August 1, 1997

Unique compensation technique tames high-bandwidth voltage-feedback op amps

Michael Steffes, Burr-Brown Corp

You may think that there's nothing new in op-amp compensation techniques. Think again. A unique and previously overlooked method allows a decompensated voltage-feedback op amp to achieve low-gain operation with high dc accuracy, high slew rate, and low harmonic distortion.

Designers seeking high slew rates and low noise for dc-coupled pulse amplifiers often must turn to extremely high-gain-bandwidth, nonunity-gain-stable, voltage-feedback op amps. The lower internal compensation capacitance, which gives these op amps the nickname "decompensated," increases slew rate, and the higher input-stage trans-conductance, g_m, which produces the ultrahigh gain bandwidth, decreases input-voltage noise.

Unfortunately, many designers have been burned trying to apply these touchy decompensated devices to low gains. Much of the popularity for the current-feedback topology comes from its superior slew rate and stability at low gains compared with high-gain-bandwidth voltage-feedback designs. However, the high-frequency performance of a current-feedback op amp also comes with poor dc accuracy and higher output noise.

Op-amp designers suggest various forms of external compensation to take advantage of the dc accuracy, low noise, and high slew rate of a decompensated voltage-feedback op amp at low signal gains. Unfortunately, previously suggested compensation schemes have many shortcomings. For example, some op amps provide access to the internal compensation node, but adding this dominant-pole compensation directly reduces the slew rate. Common lead-lag compensation techniques produce pole-zero pairs in the closed-loop response, yielding deplorable pulse response and settling characteristics.

A new external compensation method provides complete control over a simple, second-order lowpass response at low signal gains. This technique allows you to achieve a well-controlled frequency response at any inverting gain for any internally decompensated op amp. The full slew rate of the decompensated op amp is available at the output, along with an output-noise voltage density that increases with frequency. This increased output noise stems from the necessary peaking in the noise gain to achieve a flat, closed-loop frequency re-sponse. Passive postfiltering can significantly reduce the effect of this noise.

Using this external technique with a high-quality, decompensated voltage-feedback op amp provides significantly better absolute dc accuracy than high-speed current-feedback alternatives. Comparable noise and slew rate and considerably lower harmonic distortion than equivalent current-feedback options are also possible. With some extra effort, you can also use this compensation to emulate the gain-bandwidth independence of a current-feedback op amp. Gain-bandwidth independence using a voltage-feedback op amp can be useful in inverting-summing applications for which you might need to adjust the summing weights during the design process or as part of the application.

Once you understand the topology and derive the basic transfer function, you can predict the amplifier's perform-ance based on the desired signal gain and the amplifier's characteristics. Three design examples show how the compensation technique works to maximize the achievable flat bandwidth, implement a filter, or produce a gain-bandwidth-independent design (and why you would want that).

Analyze the compensation circuit

The compensation technique simply consists of adding two compensation elements, C_S and C_F, to the standard inverting op-amp configuration (Figure 1). Previous discussions of this circuit focused on using C_F to compensate for a parasitic C_S. The following analysis shows you how to set both C_S and C_F to get a well-controlled, closed-loop, second-order lowpass frequency response at any signal gain for even the most unstable op amp.

You can easily analyze this circuit using a single-pole, open-loop model for the op amp. Without C_S and C_F, a single-pole op-amp model would be inadequate because the higher order poles of a decompensated op amp wholly determine the closed-loop response at low gains. However, you'll see that the design methodology justifies this single-pole simplification with the compensation elements in place.

Besides being the only way this compensation will work, the inverting configuration offers several other benefits. With no common-mode voltage at the input, the inverting configuration for most op amps achieves high er slew rates, higher full-power bandwidth, and lower distortion. The trade-offs to getting these inverting-mode benefits are an input impedance set by R_G and a slightly higher dc noise gain for the noninverting input-voltage noise of the op amp.

You can write the Laplace transfer function for the circuit of Figure 1 in Bode-analysis form as follows:

(1)

where

(2)

(3)

and the single-pole op amp's open-loop gain is

(4)

The significant components of this transfer function are

1. .­Z_F/R_G, which would be the signal gain if the op amp were ideal (had infinite open-loop gain and bandwidth),

2. 1+Z_F/Z_G, which is the noise-gain portion of the loop gain (and also equal to the gain from the noninverting input to the output), and

3. .A(s), which is the open-loop gain over frequency for the op amp.

At dc, the denominator of Equation 1 is approximately 1, whereas the numerator is equal to ­R_F/R_G, which is the desired low-frequency signal gain. For stability analysis, it is common to look at the corresponding Bode plot (Figure 2). The magnitude portion of the Bode plot compares the magnitude of the noise gain with the magnitude of the open-loop gain, which are the top and bottom of the fraction in the denominator of Equation 1, respectively. At the frequency at which these two curves cross, which is loop-gain crossover, the loop gain drops to 1 and, in a simple op-amp application, the closed-loop bandwidth rolls off. Because a pole also exists in the numerator of Equation 1, this simple analysis is not sufficient to determine the closed-loop response.

Normally, you would also need to consider the phase of the loop-gain terms. However, Equation 1 ultimately reduces to a simple, second-order lowpass transfer function, and you proceed with the design by controlling the v₀ and Q of that transfer function. The magnitude portion of the Bode analysis provides insight into what is happening in the design, but you don't use the magnitude information to set C_S and C_F. You can disregard the phase plot for now with the assumption that loop-gain crossover will occur at a noise gain high enough for you to safely ignore the higher order poles of A(s).

Substituting the two impedances, Z_F and Z_G, and the op amp's open-loop-gain expression A(s) into Equation 1 yields

(5)

Rearranging this equation to produce a pole-zero expression for the noise-gain terms in the denominator yields

(6)

The terms in the denominator make up the loop-gain portion of this transfer function. The op amp's open-loop gain has a high dc value of A_OL and a dominant pole at v_A. The noise gain has a dc gain of 1+R_F/R_G, a low-frequency zero, and a high-frequency pole to flatten the noise gain to 1+C_S/C_F at higher frequencies. The complete Bode plot (Figure 2) shows the gain-magnitude portion for this loop gain along with a number of key frequencies that are critical to the design.

The key frequencies (in hertz) are GBP, Z₀, and P₁. GBP is simply the gain-bandwidth product of the selected op amp (GBP=A_OLv_A/2p Hz). Z₀, which equals 1/(2pR_F(C_S+C_F)), is the unity-gain (0-dB) intersection of the sloping portion of the noise-gain curve. The actual zero in the noise gain occurs at G₁Z₀=Z₁. G₁ and G₂ are the low-frequency and high-frequency noise gains, respectively.

P₁, the feedback-network pole, is equal to 1/(2pR_FC_F). This pole and Z₀ are the two things you can adjust to control the closed-loop frequency response. P₁ is also equal to Z₀G₂, which is simply Z₀ times the high-frequency noise gain set by the capacitor ratios.

Another point of interest from Figure 2 is where the projection of the sloping portion of the noise-gain curve intersects the open-loop-gain curve at the geometric mean of Z₀ and GBP. This point turns out to be the characteristic frequency, F₀, of the closed-loop second-order response (see box, "Second-order lowpass-response characteristics"). When you set P₁ to less than this geometric mean, the noise gain crosses the open-loop response at a gain equal to G₂. The noise gain crosses the open-loop response at F_C, which would equal the closed-loop bandwidth for a unity-gain-stable op amp of the same GBP operating at a noninverting noise gain of G₂.

One of the key assumptions in this analysis is that you control G₂ so that it's greater than the specified minimum stable gain for the op amp. Crossover at this high noise gain is the reason you can use a nonunity-gain-stable op amp at a low signal gain of ­R_F/R_G. There is, however, little consistency among op-amp manufacturers on the definition of minimum stable gain. Some manufacturers use a typical phase-margin target, others target a maximum peaking, and still others actually specify a gain that causes oscillation in the closed-loop response. Generally, most data sheets show a recommended minimum gain that does not cause oscillation. The goal in this design is for the noise gain to cross over the open-loop response at a noise gain, G₂, high enough for you to safely ignore the higher order poles of A(s). If the minimum stable gain on the data sheet is really a minimum operating suggestion, it should be safe to target crossover at 1.5 times that gain. This guard band is, however, an estimate and varies from part to part and from manufacturer to manufacturer. Using the macromodels that most manufacturers provide allows you to fine-tune this target.

You can extensively use the frequencies and gains in the Bode plot to gain insight into the algebraic solution for the closed-loop, second-order transfer function. Because the design seeks values for the compensation elements (C_F and C_S), the following methodology uses radian frequency units. Converting those units to the hertz shown in Figure 2 simply requires a division by 2p.

Expanding the transfer function of Equation 6 into normal monic form (writing a polynomial from highest order to lowest order with a coefficient of 1 for the highest order term) yields

(7)

where

(8)

and

(9)

Although seeing that this full transfer function ends up as a second-order lowpass response is encouraging, the individual terms still look a little intractable. With a bit of manipulation and judicious simplifications, you can develop simple expressions for v₀ and Q that show a clear path to a design methodology.

Specifically, you can simplify the terms inside the radical for v₀ by recognizing that A_OL is much greater than 1+R_F/R_G. Dropping the 1+R_F/R_G of that term, recognizing that A_OLv_A=GBP and that 1/(C_F+C_S)R_F=Z₀ (in Figure 2), and simplifying the expression for Q in the denominator yields the following equations, where G₂=1+C_S/C_F and G₁=1+R_F/R_G:

(10)

and

(11)

Referring back to the Bode plot of Figure 2, these simple equations indicate that the closed-loop, second-order response has a characteristic frequency, v₀, that is the geometric mean of Z₀ and the amplifier's GBP. Also, the ratio of that characteristic frequency to the sum of the high-frequency, loop-gain crossover fr equency (F_C) and the zero frequency in the noise gain (Z₁) sets the value of Q. If you've already selected the amplifier and the required signal gain (G₁=|SIGNAL GAIN|+1), you need only set Z₀ and P₁ (or, equivalently, G₂), to implement the compensation.

Design for maximum bandwidth

Virtually all the elements that determine the Q of the closed-loop response in Equation 11 are known. The system designer determines the amplifier's GBP and the desired low-frequency noise gain. Once you select a tar get Q, you need only set Z₀ and G₂. The key simplification to this analysis is to judiciously target a G₂ that is greater than the specified minimum stable gain for the selected op amp so that you can continue to neglect the added phase shift that the high-frequency, open-loop poles introduce. To get as much bandwidth as possible, set the target G₂ very close to the minimum stable gain. As previously suggested, the following design examples use a factor of 1.5 times the minimum stable gain. With G₂ somewhat arbitrarily set, you can then use Equation 11 to solve for Z₀. The following equation shows the solution as a quadratic equation that you must solve to set Z₀:

(12)

An exact solution for Z₀ is

(13)

However, when (G₂/G₁)>6Q², a good approximation is

(14)

After selecting G₁ and G₂ and determining Z₀, you can implicitly determine P₁: P₁=G₂Z₀. Then, you can combine the equations for Z₀ and G₂ in Figure 2 to solve for C_F and C_S:

(15)

and

(16)

Note that with a target Q of 0.707, you can substitute Equation 13 into Equation 10 to show the maximum achievable F₀, which is approximately equal to F_{­3 dB} given the following factors: a given op amp's GBP, the G₁ that corresponds to the desired signal gain, and the high-frequency gain, G₂, necessary for stability. The resulting equation shows the maximum achievable flat bandwidth using this compensation technique:

(17)

Maximize the bandwidth of a real design

One of the greatest attractions of this compensation technique is that it allows you to successfully apply a nonunity-gain-stable, voltage-feedback op amp at low signal gains and simultaneously retain the full slew rate and dc accuracy of the part. Table 1 summarizes the key specifications for a pair of good voltage-feedback op amps. The OPA627 from Burr-Brown Corp is unity-gain-stable; the OPA637 is the company's decompensated version and has a recommended minimum gain of 5. In this case, the input-voltage noise of the decompensated OPA637 is no lower than that of the OPA627, but the slew rate (and high-frequency open-loop gain) of the OPA637 is markedly higher than that of the OPA627. You can compare the OPA627 performance to the performance of the OPA637 in a complete design that uses the compensation technique.

Table 2 summarizes a gain of ­2 (G₁=3) design target for the OPA637, the resulting key frequencies in the Bode analysis of Figure 2, and the component values necessary to set up this compensation. The selected feedback-resistor value is the result of a compromise between high input impedance (R_G=R_F/(G₁­1)) and keeping the compensation capacitors greater than the parasitic values on those nodes.

To implement this circuit for testing, you must also consider the components' parasitic capacitances and test-interface requirements. To include the effect of parasitics, the actual test-circuit design (Figure 3) reduces the value of C_F by 0.2 pF and that of C_S by the 15-pF parasitic at the input of the OPA637. The test circuit also includes 50V impedance-matching resistors at the input and output to match the assumed test-equipment source and load impedances of 50V.

Adding the input-matching resistor slightly changes G₁ from 3.0 to 2.95. This change has no effect on F₀ and very little effect on Q because the G₁Z₀ portion of Equation 11 is small relative to GBP/G₂. The test circuit also shows a bias-current-cancellation resistor from the noninverting input to ground. This resistor is equal to the parallel value of R_F and R_G to improve the output dc offset that results from bias currents. With this resistor match in place, the output dc error that results from input bias currents is simply the input-offset current times the feedback-resistor value. A large capacitor shunts this noninverting-input resistor to roll off the noise terms that might arise from the resistor's Johnson noise and bias-current noise. These two components on the noninverting input are unnecessary for the FET-input OPA637 because its bias, offset, and noise-current terms are infinitesimal relative to the voltage offset and noise terms. The test circuit in Figure 3 includes these components for general application.

The test circuit's frequency response (Figure 4a) is remarkably flat for a gain-of-5-stable op amp operating at a noise gain of 3 (a signal gain of ­2). The frequency response does show slight peaking, which indicates that the Q of the actual circuit is slightly greater than 0.707 instead of the target value of 0.64. This difference in Q slightly extends the bandwidth from a target of 7.7 to 9.8 MHz and introduces some overshoot and ringing into the pulse response (Figure 4b). Apparently, either the target G₂ was too close to the minimum stable gain to exclude the effects of the higher order poles or the parasitic capacitances are different from the estimate. You can obtain a closer match between predicted and measured results at higher values of G₂.

You can compare this inverting compensation for the OPA637 to a maximum-bandwidth design using the unity-gain-stable OPA627 at a gain of 2. The inverting compensation with the OPA637 produces a slightly higher bandwidth of 9.8 MHz vs the 8 MHz of the OPA627. However, because of the slew-rate difference, the OPA627 is slew-limited for output steps greater than 2.4V, whereas the OPA637 can support nonslew-limited steps as high as 4.2V at the output. If this 4V were the input range of an ADC, the nonslew-limited pulse response that the OPA637 provides would settle to a final value more quickly than that of the OPA627.

For example, this compensation of the OPA637 provides a low-gain ADC buffer with excellent settling time for large output steps. When driving a 4V_p-p input-range, 10-bit ADC, the circuit has an absolute dc accuracy (with no trims) and peak-to-peak output noise that doesn't exceed 1/4LSB. The worst-case output dc error is 0.75 mV, and the worst-case output peak-to-peak noise is 0.9 mV. The settling time to 1/2LSB is 33 nsec.

The improvement in performance between unity-gain-stable and decompensated versions of the same op amp is even more significant if you use parts that have a wider difference in their minimum stable gains.

Predict the output noise

Any compensation technique that shapes the noise gain of a nonunity-gain-stable op amp produces higher output noise as the frequency increases. This compensation technique increases the gain for the noninverting input-voltage noise of the op amp, as the noise-gain portion of Figure 2's Bode plot shows. In most cases, the op amp's noninverting input-voltage noise dominates the total output noise for the circuit of Figure 1. Referring to the Bode plot, this input-voltage noise has a gain that starts at G₁, has a zero at Z₁ equal to G₁Z₀, and finally has second-order poles that are identical to those you set in the inverting-compensation design. The transfer function for either the noise or a signal applied to the noninverting input (V⁺) of Figure 1 is

(18)

(Refer to Equations 8 and 9 for the terms that you can place in this equation.)

One approach to describing the output noise is to compute an equivalent noise-power bandwidth (NPB) that, when you multiply it by a constant output-noise-power value, gives the same total integrated noise power as the actual frequency response. If you arbitrarily use the output noise due to the noninverting input-voltage noise amplified by G₁, which is the low-frequency output noise due to the noninverting input-voltage noise, as the constant noise value, you can calculate an equivalent NPB as

(19)

This noise is the square of Equation 18's gain magnitude integrated from a frequency of 0 to infinity, then divi ded by the low-frequency noise gain squared (G₁²). This integral simplifies considerably, and you can solve it in closed form when you target a Q of 0.707. The middle term in the denominator of Equation 19 drops out, which allows you to use integral-table solutions for forms including 1/(x⁴+c⁴). Using the terms defined in Figure 2 and assuming a Q of approximately 0.707 gives an equivalent NPB of

(20)

The last term in this equation is generally much less than 1, and you can ignore it. This equation states that the NPB is approximately equal to the single-pole bandwidth that results if you simply operate the amplifier at G₁ (a bandwidth equal to GBP/G₁) times the ratio of that bandwidth to the characteristic frequency (F₀=ˆZ₀GBP) of the actual second-order closed-loop response.

To use this calculated NPB, multiply the op amp's noninverting input-voltage noise by G₁ to compute the low-frequency spot noise at the output. Then, multiply that result by the square root of Equation 20 to get the integrated noise (E_O(RMS)). Performing these computations for the design example of Figure 3, which has a Q'0.707, gives

(21)

This analysis shows the significant increase in output-voltage noise due to the increased noise gain to G₂ by assuming a constant output noise and computing the required NPB to get the same integrated noise power as the actual output noise over frequency. Evaluating this integral for the NPB is based on the assumption that the op amp's frequency response of Equation 18 self-limits the output noise.

Another way to look at this noise is to compute the equivalent input-voltage noise that integrates to the same power over a simple lowpass Butterworth bandwidth. This approach allows an easy comparison between this technique and other approaches for getting a desired frequency response. The NPB of a simple, sec ond-order Butterworth response equals 1.11F₀=1.11F_{­3 dB} when Q=0.707 (see box). You can set up an equality to define the equivalent input-spot noise (E_M) that will integrate over an NPB set by 1.11F₀ to the same total output-noise power as the actual response as follows:

(22)

where E_N is the input-voltage noise of the op amp. The solution for E_M is

(23)

This equation states that the increase in the equivalent input-referred spot-noise voltage is proportional to the square root of the ratio of GBP/G₁ to Z₁. Evaluating this equation for the design example in Figure 3 yields an equivalent input-noise voltage of 17.1 nV/ˆHz. Multiplying this result by the low-frequency noise gain, G₁, and then by the square root of 1.11F₀ (Table 2) gives the integrated noise. This calculation gives the same 158 mV of integrated noise as Equation 21 gives. Equation 23 is useful because it clearly shows the noise penalty you pay by using this compensation.

Postfiltering can significantly reduce this effect. For instance, if you totally filter the output noise after F₀, the equivalent input noise calculated using Equation 23 decreases by half (the 1.5 inside the radical changes to 0.378, which is one-fourth of 1.5). With this postfiltering at F₀, using the compensation scheme of Figure 3 with the OPA637 at a noise gain of 3 (signal gain of ­2) has almost twice the equivalent noninverting input-referred spot-noise voltage (8.55 nV/ˆHz) as an OPA627 implementation. However, this design exhibits more than twice the slew rate of the OPA627 (Table 1) and also has considerably higher loop gain, and therefore lower harmonic distortion, for frequencies below Z₁.

Implement a second-order lowpass filter

Because the design target to this point has been the control of a second-order lowpass response--principally for pulse-response control--you can also use this topology and the corresponding performance equations to implement an arbitrarily selected second-order response. You can adapt Equations 10 and 11 for this purpose. First, assume that you've selected the amplifier, its corresponding GBP, and design targets for v₀ and Q. Now, you can select a value for either G₁ or G₂ and then solve for the other. To control high-frequency noise, first solve for G₁ in terms of G₂ using Equations 10 and 11, and then compute the constraint on G₂ to get a solution. For example, first solve Equation 10 for Z₀. Then, substitute this Z₀ into Equation 11 and solve for G₁ as follows:

(24)

and

(25)

G₁ has a solution only if G₂>(GBP3Q/v₀). Thus, for low-noise filter design, this topology is most appropriate for lower Qs and when v₀ is not orders of magnitude less than the GBP. Once you recognize this fact, you can flip Equation 25 around to solve for G₂ when you want to target a desired dc signal gain of 1­G₁:

(26)

For good results, G₂ should be at least greater than two times the minimum stable gain for the amplifier. You should recognize that this analysis applies to a unity-gain-stable op amp as well. Also, the denominator of Equation 26 should be greater than zero. Thus, GBP/Q must be greater than G₁v₀. Table 3 shows a design example and the resulting key frequencies and gains corresponding to the Bode plot of Figure 2.

The Bode plot of this design shows that P₁ occurs after the noise gain intersects the open-loop curve at an F₀ of 5 MHz. Most simplified stability discussions strongly discourage a greater-than-40-dB/decade closure rate in the loop gain at crossover. However, this design uses this higher closure rate to achieve complex closed-loop poles. Although using this approach to design a second-order lowpass filter has a limited range of applications and appears to have a relatively high output noise, the approach offers a low-sensitivity design. The most variable portion of the design is the amplifier's GBP. A 10% increase in GBP increases v₀ by 5% and decreases Q by 1.3%. This result indicates a root loci vs GBP that is principally a radial movement from the origin in the s-plane.

The first example using this compensation technique squeezes as much bandwidth as possible out of a given nonunity-gain-stable op amp operated at a noise gain G₁ less than the op amp's specified minimum. A filter-design application then shows that you can get a very stable and moderate Q design by intentionally putting P₁ above the intersection between the open-loop response and the noise gain. A third way to apply the compensation technique also exists. The Bode plot of Figure 2, along with Equations 10 and 11 for v₀ and Q, shows a way to achieve gain-bandwidth independence.

Note that F₀ is unaffected if you vary G₁ while staying below G₂ in Figure 2. Holding all other components constant and adjusting R_G in Figure 1 simply changes the noise gain at the low-frequency end of the plot. However, the noise-gain curve eventually hits and moves along the same 20-dB/decade curve that intersects 0 dB at Z₀ and the open-loop gain curve at F₀. Changes in the low-frequency noise gain, G₁, and, therefore, changes in the inverting signal gain do not affect the key Z₀ and F₀ frequencies in Figure 2. All that happens as G₁ changes is that the Q of the second-order response changes.

Considering Equation 11 along with the Bode plot for a graphical interpretation, increasing G₁ increases Z₁ and therefore slightly decreases the Q set by the ratio F₀/(F_C+Z₁). If you set the initial design point for Z₁ well below F_C, you can make significant changes in G₁ with only a slight change in Q and with no change in F₀. Thus, you can make the second-order frequency response relatively constant vs signal gain and hold all other components constant. The root loci of the second-order response to changes in R_G is a constant v₀ circle with a very slight Q sensitivity to R_G and therefore to G₁.

Making the initial Z₁ low relative to F_C is equivalent to making G₂ much greater than G₁. This setting implies that the design will target a relatively low F₀ to circumvent GBP limits and will move even closer to emulating the benefits of current-feedback op amps. You can also interpret this setting in another way. Initially setting G₂ high (with P₁<F₀) sets the closed-loop bandwidth relatively low. Then, starting at G₁=G₂, the closed-loop bandwidth should be close to F_C. As you decrease G₁, the compensation inhibits the bandwidth extension that normally occurs in a voltage-feedback amplifier as the gain decreases. Instead, the compensation shapes the noise gain to move the closed-loop response closer to that of a simple resistive noise gain of G₂.

One way to approach this design is to initially target a Q of 0.707 (maximally flat Butterworth) and to recognize that F_{­3 dB} equals F₀ in Figure 2 when Q=0.707. Then, with a target F_{­3 dB} that is significantly less than the maximum-bandwidth design, you can solve Equation 10 for the required Z₀ as in Equation 24. Then, you can select a midrange value for G₁ and set G₂ using Equation 26. Also, you can then select an R_F and use Equations 15 and 16 to set the capacitor values. Once you set these values, you can vary R_G over a range of gains with no effect on v₀ and only a slight effect on Q.

Approaching current-feedback performance

To illustrate a design with frequency-response independence for which you can change the signal gain without strongly impacting the frequency response (Figure 5a), set up the OPA637 for a flat second-order response with a nominal F₀=F_{­3 dB}=5 MHz with Q=0.707 at a midrange gain (Table 4). As in the maximum-bandwidth design, the measured small-signal frequency response (Figure 5b) has a Q that is a little higher than expected. In both designs, the higher order poles of the open-loop response appear to cause a slight increase in the closed-loop Q.

The scale on Figure 5b's plot is 1 dB/div to show fine detail. As the signal gain changes from ­1 to ­7--corresponding to a change in the dc noise gain, G₁, from 2 to 8--the ­3-dB bandwidth changed only from 6.1 to 4.8 MHz. In other words, a four-times increase in the gain of this voltage-feedback op amp produces only a 21% decrease in bandwidth. Decreasing the target bandwidth further by increasing G₂ produces results with a better match to theory and an even more insensitive design. Moving this design target down in frequency to get closer to gain-bandwidth independence increases the output noise. Using a high-gain-bandwidth voltage-feedback op amp in this fashion approaches the gain-bandwidth independence and slew rate of current-feedback designs and even brings along with it the higher noise you normally see with current-feedback parts.

The inverting-summing configuration (Figure 6) is another good application for this compensation technique when set up for gain-bandwidth independence. This configuration sums multiple signals to the output by combining the signals at the inverting node. Inverting summing is one common application for current-feedback op amps because of their approximate gain-bandwidth independence. Now, you can achieve some of those same benefits using this external compensation and still get the exceptional dc accuracy of a part such as the OPA637.

For this circuit, each channel sees a signal gain equal to ­R_F/R_G. Without compensation, the noise gain increases as you add each channel. When you use a voltage-feedback op amp, this increased noise gain always leads to a decreased bandwidth for all inputs. However, using the compensation technique, you can add, remove, and adjust the gain of individual channels with a relatively minor impact on their frequency response for any input to the output. Applying this compensation technique to a nonunity-gain-stable op amp can give good wideband performance.

Acknowledgment

The author would like to acknowledge Dr Aram Budak, retired professor of electrical engineering, Colorado State University (Fort Collins), for his enlightening emphasis on wringing the intuition out of the equations.

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