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Normalized bandwidth, fc /fQ Fig. 6-16 Gain-bandwidth diagram for cascaded and distributed amplifiers.

situation for the two kinds of amplification is depicted in Fig. 6-16.1 Here the actual gain of the amplifier is plotted as a function of normalized bandwidth. For a single-stage RC amplifier the gain is unity (0 db) for a band-

1 The equations for the lines in the graph of Fig. 6-16 may be obtained by assuming that the over-all bandwidth fc, t of a cascaded RC amplifier is related to the stage bandwidth /c,i by fc,t =fc,i/\rn- The gain-bandwidth product of the tube is [Eq. (3-89)]. Then the gain of n stages becomes

This is the equation for the left-hand lines in Fig. 6-16.

For the distributed amplifier the gain is given by Eq. (6-28), with N — nm substituted,

VvVcj/

This is the equation for the gain of the distributed amplifier. Note the difference in the definitions for C in the equation for /o for the two kinds of amplifier. Also note that the graph serves only as a guide because the usable bandwidth of a distributed amplifier is not as great as fc, the filter cutoff frequency.

width equal to the gain-bandwidth product of the tube. The gain varies inversely with bandwidth as shown for the line marked "1 tube," which could be regarded as the simplest cascaded or distributed amplifier. In the cascaded amplifier increasing the number of stages changes the slope of the line (A » l//e") but moves the intercept of the line to the left since the bandwidth decreases as the number of stages is increased (unity-gain intercept = 1 /y/n). Note that the dashed lines which indicate the gain for an m-stage nondistributed amplifier define a forbidden region to the right of all the lines which it is impossible to enter with a cascaded amplifier. For example, with RC stages a gain of 40 db with a bandwidth of 0.25/o cannot be obtained. The use of more complicated interstages simply has the effect

Fig. 6-17 Split-band amplifier.

of multiplying the abscissa by the ratio of the bandwidth of the network to the bandwidth of an RC stage having the same gain. (This ratio is similar to 77 defined in Chap. 4.) An improvement ratio greater than 3 is unlikely with practical networks. Even with such a complicated network, 40 db of gain could be obtained with only about 0.6/0 bandwidth.

The solid curves represent the situation for distributed amplifiers: here the gain (without cascading) is proportional to the number of tubes and is inversely proportional to frequency. Note that gain is obtained in the region which is excluded for cascaded amplifiers. On the assumption that the same laws of bandwidth reduction as used previously apply to cascaded distributed amplifiers, lines giving the gain may be drawn for more complicated combinations. Two such lines are shown, each for three stages, but one for 4 tubes per stage and one for 10 tubes per stage. The bandwidth for a 12-tube amplifier at which the distributed-amplifier approach gives less than a cascaded amplifier is 0.14/0. Note, however, that each distributed stage is giving = 24.7 db gain, which is more than the optimum for a minimum number of tubes—hence an example with a smaller number of tubes per stage would give better results.

The decision to select the distributed amplifier is easy when the gain and bandwidth required fall outside those obtainable with cascaded amplifiers, but the choice becomes a matter of economics if either type of amplifier would suffice. One additional consideration may enter into the final selection. In the case of an output stage which must develop a considerable output-voltage swing, the distributed amplifier is advantageous because the total plate-current swing which develops the output voltage is n/2 times the plate-current swing of one tube. This property has been utilized to realize wideband power amplifiers where each tube in the distributed chain may be a vhf power tetrode.

6-6 Distributed Amplifiers Using Transistors. Obtaining a distributed amplifier with transistors for active elements is a considerably more difficult task because of two principal problems: (1) the input admittance of the transistor has a considerable conductance component, which loads the input line, and (2) the device is not unilateral, and feedback effects result which are difficult to account for. At least one such successful amplifier has been constructed and gives reasonable performance.1 The need for such amplifiers is somewhat open to question with the advent of transistors with extremely large gain-bandwidth products. Transistors with gain-bandwidth products of 5,000 Mc have been constructed which enable amplifier bandwidths of 1,000 Mc or more to be obtained. At such a bandwidth lumped-constant circuits are no longer practical; consequently a further increase in bandwidth cannot be obtained by the distributed-amplifier techniques unless some way of utilizing coaxial circuits can be found.

6-7 Split-band Amplifier. The split-band amplifier, sometimes called the parallel-chain amplifier or divided-band amplifier, has been proposed at various times and is the subject of a limited amount of recent research.2 The basic structure consists of two (or more) amplifiers in parallel, each providing gain over a portion of the entire passband needed, as depicted in Fig. 6-17. The individual amplifiers may be either cascade or distributed. Although the ultimate performance of this split-band structure holds great promise, there is difficulty in designing the branching networks Ar1 and N2 and the characteristics of each amplifier so that the entire assembly has the desired frequency response, particularly in the critical "crossover" region.

1 P. H. Rogers and L. H. Enloe, "Transistor Distributed Amplifier," U.S. Signal Corps Contract DA-36-039 SC-75021, Final Report, Mar. 15, 1958-Feb. 1, 1959, Applied Research Laboratory, University of Arizona, Tucson, Arizona.

2 J. C. Linvill, Amplifiers with Prescribed Frequency Characteristics and Arbitrary Bandwidth, M.I.T. Research Lab. Electronics Tech. Rept. 163, July 7, 1950; H. A. Wheeler, "Maximum Speed of Amplification in a Wideband Amplifier," Wheeler Monograph 11, Wheeler Labs., Inc., Great Neck, N.Y., July, 1949.

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