The third part of our series to explain the nature, characteristics, benefits, and caveats of composite amplifiers.

This is the third part in our series explaining the nature, characteristics, benefits, and caveats of composite amplifiers. The four parts of the series include:

- Part One: When Cascaded Amplifiers are Not an Option
- Part Two: The Composite Amplifier Choice
- Part Three: Composite Amplifier Closed-Loop Frequency Response
- Part Four: Using the Composite Amplifier to Tame DC Offset and Noise

# Composite Amplifier Topology

Figure 14 illustrates a general composite amplifier to be analyzed. The bandwidth of each stage is determined by its gain-bandwidth product and its voltage gain. Each op amp is assumed to have dominant-pole frequency compensation and be stable down to unity voltage gain (0 dB).

To maximize the bandwidth of the composite amplifier, the usual approach is the make Av1 and Av2 equal. (More will be said about this later.)

The AD712 is described to be a precision, low-cost, high-speed BiFET dual (two-channel) op amp. It is to be used in a composite amplifier configuration which provides a voltage gain of 1000. Assume the two amplifiers are matched perfectly. We shall use Multisim (Figure 15) to verify the open-loop voltage gain (*A _{VOL}*)

_{, }the open-loop dominant corner frequency (

*f*), and the gain bandwidth product

_{H(OL)}*(*

*f*) of the AD712 op amp’s SPICE model. We shall use the model values for our calculations. Resistors

_{T}*R*and

_{1}*R*ensure the op amp receives proper DC bias. Capacitor

_{2}*C*eliminates any possibility of AC negative feedback. The Multisim Bode plotter provides us with the op amp model parameters.

_{1}The simulation results indicate an open-loop DC voltage gain of 106 dB, an open-loop corner frequency of 25 Hz and a gain-bandwidth product of 4.3 MHz. Next, we determine the required voltage gain of the second stage.

Ideally, the first and second stages will both possess voltage gains of 31.623. Standard 1%-tolerance resistors were used to obtain the required voltage gains. Figure 16 shows the Multisim circuit. Note the oscilloscope is AC coupled to block any DC offset. DC offset will be addressed later.

Observe the positive peak is 4.970 V, the negative peak is -4.990 V, and the peak-to-peak out voltage is 9.958 Vp-p. The peak-to-peak value is -0.42 percent lower than the expected ideal value of 10 Vp-p.

# Understanding the Composite Amplifier Closed-Loop Response

Using the AD 712 op amp model parameters determined as shown in Figure 15, the Bode straight-line approximation of the amplitude frequency response can be drawn as shown in Figure 17.

The second stage has a closed-loop voltage gain (*A _{v2}*) of 31.7. This corresponds to a decibel voltage gain of 30.0 dB. The closed-loop response can be obtained by superimposing the closed-loop gain on the open-loop response as indicated in Figure 18. The corner frequency of the second stage

*f*can be determined graphically. However, we can use the voltage gain and the gain-bandwidth product to obtain greater accuracy.

_{H2}Since the closed-loop gain intersects where the open-loop response has a slope of -20 dB/decade, the amplifier is stable and will not oscillate. (The basic stability rules tell us that an intersection at -40 dB/decade is marginally stable and -60 dB/decade or greater intersection is unstable and will probably oscillate.)

When amplifiers are cascaded inside a composite amplifier, their voltage gains multiply. Their corresponding voltage gains in decibels add together. In this composite amplifier the open-loop voltage gain *A _{VOL}(dB)* response can be graphed using Bode approximations. Graphical addition is used as shown in Figure 19. Note the composite amplifier open-loop response has a transition frequency

*f*of about 4.3 MHz. This “

_{T(COMP)}*f*” does not work like our previous encounters since the open-loop gain does

_{T}*not*roll off at a constant -20 dB/decade. In this instance, we are finding the bandwidth graphically.

The composite amplifier open-loop response can be verified using Multisim. The circuit is provided in Figure 20. Capacitor *C _{1}* is used to eliminate the negative feedback. The permits us to obtain the open-loop amplitude frequency response of the composite amplifier.

The open-loop frequency response is given in Figure 21. In Figure 21(a) the cursor is positioned to verify the low-frequency open-loop gain. A gain of 135.3 dB is indicated. In Figure 19 a gain of 136 dB was predicted. Figure 21(b) indicates the first corner frequency. It should be -3dB from the low-frequency gain (135.3 dB – 3 dB = 132.3 dB) and is at 28 Hz. (Figure 19 shows the dominant pole at 25 Hz.) Figure 21(c) and (d) are used to verify the slope is indeed -20 dB/decade. The second corner frequency is determined via the cursor in Figure 21(e). This occurs at about 60 dB at 136 kHz, which agrees with the value of 136 kHz indicated in our Bode approximation (Figure 19).

The slope for frequencies beyond 136 kHz becomes -40 dB/decade and moving the cursor to the location where the open-loop gain crosses the 0 dB axis indicates a transition frequency *f _{T(COMP)}* of 4.5 MHz at a gain of 0.118 dB (Figure 21(f)), which is reasonable compared to the 4.3 MHz value indicated in Figure 19.

The Bode approximation of the closed-loop frequency response plot is shown in Figure 22. The closed-loop gain of 1000 (60 dB) is superimposed on the open-loop response of the composite amplifier. The intersection between the closed-loop gain and the open-loop response provides the crossing frequency *f _{c}.* (The crossing frequency is the point at which the loop gain response crosses the 0 dB or unity point.) The circuit has been designed to have the closed-loop gain intersect at the second corner frequency

*f*.

_{H2}The crossing frequency *f _{c} *permits

*us to calculate the crossing angle*

*q*

*. The crossing angle is used to find the phase margin*

_{c}*q*

*. The phase margin determines the stability of the amplifier circuit and determines any peaking that might occur in the frequency response.*

_{pm}A phase margin of 45 degrees is stable but will result in some slight peaking. The Multisim circuit and the closed-loop response are provided in Figure 23.

Larger (greater than 45 degrees) phase margins improve stability but make the amplifier response more “sluggish”. Smaller (less than 45 degrees) phase margins bring the amplifier closer to oscillation. However, the amplifier output can respond more quickly to abrupt changes in the input signal.

The voltage gain of the second stage controls the amount of peaking.** **This is because it determines the second breakpoint in the open-loop frequency response.

Assume the voltage gain of the second stage (*AV2*) in the composite amplifier is ** decreased** from 31.7 to 26.0. (

*R4B*is lowered from 10.7 kâ„¦ to 4.99 kâ„¦.)

The bandwidth (corner frequency) of the second stage will ** increase **from 136 kHz to 165 kHz. This means the second break point of the composite amplifier open-loop response will be moved to 165 kHz.

Consequently, the crossing frequency is much ** lower relative to fH2**. This

**and there will be**

*increases the phase margin***. See Figure 24(a).**

*less peaking*Assume the voltage gain of the second stage (*Av2*) of the composite amplifier is ** increased** from 31.7 to 51.0. (

*R4B*is increased from 10.7 kâ„¦ to 30 kâ„¦.)

The bandwidth (corner frequency) of the second stage will ** decrease **from 136 kHz to 84.3 kHz.

As a result, the crossing frequency is much ** higher relative to fH2**. This

**and there will be**

*decreases the phase margin***. See Figure 24(b). The relationships are summarized in Figure 25.**

*more peaking*# Review and Conclusions

A composite amplifier employs local (sometimes called “nested”) negative feedback as well as an overall negative feedback loop. By using a resistive network like that incorporated in a non-inverting amplifier to provide DC biasing, and a very large capacitor to eliminate any negative feedback, the open-loop frequency response of an amplifier can be obtained using Multisim. To maximize the bandwidth of a composite amplifier, the voltage gains of the individual stages are made equal. In the case of two stages, we take the square root of the desired overall gain, and in the case of three stages, a cube root is required. A quick inspection of closed-loop stability can be conducted. If the second stage closed-loop gain is superimposed on the open-loop response, the slope at the intersection yields an indication of stability. The same stability rules apply to the overall voltage gain of the composite amplifier. An intersection where the slope is -20 dB/decade is stable, at -40 dB/decade is marginally stable, and at -60 dB/decade or greater is unstable and will quite likely oscillate.

The intersection of the second stage gain with the composite amplifier open-loop response will produce a second corner frequency. The open-loop corner frequency pole and the second corner frequency pole can contribute up to -180^{o} of phase shift which reduces the phase margin. Small phase margins produce pronounced peaking in the composite amplifier’s frequency response. Large phase margins reduce and can eliminate peaking in the composite amplifier’s frequency response. The voltage gain of the second stage can be used to control the phase margin by moving the second corner frequency. More gain means more peaking while less gain results in less peaking.

In the fourth and final part of this series, we’ll explore the DC offset and AC noise reduction made possible by composite amplifiers. These capabilities are why the composite amplifier provides a superior performance when compared to the cascaded amplifier approach.