. 7, pp. 536-541, October, 1930.

2 R. Schienemann, Tragerfrequenzverstarker groszer Bandbreite mit gegeneinander verstimmten Einzelkreisen, Telegraphen Fernsprech Tech., 1939, pp. 1-7.

3V. D. Landon, Cascade Amplifiers with Maximal Flatness, RCA Rev., vol. 5, pp. 347-362, 481-497, January and April, 1941.

for first exploiting the stagger-tuning technique 1 used in connection with wideband intermediate-frequency amplifiers in the receiver of a radar system.

Wallman's work provided usable data for synthesizing the maximally flat amplitude response with single-tuned amplifier stages. This was extended by Baum 2 to include the equal-ripple function and by Trautman and other workers to include other interstage networks.3

The principal elements of the technique have already been described. In Chap. 9 there were presented the pole locations for three kinds of gain functions, yielding maximally flat or equal-ripple amplitude response or maximally flat time delay (linear phase). In Chap. 7 there were developed the equations for the gain function of one single-tuned amplifier stage, and in Chap. 8 the gain function was factored to yield the relationship between the poles and the element values for the single-tuned circuit. Now all that remains is to assign a single-tuned stage for each pole of the desired over-all gain function. Then from the pole locations we shall be able to determine the stage element values, expressed usually in terms of the tuning (center frequency a>0) and the bandwidth (or Q).

We shall follow Wallman's convention of distinguishing three cases, depending upon the relationship of bandwidth to center frequency. The first case is narrow-band, where the bandwidth is less than 5 per cent of the center frequency. At the other extreme is the wideband case, where the bandwidth is 30 per cent or more of center frequency. In between is what Wallman calls the "asymptotic," or intermediate, case.

10-1 The Narrow-band Case. The narrow-band case gives arithmetic symmetry of the amplitude response and is the case where the zeros at the origin and the conjugate poles are neglected. The single pole has the coordinates shown in Fig. 10-1, which depicts the p plane normalized by 2 ir to give band widths in cycles per second instead of radians per second. Notice that the horizontal coordinate of the pole is fo/2Q, which is also B/2, where B is the 3-db bandwidth of the single-tuned circuit as given in

1H. Wallman, Stagger Tuned I-F Amplifiers, M.I.T. Radiation Lab. Rept. 524, February, 1944; the essential content of this report appears as chap. 4 in G. E. Valley, Jr., and H. Wallman (eds.), "Vacuum Tube Amplifiers" (vol. 18, M.I.T. Radiation Laboratory Series), McGraw-Hill Book Company, Inc., New York, 1948.

2 R. F. Baum, Design of Broad-band I-F Amplifiers, J. Appl. Phys., vol. 17, pp. 519-529, 921-930, 1946.

3 D. L. Trautman, Jr., Maximally Flat Amplifiers of Arbitrary Bandwidth and Coupling, Electronics Research Lab., Stanford, Tech. Rept. 41, Feb. 1, 1952; J. S. Eddy, Stagger Tuned Amplifiers with Double-tuned Interstages, Electronics Research Lab., Stanford, Tech. Rept. 29, January, 1951; D. L. Trautman and J. A. Aseltine, Equal-ripple Bandpass Amplifiers, Univ. Calif., Los Angeles, Dept. Eng. Rept. 51-9, August, 1951; M. M. McWhorter, The Design, Physical Realization and Transient Response of Double-tuned Amplifiers of Arbitrary Bandwidth, Electronics Research Lab., Stanford, Tech. Rept. 58, February, 1953.

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