IEEE T R A N S A ~ I O N S ON CIRCUITS AND SYSTEMS, VOL. 37, NO. 5, MAY 1990

Hybrid w Common Base Analysis

IZZAT DARWAZEH AND BRETT WILSON

655

Abstruct -A high-frequency analysis of the bipolar common base configuration is developed with particular application to the design of low input impedance optical fiber receivers tolerant of source capaci- tance.

INTRODUCTION While the bipolar transistor common base configuration has

found frequent use in amplifier cascode arrangements it has rarely been employed as an input stage. However, the low input resistance of the common base configuration makes it attractive for use as an input stage for current and transimpedance ampli- fiers, where a low input resistance is a desirable feature. This is especially so for the case of optical transimpedance amplifiers intended for use with photodiodes, for which the dominant factor affecting bandwidth in traditional amplifier designs is the input time constant [l], [2] . A transimpedance amplifier exhibit- ing a low resistance input will therefore free the designer from reliance on expensive ultralow capacitance photodiodes ( < 1 pF) and offer greater realizable bandwidths from lower specification photodiodes.

The surprisingly small amount of material that appears to have been published concerning the common base configuration has only concentrated on low frequency modeling [3] , [4] . In contrast, this paper presents a study of the high frequency input impedance behavior of the common base configuration taking into account factors not considered in earlier works. The results show dependence on transistor type and operating parameters, indicating that careful choices may be necessary for optimum performance.

THEORY The input impedance of a common base stage may be de-

duced by analyzing the hybrid r equivalent circuit model as illustrated in Fig. 1. This model has been shown previously to be valid up to one-third of the transistor's transition frequency fr [5]. Setting both the base-collector capacitance Cp and the collector-emitter feedback capacitance C y to zero for the mo- ment, we obtain

where Y, is the parallel combination of C , and re. The input impedance Zi,(S) may be written

Using the identities w = 2 r f , regm = LY (common base current gain) and f T = ( 2 r C , r e ) - l , then R J f ) and X i n ( f ) may be

Manuscript received January 17, 1989. This letter was recommended by Associate Editor T.R. Viswanathan.

The authors are with the Department of Electrical Engineering and Elec- tronics, Digital Communications Sub-Group, UMIST, Manchester M60 IQD, U.K.

IEEE Log Number 8927677.

Emitter Collector

Fig. 1. Hybrid T common base model.

expressed as

(3)

x i n ( f ) =2rfC,r?(gmrbb'-1)'[1f(f/fT)Z] -'. ( 4 ) For frequencies less then fr/3 and values of LY > 0.95 (corre- sponding to h , > 20), then Zi, can be approximated to an error of less than 10% as

zin(f) = re + j ( 2 r f ) C , r ? X (5) where the parameter X is defined as ( r b b , / r e - 1 ) .

Hence the input impedance of a common base stage can be modeled as a series R-L circuit, but where L may be positive, negative or zero, depending upon the value of X . Zero input reactance will only be obtained when rbb2 = re.

The foregoing analysis is only valid if the feedback capaci- tance C, is negligible. In practice C y has a range of values 0.5-1 pF for a typical high frequency transistor such as a BFT24 or BFY90. Since a common base stage exhibits a positive voltage gain of approximately gmR,, then C y appears at the input as a negative Miller multiplied capacitance C,, given by

C , = C y ( l - g m R L ) .

The modified input impedance of the parallel combination will be

Considering only frequencies below fT /3, the input impedance will be purely resistive at a certain critical value of R,, nomi- nated as R,,, and given by

.-

For values of RL greater than R,, the input reactance will be positive, and negative below R,,. A higher value of RL,, and consequently a higher possible voltage gain at a wider band- width, can be obtained by using a transistor with low values of rbb, and Cy.

COMPUTER SIMULATION

Variation of common base input resistance and reactance with frequency was studied using the previous equations, a commercial computer analysis package (Circuit Modeller, Harcourt Systems) and typical operating conditions for a popu- lar high frequency transistor, type BFT24. Plots of R i , and X i , at an emitter current of 150 p A are shown in Figs. 2 and 3,

0098-4094/90/0500-0655$01 .OO 01990 IEEE

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, VOL. 37, NO. 5, MAY 1990

FT = 1.2 GHz

Cn= 0.8 PF

c,= cy = 0

- Equaticn (3)

J x rbs = r2

200

Conditions and

\

10 Frequency I30 (MHz) XKW]

Fig. 3. Common base input reactance versus frequency

400.

300 Cross-over

resistance

RLX (nl 200

IO0

0

- Equation (71 (C,,= 0)

Conditions as Figs. 2,3 except C8 z 0.5pF.

0 100 200 300 400 rb6 (n) Fig. 4. Variation of crossover resistance R,, against rhb.,

respectively, for three different values of rbb,. Results from (31-6) are indicated by solid lines with spot frequency values computed by Circuit Modeller.

A plot of the crossover resistance R,, versus rbb, (at a fixed emitter bias current) is illustrated in Fig. 4, where the solid line represents the results from (7), along with the spot frequency simulation results for the case when C, = 0. Taking into account the collector-base capacitance C, (0.3 pF for BFT24) produces

a deviation of less than 10% from the values obtained from (7), in which C, is set to zero.

Curves in the form of Figs. 2-4 along with a knowledge of rbb, for a particular transistor can assist the designer of common base input transimpedance amplifiers by indicating the high frequency trends for input impedance and hence the restrictions on closed-loop performance. In addition, the variation of R,, with rbbf will often dictate the optimum voltage gain for a common base input stage and therefore determine the distribu- tion of gain throughout a multistage design to obtain optimum bandwidth and closed-loop gain simultaneously.

PRACTICAL APPLICATION

A number of three-stage optical transimpedance amplifiers has been constructed using common base input stages designed in accordance with the principles outlined in the previous sec- tions. In each case the advantage gained was a wide bandwidth insensitive to high values of photodiode capacitance due to the very low input resistance. For example, a common base design with a 5-pF photodiode displayed an almost identical bandwidth to a previously published common collector design using the same transistors, but requiring a photodiode with an ultralow capacitance of 0.8 pF [6]. In addition, it has also been possible to construct a low-noise optical transimpedance amplifier using discrete components suitable for use with the emerging fiber distributed data interface (FDDI) standard using this approach.

CONCLUSION

This paper has illustrated the usefulness of common base input stages and presented analytical tools for the design of such circuits. The input impedance of a common base stage has been shown to be a strong function of high frequency transistor parameters, indicating that careful selection of the transistor and its operating conditions is necessary to obtain optimum bandwidth and stability.

REFERENCES [l] I. Danvazeh, “Fibre optic receiver design,” M.Sc. thesis, Univ. of

Manchester Inst. of Science and Technology, UK, 1986. [2] T. V. Muoi, “Receiver design for high speed optical fibre systems,”

J . Lightwav Technology, vol. LT-2, pp. 243-267, June 1984. [3] S. Hakim, Junction Transistor Circuits Analysis. London, England: Wi-

ley, 1962. [4] V. Uzunoglu, Semiconductor Network Analysis and Design. London,

England: McGraw-Hill, 1964. [5] L. Giacoletto, “Study of p-n-p junction transistors from DC through

medium frequencies,” RCA Rev., vol. 15, no. 4, pp. 506-562, Dec. 1954. [6] B. Wilson and 1. Danuazeh, “Transimpedance optical preamplifier with

a very low input resistance,” Electron. Lett., vol. 23, no. 4, pp. 138-139, Feb. 1987.

Generation of OTA-C Filter Structures from Active RC Filter Structures

P. V. ANANDA MOHAN

Recently, realization of continuous-time filters based on oper- ational transconductance amplifiers (OTAs) and capacitors has

Manuscript received April 21, 1989; revised July 25, 1989. This letter was

The author is with Transmission Research and Development, Indian Tele-

IEEE Log Number 8930890.

recommended by Associate Editor T. R. Viswanathan.

phone Industries Ltd., Bangalore-560 016, India.

0098-4094/90/0500-0656$01.00 01990 IEEE