Characteristics of Current-Feedback Op-Amps: Benefits of CFA Design vs. VFAs

In this article, we’ll take a more detailed look at the functionality and characteristics of current-feedback amplifiers (CFAs).

A current-feedback amplifier is a form of op-amp which most commonly serves as the error amplifier of a negative-feedback circuit where the input error is a current.

In this article, we'll talk about the step responses, slew rates, input buffers of CFAs.

CFA Series

This article is part of a series. Though this article is designed to be useful on its own, you may consider reading the preceding part before continuing. 

The rest of the series can be found here:

• Part I: Introduction to the CFA: Current-Feedback Amplifiers vs. Voltage-Feedback Amplifiers
• Part II: Characteristics of Current-Feedback Op-Amps: Benefits of CFA Design vs. VFAs
• Part III: Applications and Limitations of the Current-Feedback Amplifier: Dual CFAs and Composite Amplifiers

In the previous article, we highlighted some unique features of the current-feedback amplifier (CFA) using the idealized model (presented as Figure 1b in the previous article):

 

Figure 1. A noninverting amplifier using the idealized model of the CFA

 

We now wish to investigate how a practical CFA lives up to the above ideal expectations.

It turns out that a primary source of deviation from the ideal is the fact that the input buffer exhibits a non-zero output impedance r_n, so we shall now work with the more realistic model of Figure 2a.

 

(a)                                                    (b)

Figure 2. Investigating the effect of the input buffer’s output resistance r_n upon the feedback factor ß. 

 

We note that the following equations still hold from when we first introduced them in the previous article (where they were presented as Equations (8) and (9). We'll repeat them here for convenience:

 

Equation (1)

 

Equation (2)

 

However, we now have V_n ≠ V_p because of the voltage drop across r_n. In fact, Ohm’s law gives V_p – V_n = r_nI_n, or, if we recall that V_p = V_i,

 

Equation (3)

 

Substituting Equation (3) into Equation (2), we eliminate V_n. Collecting for I_n and then substituting into Equation (1), we eliminate I_n to obtain an expression involving only V_o and V_i. Collecting once again and solving for the ratio V_o/V_i gives the closed-loop gain A, which we express as 

 

Equation (4)

 

where

 

Equation (5)

 

and

 

Equation (6)

The presence of r_n has no effect upon A_ideal. However, it raises the 1/ß curve, and in so doing it reduces both the loop gain T and the crossover frequency f_x, compared to the idealized case r_n = 0, for which T = z/R_F and f_x = f_t. (Henceforth, we visualize f_t as the crossover frequency extrapolated to the limit r_n → 0.)

 

Example: The Effect of r_n in a DC Circuit

To get an idea, let us rework the DC example from the first article (presented there as Figure 2b)—but with r_n = 40 Ω in place.

 

(a)                                                              (b)

Figure 3. Visualizing DC voltages and currents for the cases (a) r_n = 40 Ω and (b) r_n = 0.

 

Using Equation (6), we find T = 303.03 (a drop from T = 400 from the circuit in the previous article). Then we find A via Equation (4), I_n via Equation (1), V_p – V_n via Ohm’s law, and V_n via Equation (3).

Moreover, we calculate the currents through R_G and R_F via Ohm’s law. The results are visualized in Figure 3a (for easy comparison, the example from the previous article is repeated in Figure 3b).

It is apparent that the most noticeable effects of r_n are to cause V_n ≠ V_p, and also to contribute a slight reduction in V_o due to the decrease of T from 400 to 333.

The Closed-Loop AC Response

We now wish to take a closer look at the crossover frequency f_x of Figure 2b.

As discussed in our comparison of CFAs and VFAs, this frequency approximates the –3-dB frequency of the closed-loop response A(jf).

Since z(jf) is of the dominant-pole type, the GBP = |z| × f is constant on the sloped portion of the curve, so we can write 

 

Equation (7)

 

Solving for f_x gives, after simplification,

 

Equation (8)

 

This expression is reminiscent of the VFA equation we presented in the previous article as Equation (16), except for the presence of the term r_n/R_F, which is a well-designed CFA is such that r_n/R_F << 1. Consequently, there is a bit of gain-bandwidth tradeoff also in CFAs, but this is much lighter than in VFAs. For instance, in the circuit with r_n = 40 Ω and R_F = 1.25 kΩ of Figure 3a, adjusting R_G for (1 + R_F/R_G) = 1, 10, and 100 V/V, we get f_x = f_t/1.032, f_t/1.32, and f_t/4.2, as shown in Figure 4.

 

Figure 4. Illustrating the effect of r_n = 40 Ω upon the closed loop bandwidth for A_ideal = 0, 20, and 40 dB.

 

These compare quite favorably with the VFA values of f_x = f_t, f_t/10, and f_t/100. 

Step Responses

We conclude our VFA–CFA comparison by taking a look at the step responses. Turning first to the VFA, we use the simplified model of Figure 3a, which is typical of many VFAs. We shall focus on the input stage (Q₁ through Q₄), so we lump together all subsequent stages into a single inverting stage assumed to have gain –a₂. (The purpose of C_c is to provide an open-loop response of the dominant-pole type.)

The bias current I_E splits between Q₁ and Q₂ to form i₁ and i₂ (for simplicity, we are assuming negligible BJT base currents). Now, i₁ flows into the diode-connected transistor Q₃, and since Q₄, its matched twin, is subjected to the same base-emitter voltage drop as Q₃, then Q₄ will just mirror Q₃’s current i₁, this being the reason why the Q₃-Q₄ pair is said to form a current mirror. By KCL, the capacitor current is i₁ – i₂. 

 

(a)                                                         (b)

Figure 5. (a) Simplified VFA model connected as a voltage follower, and step responses: small-signal exponential transient (top), and slew-rate-limited ramp (bottom). 

 

When v_O = v_I, the circuit is said to be balanced because i₁ = i₂, so the capacitor current is i₁ – i₂ = 0. If we now apply an input step of suitably small magnitude V_m, we are making Q₂ less conductive and Q1 more conductive, thus unbalancing the circuit to give i₁ – i₂ > 0. This will cause C_c to charge up and produce a transient at the output, which in turn will gradually reduce the initial imbalance via negative feedback. Just as in the case of a plain R-C network, we get an exponential transient, and its time constant is τ = 1/(2πf_t), as shown in Figure 5b, top. (For the 741 op-amp, which has f_t = 1 MHz, we have τ = 159 ns.)

Now, if we increase V_m, we’ll reach a point at which all of I_E will be diverted to Q₁, causing C_c to charge at a constant rate, as shown in Figure 5b, bottom. This is the maximum rate at which v_O can swing. Aptly called the slew rate (SR), it is easily found via the capacitance law to be 

 

      

Equation (9)

For the 741 op-amp, which uses I_E = 20 µA and C_c = 30 pF, we get SR = 0.67 V/µs. The maximum amplitude V_m before the onset of slew-rate limiting is obtained by equating the initial slope of the exponential transient to SR, or V_m/τ = SR, which gives V_m = I_E/(C_c×2πf_t ). For the 741 op-amp, we get V_m = 116 mV. Under slew-rate limiting, v_O ramps up at a constant rate until it comes within 116 mV of the final value, after which it completes the rest of the transient in an exponential fashion. 

 

Step Responses of a CFA

Let us now turn to the step response of the CFA, but using the circuit schematic of Figure 6, which will also help us better understand the CFA’s overall internal workings.

We make the following observations:

• The function of Q₁ and Q₂ is to form a low-output-impedance push-pull stage, while Q₃ and Q₄ provide a Darlington-type function to increase the input impedance. Also, the base-emitter voltage drops of Q₃ and Q₄ are meant to compensate in a complementary fashion for those of Q₁ and Q₂ so as to eliminate any DC offset between nodes V_n and V_p. This is the input buffer, represented at the bottom of Figure 6 as a unity-gain buffer with output resistance r_n.
• In negative-feedback operation, the current I_n drawn by the external feedback network splits between Q₁ and Q₂ such that I_n = I₁ – I₂, by KCL (again, we are assuming negligible BJT base currents).
• The trios Q₅-Q₆-Q₇ and Q₈-Q₉-Q₁₀ form high-quality current mirrors of the so-called Wilson type, for the purpose of mirroring I₁ and I₂, respectively, in and out of an important node called the gain node (GN). Denoting GN’s equivalent impedance towards the ground as z, it is apparent that the net current into z is a replica of the inverting-input current I_n itself, so we model the entire action of the mirrors by means of a single unity-gain current-controlled current source (CCCS), as shown at the bottom.
• BJTs Q₁₁ through Q₁₄ form the output buffer, identical in topology to the input buffer Q₁ through Q₄ (for simplicity, its output resistance r_o is usually ignored because it plays a much lesser role than r_n). Thanks to this buffering action, we write V_o = zI_n and we model the CFA with a CCVS as in Figure 1.
• The impedance is modeled as the parallel combination of equivalent resistance R_gn and capacitance C_gn, or z = R_gn||[1/(j2πfC_gn)]. Expanding,

 

Equation (10)

 

With reference to Figure 2b, we can easily find an expression for f_t by imposing z₀ × f_p = R_F × f_t, obtaining

 

 

Equation (11)

 

In a well-designed CFA, R_gn is on the order of 10⁶ Ω, C_gn is in the picofarad range, and R_F is on the order of 10³ Ω. The time constant τ = (R_FC_gn) is then in the nanosecond range. 

Figure 6. Circuit schematic of a CFA (top) and its constituent blocks (bottom). 

 

We are now in the position to state that there is no slew-rate limiting in CFAs because the input buffer will deliver to GN whatever current it takes to ensure an exponential transient at the output, regardless of the input step size V_m. For instance, the circuit of Figure 3a, in response to an input step with V_m = 1 V, will provide an initial current of I_n = V_p/[r_n + (R_G||R_F)] = 6.06 mA.

Were we to remove R_G in order to operate the CFA as a unity-gain voltage follower with a 10 V input step, the initial current would be I_n = V_p/(r_n + R_F) = 7.75 mA, much larger than the maximum current I_E = 20 µA available in the 741 op-amp!

CFAs are well suited to applications that might suffer from slew-rate-induced distortion and nonlinearity.

 

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Continue reading in Part II: Benefits of CFA Design vs. VFAs.