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Download this article in PDF format. (273 KB) Compensating Current Feedback Amplifiers in Photocurrent Applications
ideal CFA is independent of its closed-loop gain, thus allowing the CFA to deliver excellent harmonic distortion and bandwidth performance irrespective of its closed-loop gain. Due to their very low input bias current and input current noise, FET-input op amps are often given the highest consideration for TIA applications, particularly those that use low output current devices, such as photoelectric elements, as the input current source. While FET-input amplifiers do excel in many of these applications, their speed can be insufficient in systems that require faster performance. Thus, CFAs are increasingly being used as TIAs in faster systems that can tolerate more noise. This article deals with how the parasitic capacitance of a photodiode or other light-to-current transducer affects a CFA operating as a TIA, and how to properly compensate the amplifier for this capacitance. Some introductory material regarding CFA operation is provided, as well as occasional parallels between CFA and VFA analyses. Analysis of the “noise gain” of VFA circuits or “feedback impedance” of CFA circuits is not used. Instead, classical feedback theory using loop gain is used to avoid difficulties incurred when moving between current and voltage domains (loop gain is always a dimensionless quantity) and because the theory itself presents Bode plots that are straightforward and easy to use.
The closed-loop gain of this TIA can be expressed as
Equation 1 shows that as Z approaches infinity, the TIA gain approaches its ideal value of R Unfortunately, ideal CFAs do not exist, so practical devices use the next best thing: a unity-gain buffer across their inputs. A current mirror reflects the error current to a high-impedance node where it is converted to a voltage, buffered, and fed to the output, as shown in Figure 2.
As long as R
and the loop gain is .
_{o} = 0, this capacitance is fully bootstrapped, so it has no effect on the closed-loop response. In a real CFA, R_{o} > 0, and the parasitic capacitance influences the response, potentially causing the circuit to become unstable. In addition, like the open-loop gain, A, in a VFA, the magnitude of Z in a real CFA is large at low frequency and rolls off with increasing frequency, and the phase shift lags more with increasing frequency. To first order, Z(s) can be characterized with a single dominant pole at s = p and dc transimpedance of Z_{o}, as shown in Equation 3. High frequency poles in Z(s) will be considered later.
The circuit in Figure 3 includes the parasitic capacitance, C, and the transimpedance, Z(s). Note that the CFA’s inverting input capacitance can be absorbed into C.
Equation 4 is derived by performing KCL at the inverting input.
The error current, i
Combining Equation 4 and Equation 5 produces the following result for the closed-loop TIA gain of the circuit in Figure 3:
The loop gain is evident in Equation 6 and is given by
The loop gain contains two poles, a low-frequency pole at
_{F} to ensure stability (45° is often the minimum acceptable phase margin). From here on, Z(s) will include a high-frequency pole at s = p, along with the dominant pole _{H}s = p.To ensure that the feedback impedance does not go to zero, common advice says that we shouldn’t use a feedback capacitor in any CFA circuit. It’s not that simple, however, since the feedback capacitor introduces phase shift, in addition to magnitude changes. This section looks at what happens when a feedback capacitor is added to a CFA-based TIA, omitting the parasitic input capacitance for the moment. Adding a feedback capacitor, C
If R
The loop gain is then
The loop gain has a dominant pole at In the Bode plot, the zero due to C
The zero produces increasing magnitude and leading phase shift with increasing frequency, which can, in some situations, be a good thing from a stability standpoint. In the system modeled in Figure 4, however, the zero pushes out the point where the loop gain crosses 0 dB, and the pole at _{F}, using Equation 2 and the two-pole version of Z(s), as expressed in Equation 11.
Figure 4 shows that the amplifier is stable without C
_{F} to a CFA is understood in a general sense, it can be shown that C_{F} can be safely used to compensate for the parasitic shunt capacitance of an input current source.The closed-loop gain of the circuit in Figure 3 is indicated in Equation 6. In order to see what happens to this circuit when a feedback capacitor is added, R
The closed-loop gain of the circuit in Figure 5 is given in Equation 12
from which the loop gain can be determined to be
The zero due to CF in Equation 13 is the same as the zero in Equation 10, but the pole due to
C The addition of C to C
Equation 14 shows the simple formula to calculate the value of C
The main difficulty encountered when using Equation 14 is determining R The response of the second system is governed by the loop gain and can be modeled by a first-order transfer function as long as the loop gain magnitude crosses 0 dB at –20 dB/decade. Basic feedback theory shows that if this roll-off condition is met, the closed-loop gain magnitude of the second system is approximately unity when the loop gain magnitude is >>1, and follows the loop gain magnitude when the loop gain magnitude is <<1. The 3-dB point in the closed-loop gain occurs at the frequency where the loop gain magnitude crosses 0 dB(if the slope is a little faster than –20 dB/decade, some peaking will occur in the closed-loop response near the 0-dB crossover point). In a stable amplifier, the second system can, therefore, be approximated as a first-order, low-pass filter with unity gain in the pass-band and cutoff frequency equal to the frequency, where the loop gain magnitude crosses 0 dB. The transfer function of the first system is the reciprocal of the feedback factor and has a simple first-order, low-pass response with a dc value of RF and corner frequency of . Intuitively, the additional pole due to C
_{o} = 1 MΩ, p = –2π (100 kHz),p _{H} = –2π _{o} = 50 Ω, and R_{F} = 500 Ω. The magnitude of the loop gain is found by taking the magnitude of Equation 11 with these values.
which equals 1 at approximately The loop gain phase shift at 145 MHz is given
resulting in approximately 54° of phase margin, which is a reasonable place to start for a basic CFA with no parasitic capacitances. Figure 6 shows the simulation of the response of this model to a 1-ns rise time current step input.
The response is clean, with minimal ringing—just what would be expected with 54° of phase margin. The step response of the same amplifier with 50 pF of parasitic capacitance added between the inverting input and ground is shown in Figure 7.
The vertical scale in Figure 7 is the same as it is in Figure 6, but the trace was moved down one division to accommodate the ringing. The excessive ringing is clear, and this amplifier clearly has a phase margin problem. The amplifier can be stabilized by adding a feedback capacitor determined by Equation 14, which is calculated to be 5 pF.
The bandlimiting due to the pole in the closed-loop gain is evident. The loop gain 0-dB crossover for the original amplifier was determined to be 145 MHz, which corresponds to a time constant of approximately 1.1 ns in a first-order system, and the R Reducing C
It’s clear that some experimentation may be necessary to get the best value for C
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Analysis and Design of Analog Integrated Circuits. John Wiley & Sons, Inc., 1977. Lundberg, Kent. “Feedback Control Systems.” M.I.T. Course Notes. Roberge, James K.
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