Questions and Answers on How Current Feedback Operational Amplifiers Work

Q: I don't quite understand how current feedback op amps work compared to regular op amps. I heard that current feedback op amps have a constant bandwidth and do not change with gain. How is that achieved? Is it the same as a transimpedance amplifier?

A: Before we examine the circuit, let's define the concepts of voltage feedback op amp (VFA), current feedback op amp (CFA), and transimpedance amplifier. As the name implies, voltage feedback refers to a closed-loop structure where the error signal is in the form of a voltage. Traditional op amps use voltage feedback, that is, their inputs respond to voltage changes, resulting in a corresponding output voltage. Current feedback refers to a closed-loop structure where the error signal used as feedback is in the form of a current. CFAs have one input that responds to an error current instead of an error voltage, resulting in a corresponding output voltage. It should be noted that the open-loop structure of both op amps has the same closed-loop result: the differential input voltage is zero and the input current is zero. An ideal voltage feedback op amp has two high impedance inputs, which results in zero input current, and uses voltage feedback to keep the input voltage at zero. In contrast, a CFA has one low impedance input, which results in zero input voltage, and uses current feedback to keep the input current at zero. The transfer function of a transimpedance amplifier is expressed as the ratio of output voltage to input current, indicating the open-loop gain Vo/Iin expressed in ohms (Ω). Therefore, CFA can be called a transimpedance amplifier. Interestingly, the VFA closed-loop structure can also form a transimpedance characteristic. As long as the low-resistance summing node is driven by a current (such as the current from a photodiode), a voltage output can be generated, and its output voltage is equal to the product of the input current and the feedback resistor. More interestingly, since ideally, any op amp application circuit can be implemented using voltage feedback or current feedback, the above I-V conversion can also be achieved using current feedback. Therefore, when using the concept of transimpedance amplifier, it is necessary to understand the difference between current feedback op amps and ordinary op amp closed-loop I-V conversion circuits, because the latter can also exhibit similar transimpedance characteristics. First, look at the simplified model of VFA (see Figure 1). The common-phase gain amplifier circuit amplifies the common-phase amplifier principle diagram with an open-loop gain A(s).

Bode plot Figure 1

Simplified model of VFA differential mode voltage (V IN+ -V IN- ), a part of the output voltage is fed back to the inverting input terminal through the voltage divider circuit composed of RF and RG. To derive the closed-loop transfer function VO/V IN+ of the circuit, assume that the current flowing into the input terminal of the op amp is 0 (input impedance is infinite); the two input terminals are approximately equal (connected as negative feedback and the open-loop gain is very high). This gives:
VO=(V IN+ -V IN- )A(s),
V IN- =RGRG+RFVO
Substituting and rearranging,
VOV IN+ =(1+RFRG)1
1+1/LG, where LG=A(s)1+RF/RG
The closed-loop bandwidth refers to the frequency when the loop gain (LG) drops to 1 (0dB). 1+RF/RG This term is called the noise gain of the circuit
; for the same-phase amplifier circuit, it is also the signal gain. From the Bode plot, it can be found that the closed-loop bandwidth of the circuit is the intersection of the open-loop gain A(
s) and the noise gain NG. The increase in noise gain reduces the loop gain, which reduces the closed-loop bandwidth. If A(s)
decreases at 20dB/decade, the amplifier's gain-bandwidth product is constant, meaning that for every 20dB increase in closed-loop gain,
the closed-loop bandwidth decreases by 10 times.

Now consider the simplified model of the CFA, as shown in Figure 2. The non-inverting input is the high impedance input of the unity gain buffer, and the inverting input is the low impedance output of the unity gain buffer. The buffer allows the error current to flow into or out of the inverting input, and the unity gain causes the inverting input to follow the non-inverting input. The error current reflects off the high impedance node, converting the error current into a voltage that is buffered and output. The high impedance node impedance Z(s) is frequency dependent, and it is similar to the open-loop gain of the VFA, with a high DC value and a 20dB/decade drop.

Bode diagram of the principle diagram of the same phase amplifier

Figure 2 Simplified CFA model

When the buffer maintains V IN+ =V IN-, the closed-loop transfer function is obtained by summing the current at the V IN- node . Assuming the buffer output resistance is 0, that is, RO=0,
VO-V IN- RF
+-V IN- RG+I ERR =0 and I ERR =VOZ(s
)
Substituting into the solution, we get:
VOV IN+ =(1+RFRG)1
1+1/LG, where LG=A(s)1+RF/RG
Although the CFA closed-loop transfer function
is the same as the V FA, the CFA loop gain (1/LG) depends only on the feedback resistor RF, not (1+RF/RG), so the CFA's
closed
-loop bandwidth will change with the resistance of RF, not with the noise gain (1+RF/RG). From the Bode plot, it can be seen that the intersection of RF and Z(s) determines the loop gain, and thus determines the closed-loop bandwidth f CL of the circuit. Obviously, one advantage of the CFA is that the gain-bandwidth product is not a constant. In fact, the output resistance RO of the CFA input buffer is not ideal, and is generally 20 to 40Ω. The existence of this resistor changes the size of the feedback resistor. The voltages at the two input terminals are not completely equal. Substitute V IN- =V IN+ -IERR RO into the previous equation. Solve for VO/V IN+ and we get

VOV IN+ =(1+RFRG)1
1+1/LG,
where LG=Z(s)RF-RO(1+RF/RG)
The additional term in the feedback resistor means that the loop gain actually depends to some extent on the closed-loop gain of the circuit. When the closed-loop gain is low, RF plays a dominant role; when the closed-loop gain is high, the second term RO(1+RF/RG) increases, the loop gain decreases, and thus the closed-loop bandwidth decreases.

It should be made clear that if RG is disconnected and the output is shorted to the inverting input (like a voltage follower), the loop
gain will be very large. For a VFA, the feedback is maximized if the entire output voltage is fed back to the input. The maximum current feedback is limited by the short-circuit current. The smaller the feedback resistor, the greater the feedback current. As can be seen in Figure 2, when RF =
0, the frequency of the intersection of Z(s) and the feedback resistor is very high, in the region of high-order poles. For a CFA, the high-order poles of Z(s)
will cause an increase in high-frequency phase shift, which will cause resistor instability when the phase shift is greater than 180°. Because the optimum value of RF
changes with closed-loop gain, the Bode plot is useful in determining bandwidth and phase margin at different gains. Reducing the phase
margin increases the closed-loop bandwidth, but this will cause peaking in the frequency domain and overshoot and damping ringing in the time domain. The product data sheet of a current-fed
device will give the optimum value of RF at different gains.

CFA has excellent slew rate characteristics. Although it is possible to design a VFA with a high slew rate,
CFA has a faster slew rate due to its inherent characteristics. In traditional VFAs, the slew rate is limited by the charge and discharge current of the internal compensated capacitor at light loads
. When a large transient signal is input, the input stage is saturated and only its long tail circuit current charges or discharges the compensation node. For
CFA, the low input impedance allows large transient currents to flow into the amplifier as needed, and the internal current mirror transfers this input current to the compensation
node for fast charging and discharging. In theory, it is proportional to the size of the input step signal. The higher the slew rate, the faster the rise time
, the lower the distortion and linearity error caused by the slew rate, and the wider the large signal frequency response. In practice, the slew rate
is limited by the saturation current of the current mirror (10~15mA) and the slew rate of the input and output buffers.

Q: What is the DC accuracy of the CFA?

答：正像使用VFA一样，CFA的直流增益精度可以从它的传递函数算出，基本上
是其内部互阻抗与反馈电阻之比。典型情况下，内部互阻抗为1MΩ，反馈电阻为1kΩ，RO
为40Ω，那么单位增益的增益误差约01%。增益较高时，增益误差显著增大。CFA很少用于
高增益场合，尤其是当要求增益绝对准确时。

In many applications, settling time is still more important than gain accuracy. Although CFAs have fast rise times,
many CFA data sheets only specify settling times to 0.1% accuracy because thermal settling tails are a major factor affecting settling time accuracy. Now consider the complementary input buffer shown in Figure 3, where the offset
voltage between V IN+ and V IN- is the difference between the V BE voltage of Q1 and the V BE voltage of Q3. When the input is 0, the two V BE voltages should match, with a small offset between V IN+ and V IN-. Apply a positive step input signal to V IN+, which reduces the V BE voltage on Q3, reducing its power dissipation and increasing Q3's V BE value. The voltage V CE on Q1, which is connected in diode form, does not change, so its V BE does not change. If the two inputs have different offset voltages, their accuracy will be reduced. The same problem exists in the current mirror circuit. An input step change at the high impedance node will change the V CE value of Q6, thereby changing the V BE value of Q6, but the V BE of Q5 remains unchanged. The change in V BE will cause an error current to be fed back to V IN-. Since the error current is multiplied by RF, an output offset voltage will be generated. In addition, the power consumption of each transistor is only in a small area. Because the area is too small, thermal coupling between devices cannot be achieved. In applications, the use of an inverting amplifier structure can eliminate the common-mode input voltage, thereby reducing the thermal error of the input stage.

Figure 3 CFA input stage and current mirror circuit

Q: Under what circumstances does thermal tailing become a problem?

A: Thermal tailing is related to the frequency and waveform of the signal. Thermal tailing does not appear immediately, and
the temperature coefficient of the transistor (determined by the process) will determine the time required for temperature change, parameter change and recovery. Op
amps manufactured by Analog Devices using a high-speed complementary bipolar process (CB process) do not show obvious thermal
tailing at input frequencies above several kilohertz because the input signal changes too quickly. Communication systems are generally more concerned with spectral characteristics, so
the additional gain error that thermal tailing may introduce is not important. Step waveforms, such as those used in imaging applications, are adversely affected by thermal tailing when the DC level changes.
For these applications, CFAs do not provide sufficient settling time accuracy. Q: Now I understand how a CFA works, but I am still unclear about how to use it in a circuit. Does the low input impedance of the CFA's inverting input mean that I cannot use reverse amplification?

A: Remember that the CFA works in an inverting fashion because its inverting input is a low impedance node.
The summing node of VFA is at the feedback

After the loop is established, it is characterized by low input impedance. In fact, the CFA works very well in reverse mode because of its inherent low input impedance, keeping the summing node at "ground" and having this characteristic before the feedback loop is established. In high-speed applications, the VFA summing node will have voltage spikes, but the CFA circuit will not have voltage spikes. You may also recall that the advantages of operating the CFA in reverse include maximizing the input slew rate and reducing settling time errors due to thermal tailing. Q: This means that I can use a CFA to form a current-to-voltage (I-V) converter, right?

A: Yes. CFAs can be used to form I-V converters, but there are some limitations: The bandwidth of the CFA changes directly with the feedback resistance, and the current noise of the reverse input can become very high. When amplifying small currents, because the signal gain increases linearly with the resistance, and the resistor noise increases as R, a larger feedback resistor means a higher signal-to-noise (resistor noise) ratio. Doubling the feedback resistance doubles the signal gain, while the resistor noise only increases by a factor of 1.4. Unfortunately for the CFA, the effect of the noise is doubled and the signal bandwidth is halved. Therefore, the high current noise of the CFA prevents its use in many photodiode circuits. When the noise requirements are not very strict, choose an appropriate feedback resistor based on the bandwidth requirements and use another stage to increase the gain.

Q: I noticed that the current noise of the CFA is quite high. Will this limit my ability to use it?

A: You are right. The current noise at the inverting input of the CFA is relatively high, about 20~30pA/Hz. However, compared with similar VFAs, the input voltage noise of the CFA is very low, generally less than 2nV/Hz, and its feedback resistor is also very small, usually less than 1kΩ. When the gain is 1, the main noise source of the CFA is the noise current flowing through the feedback resistor at the inverting input. The 20pA/Hz input noise current and the 750Ω RF generate a 15nV/ voltage noise at the output, which becomes the main noise source. When the gain is increased (reducing the input resistor RG), the output voltage noise generated by the input current noise does not increase, and the input voltage noise of the op amp becomes the main noise source. For example, when the gain is 10, the noise voltage generated by the input noise current at the output is only 1.5nV/, which is added to the input noise voltage of the amplifier in the form of the square root of the square sum (RSS), so the total input noise voltage is only 2.5nV/ (ignoring the resistor noise). Therefore, CFA is very attractive in low-noise applications.

Q: What happens if a CFA is used to form a four-resistor differential amplifier? Will it be unsuitable for this type of circuit because the resistances at the two input terminals of the CFA are unbalanced?

A: You asked a good question! This is a common misunderstanding of CFAs. The two input resistors of a CFA are indeed mismatched, but
the transfer function of an ideal differential amplifier can still be used. What will happen if the two input resistors are not the same? At low frequencies, the CMR of a four-resistor differential amplifier is determined by the external resistor ratio matching. A 0.1% resistor matching corresponds to a CMR of about 66dB; at high frequencies, the issue to be concerned about is the matching of the time constants formed by the input impedances. High-speed VFAs usually have very well matched input capacitors, with CMR reaching 60dB at 1MHz. Since the input stage of a CFA is unbalanced, its input capacitors cannot be well matched. This means that in order to reduce the time constant mismatch, an external resistor (100 to 200Ω) must be connected to the non-inverting input of some op amps. If the resistor is carefully selected, a CFA can also produce high-frequency CMR comparable to that of a VFA.
The addition of external hand-tuned capacitors can further improve the performance of VFAs and CFAs at the expense of some signal bandwidth. If higher performance is required, it is best to choose a monolithic high-speed differential
amplifier, such as the AD830. Without resistor matching, it has a CMR greater than 75dB at 1MHz and about 53dB at 10MHz.

Q: How do you think the feedback capacitor will adjust the amplifier bandwidth? Will the low impedance at the inverting input make the CFA less sensitive to the bypass capacitor at this node? What about capacitive loading?

A: First consider the case where there is a capacitor in the feedback loop. For the VFA, this creates a pole within the noise gain range, but for the CFA, a pole and a zero appear within its feedback resistance range, as shown in Figure 4. Remember that the phase margin at the intersection of the feedback resistance and the open-loop mutual resistance determines the closed-loop stability. The feedback resistance of capacitor CF in parallel with RF is:
ZF(s)=［RF+RO(1+RFRG)］1+sCFRFRG
RORFRG+RFRO+RGRO1_sCFRF

Figure 4 Capacitor feedback capacitor function

[page]The pole appears at 1/2πRFCF, and the zero appears at 1/［2π(RF∥RG∥RO)CF］. If
the frequency at the intersection of ZF and ZOC is too high, the open-loop phase shift will be too large and cause instability. For the integrator circuit, if RF→∞, the pole
appears at low frequency, and there is almost no resistance to limit the loop gain at high frequency. In order to limit the high-frequency gain of the loop, a resistor
is connected in series with the integrating capacitor to limit the high-frequency loop gain, which can stabilize the current feedback
integrator. CFA is not suitable for reactive feedback filter structures, such as feedback filters with parallel resistors and capacitors, but
the Sallen-Key filter constructed with CFA is an exception because it is used as a fixed gain unit circuit. In short, it is not desirable to connect capacitors at both ends of the CFA's RF. Another issue to consider is the effect of the bypass capacitor on the inverting input of the CFA. Remember VFA, the bypass capacitor will establish a zero on the noise gain, increase the rate of closure between the noise gain and the open-loop gain, and if frequency compensation is not performed, excessive phase shift will cause circuit instability. For CFAs, bypass circuits have the same effect, but this issue is less discussed. The feedback resistance expression for the additional input bypass capacitor can be written as:
ZF(s) = [RF + RO (1 + RFRG)] [1 + sC IN RFRGRO] RFRG + RFRO + RGRO] The zero occurs at 1/[2π(RF∥RG∥RO)C ON ], see f Z1 in Figure 5. This zero causes the CFA to have the same trouble as the VFA, but the zero has a higher corner frequency due to the low inverting input impedance. Consider a wideband VFA with RF = 750Ω, RG = 750Ω, and C IN = 10pF. The zero frequency at 1/[2π(RF∥RG)C IN ] is about 40MHz. A CFA with RO of 40Ω and the same other circuit parameters will raise the zero to about 400MHz. For both op amps with a unity gain bandwidth of 500MHz, the VFA needs feedback capacitor compensation to reduce the effect of C IN and reduce the signal bandwidth. Although the CFA has some additional phase shift due to the zero, the impact of C IN is not as great as that of the VFA because the corner frequency is ten times higher. The CFA has a larger signal bandwidth than the VFA and can be compensated if flatness or optimal pulse response is required in the passband. To reduce the closing speed between ZF and ZOL, a small capacitor in parallel with RF can improve the response. To ensure at least 45° of phase margin, the feedback capacitor should be selected to be placed at the pole where ZF and ZOL intersect, as shown at point fP in Figure 5. Please do not forget the
impact of the high-frequency zero fZ2 generated by the feedback capacitor.

Figure 5 The role of the bypass capacitor at the inverting input

The load capacitance in a CFA presents the same problems as in a VFA: increased error signal phase shift, reduced phase margin, and possible
instability. There are several recognized circuit methods for handling capacitive loads, but for high-speed op amps, the best method is to
connect a resistor in series with the output of the op amp (see Figure 6). With the resistor in series with the load capacitance outside the feedback loop, the amplifier is not directly

Figure 6 Series output TV driving capacitive load

Drive purely capacitive loads. CFAs can also add RF to reduce loop gain. No matter what method is used,
there will always be some loss in bandwidth, slew rate, and settling time. It is best to optimize the specific amplifier circuit experimentally based on the required characteristics, such as fastest rise time, fastest
settling time to a specified accuracy, minimum overshoot, or passband flatness.

Q: Why don't any of your CFAs offer true single-supply operation and allow the signal to swing to one
or both of the supplies?

This is one of the reasons why people like VFA circuit structure. The amplifier should provide good current driving capability. And to make the signal swing close to the power supply voltage, a common emitter output stage is usually used instead of a general emitter follower as the output stage. The common emitter output stage allows the output swing to be close to the power supply voltage, only differing from the V CE saturation voltage drop of the output transistor. In existing manufacturing processes, this type of output stage does not provide the speed of an emitter follower, partly because it increases the complexity of the circuit and has a higher inherent output impedance. Since CFA was developed specifically for ultra-high-speed op amps and current output, the
output stage uses an emitter follower circuit as its unique design. With the development of high-speed op amp manufacturing processes, such as Analog Devices' ultra-high-speed complementary bipolar process (XFCB), it is now possible to design common emitter output ultra-high-speed op amps (such as AF8041) with a bandwidth of 160MHz, a slew rate of 160V/μs, and a single +5V power supply. This op amp uses voltage feedback, and although current feedback is also used to some extent, its speed is still limited by the output stage. The slew rate of VFA and CFA, which use emitter followers made in XFCB process as output stages, is much faster than that of AD8041. In addition, the single-supply op amp input stage uses PNP differential pairs, which allows the common-mode input range to be as low as the lower limit of the power supply (usually the ground potential). Designing such an input stage for CFA is the main problem currently faced.

However, CFAs can be used in single-supply applications. Analog Devices offers many op amps that operate from single supplies of +3V and 15V. It is important to remember that in applications, devices will only work well off single supply if the signal is within the allowed input and output voltage ranges. This requires level shifting or AC coupling and biasing to the appropriate range. In most single-supply systems, this requirement has already been taken into account. If the system dynamic range must reach one or both of the positive and negative power supply limits, or if maximum headroom is required in an AC-coupled application, a CFA may not be the best choice. Output swing performance between the positive and negative supply limits is also a consideration when driving large loads. Many supply-limited devices cannot output close to the supply limits when driving 50Ω or 75Ω cables because the V CESA saturation voltage increases as the output current increases. If you really need supply-limited output performance, then don't choose a CFA. If you require ultra-high speed and current output, this is where CFAs come in handy.