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**Noise Considerations for Chopper-Stabilized Op Amps**
A voltage feedback (VFB) op amp is distinguished from a current feedback (CFB) op amp by circuit topology. The VFB op amp is certainly the most popular in low frequency applications, but the CFB op amp has some advantages at high frequencies. We will discuss CFB in detail later, but first the more traditional VFB architecture.

Early IC voltage feedback op amps were made on "all NPN" processes. These processes were optimized for NPN transistors— the "lateral" PNP transistors had relatively poor performance. Some examples of these early VFB op amps which used these poor quality PNPs include the 709, the LM101 and the 741 (see Chapter H: "Op Amp History").

Lateral PNPs were generally only used as current sources, level shifters, or for other noncritical functions. A simplified diagram of a typical VFB op amp manufactured on such a process is shown in Figure 1-97 (opposite).

The input stage is a differential pair (sometimes called a long-tailed pair) consisting of either a bipolar pair (Q1, Q2) or a FET pair. This "g

_{m}" (transconductance) stage converts the small-signal differential input voltage, v, into a current, i, and its transfer function is measured in units of conductance, 1/Ω, (or mhos). The small-signal emitter resistance, r_{e}, is approximately equal to the reciprocal of the small-signal g_{m}.
The formula for the small-signal g

_{m}of a single bipolar transistor is given by the following equation:
where IT is the differential pair tail current, IC is the collector quiescent bias current (IC = I

_{T}/2), q is the electron charge, k is Boltzmann's constant, and T is absolute temperature. At +25°C, V_{T}= kT/q= 26mV (often called the thermal voltage, V_{T}).
Figure 1-97: Voltage feedback (VFB) op amp designed on an "all NPN" IC process

As we will see shortly, the amplifier unity gain-bandwidth product, f

_{u}, is equal to g_{m}/2πC_{P}, where the capacitance C_{P}is used to set the dominant pole frequency. For this reason, the tail current, I_{T}, is made proportional to absolute temperature (PTAT). This current tracks the variation in r_{e}with temperature thereby making g_{m}independent of temperature. It is relatively easy to make C_{P}reasonably constant over temperature.
The Q2 collector output of the g

_{m}stage drives the emitter of a lateral PNP transistor (Q3). It is important to note that Q3 is not used to amplify the signal, only to level shift, i.e., the signal current variation in the collector of Q2 appears at the collector of Q3. The collector current of Q3 develops a voltage across high impedance node A, and C_{P}sets the dominant pole of the amplifier. Emitter follower Q4 provides a low impedance output.
The effective load at the high impedance node A can be represented by a resistance, R

_{T}, in parallel with the dominant pole capacitance, C_{P}. The small-signal output voltage, v_{out}, is equal to the small-signal current, i, multiplied by the impedance of the parallel combination of R_{T}and C_{P}.
Figure 1-98 below shows a simple model for the single-stage amplifier and the corresponding Bode plot. The Bode plot is conveniently constructed on a log-log scale.

Figure 1-98: Model and Bode plot for a VFB op amp

The low frequency breakpoint, f

_{O}, is given by:
Note that the high frequency response is determined solely by g

The unity gain-bandwidth frequency, f_{m}and C_{P}:_{u}, occurs where |v_{out}| = |v|. Letting ω = 2πf_{u}and |v_{out}| = |v|, Eq. 1-35 can be solved for f_{u},
We can use feedback theory to derive the closed-loop relationship between the circuit's signal input voltage, v

_{in}, and its output voltage, v_{out}:
At the op amp 3dB closed-loop bandwidth frequency, f

_{cl}, the following is true:
This demonstrates the fundamental property of VFB op amps: The closed-loop bandwidth multiplied by the closed-loop gain is a constant, i.e., the VFB op amp exhibits a constant gain-bandwidth product over most of the usable frequency range.

As noted previously, some VFB op amps (called de-compensated) are not stable at unity gain, but designed to be operated at some minimum (higher) amount of closed-loop gain. However, even for these op amps, the gain-bandwidth product is still relatively constant over the region of stability.

Now, consider the following typical example: I

_{T}= 100μA, C_{P}= 2pF. We find that:
Now, we must consider the large-signal response of the circuit. The slew-rate, SR, is simply the total available charging current, I

_{T}/2, divided by the dominant pole capacitance, C_{P}. For the example under consideration,
The full-power bandwidth (FPBW) of the op amp can now be calculated from the formula:

where A is the peak amplitude of the output signal. If we assume a 2V peak-to-peak output sinewave (certainly a reasonable assumption for high speed applications), then we obtain a FPBW of only 4MHz, even though the small-signal unity gain-bandwidth product is 153MHz! For a 2V p-p output sinewave, distortion will begin to occur much lower than the actual FPBW frequency. We must increase the SR by a factor of about 40 in order for the FPBW to equal 153MHz. The only way to do this is to increase the tail current, IT, of the input differential pair by the same factor. This implies a bias current of 4mA in order to achieve a FPBW of 160MHz. We are assuming that C

_{P}is a fixed value of 2pF and cannot be lowered by design. These calculations are summarized below in Figure 1-99.
Figure 1-99: VFB op amp bandwidth and slew rate calculations

In practice, the FPBW of the op amp should be approximately 5 to 10 times the maximum output frequency in order to achieve acceptable distortion performance (typically 55-80dBc @ 5 to 20MHz, but actual system requirements vary widely).

Notice, however, that increasing the tail current causes a proportional increase in g

_{m}and hence f_{u}. In order to prevent possible instability due to the large increase in f_{u}, g_{m}can be reduced by inserting resistors in series with the emitters of Q1 and Q2 (this technique, called emitter degeneration, also serves to linearize the g_{m}transfer function and thus also lowers distortion).
This analysis points out that a major inefficiency of conventional bipolar voltage feedback op amps is their inability to achieve high slew rates without proportional increases in quiescent current (assuming that C

_{P}is fixed, and has a reasonable minimum value of 2 or 3pF).
This of course is not meant to say that high speed op amps designed using this architecture are deficient, just that there are circuit design techniques available which allow equivalent performance at much lower quiescent currents. This is extremely important in portable battery operated equipment where every milliwatt of power dissipation is critical.

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