Abstract
AThe transimpedance limit describes the maximum transimpedance that a transimpedance amplifier (TIA) can attain for a given bandwidth and technology. We analyze and compare this limit for a wide variety of TIA topologies thus exposing their relative merits. The topologies considered are the shunt-feedback TIA with single and multistage amplifier, the shunt-feedback TIA with feedback capacitor, the shunt-feedback TIA followed by a post amplifier, the shunt-feedback TIA with a current amplifier, the common-base/gate feedforward TIA, the shunt-feedback TIA with a common-base/gate input stage, and the shunt-feedback TIA with a regulated-cascode input stage. The analysis includes a discussion of the conditions under which the limit is realizable.
Index Terms—Amplifiers, circuit theory, current-mode circuits, feedback, feedforward, optical communication systems, transimpedance amplifiers.
I. INTRODUCTION
THE transimpedance limit is a powerful concept revealing the tradeoffs between transimpedance, bandwidth, and technology of a transimpedance amplifier (TIA). The transimpedance limit of the shunt-feedback TIA with a single-pole voltage amplifier was originally derived and discussed by Mohan et al. [1]. For reference, we briefly present this result here. Our derivation is based on [2] and is somewhat different from the original (avoiding some of the approximations and taking stability explicitly into account), but the results are identical. The shunt-feedback TIA under discussion is shown in Fig. 1. The signal source is shown as a photodetector, but any capacitive source is applicable. The photodetector capacitance and the voltage amplifier input capacitance are in parallel and can be combined into . The voltage amplifier has the single-pole transfer function , where is the DC gain and is the pole frequency. Moreover, it has an infinite input resistance and zero output resistance. With these assumptions, the transimpedance, , of the circuit in Fig. 1 can be found easily as (1) Manuscript received September 25, 2009; revised November 10, 2009; accepted November 16, 2009. Date of publication February 05, 2010; date of current version August 11, 2010. This paperwas recommended by Associate Editor G. Palumbo. The author is with Ikanos Communications, Inc., Red Bank, NJ 07701 USA (e-mail: esackinger[at]ikanos.com). Digital Object Identifier 10.1109/TCSI.2009.2037847 Fig. 1. Shunt-feedback TIA. where (2) (3) (4) For the amplitude response of (1) is maximally flat (Butterworth response). The TIA’s 3-dB bandwidth is found by solving . Requiring that the response is free of amplitude peaking, , it can be shown that the 3-dB bandwidth of (1) is bounded by the simple expression , where the equality is reached for . Expressing in terms of with (2) and inserting into (3) results in the transimpedance limit [1] (5) The product is the gain-bandwidth product of the voltage amplifier, which is roughly proportional to the technology parameter . The capacitance is a measure of the photodetector technology. (For noise reasons, is chosen to be approximately equal to and thus [e.g., see [2], [3]].) In summary, (5) defines the maximum DC transimpedance that the TIA can reach for a given 3-dB bandwidth, , and technology, . Two remarkable conclusions follow from (5). First, the transimpedance degrades with the the square of the bandwidth and not linearly, as sometimes believed. This is a consequence of the voltage amplifier’s finite gain-bandwidth product. For the unrealistic case of a voltage amplifier with infinite bandwidth, the transimpedance would degrade linearly with the bandwidth. This square lawalso implies that the transimpedance-bandwidth product, , is a questionable figure of merit because it grows indefinitely for small values of .


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