FEEDBACK AND OPERATIONAL AMPLIFIERS (Some selected section from CHAPTER 3 of the book "The Art of Electronics", written by Paul Horowitz and Winfield Hill, Cambridge University Press , 1985.)

	BASIC OP-AMP CIRCUITS
	The golden rules for working out op-amp behavior
	Departures from ideal op-amp performance
	Integrators
	COMPARATORS AND SCHMITT TRIGGER
	FEEDBACK WITH AMPLIFIERS
	FEEDBACK AMPLIFIER FREQUENCY COMPENSATION

3.11 Departures from ideal op-amp performance

The ideal op-amp has these characteristics:

1. Input impedance (differential or common mode) = infinity
2. Output impedance (open loop) = 0
3. Voltage gain = infinity
4. Common-mode voltage gain = 0
5. V_out= 0 when both inputs are at the same voltage (zero "offset voltage")
6. Output can change instantaneously (infinite slew rate)

Real op-amps depart from these characteristics in the following ways.
 
 

Input current

The input terminals sink (or source, depending on the op-amp type) a small current called the input bias current, I_B, which is defined as half the sum of the input currents with the inputs tied together (the two input currents are approximately equal and are simply the base currents of the input transistors). For the 741 the bias current is typically 80nA (0.08mA). The significance of input bias current is that it causes a voltage drop across the resistors of the feedback network, bias network, or source impedance.

Op-amps are available with input bias currents down to a nanoamp or less for (bipolar) transistor-input circuit types or down to a few picoamps (10^-6mA) for FET input circuit types. The very lowest bias currents are typified by the superbeta Darlington LM 11, with an input current of 25pA, and the MOSFET ICH8500, with an input current of 0.01 pA. In general, transistor op-amps intended for high-speed operation have higher bias currents.
 
 

Input offset current

Input offset current is a fancy name for the , difference in input currents between the two inputs. Unlike input bias current, the offset current, l_os, is a result of manufacturing variations, since an op-amp"s symmetrical input circuit would otherwise result in identical bias currents at the two inputs. The significance is that even when it is driven by identical source impedances the op-amp will see unequal voltage drops and hence a difference voltage between its inputs. Typically, the offset current is about onetenth the bias current. For the 741, I_offset = 10nA, typical.
 
 

l  Input impedance

Input impedance refers to the differential input resistance (impedance looking into one input, with the other input grounded), which is usually much less than the common-mode resistance (a typical input stage looks like a long-tailed pair with current source). For the 741 it is about 2MW. FET-input op-amps typically have R_in~ 10¹² ohms or more. Because of the input bootstrapping effect of negative feedback (it attempts to keep both inputs at the same voltage, thus eliminating most of the differential input signal), Z_in in practice is raised to very high values and usually is not as important a parameter as input bias current.
 
 

Common-mode input range

The inputs to an op-amp must stay within certain voltage range, typically less than the full supply range, for proper operation. If the inputs go beyond this range, the gain of the op-amp may change drastically, even reversing sign! For a 741 operating from ± 15 volt supplies, the common-mode input range is ± 12 volts. There are op-amps available with common-mode input ranges down to the negative supply (e.g., the LM358, a dual op-amp in mini-DIP package, or the 3130/3140 series) and up to the positive supply (the 301 /307, or the 355-357 series, for instance). In addition, there are maximum allowable input voltages beyond which damage will result. For the 741, they are ± 15 volts or the supply voltages, whichever are less.
 
 

Dífferential input range

Some op-amps allow only a limited voltage between the inputs, sometimes as small as ±0.5 volt, although most are more forgiving, permitting differential inputs nearly as large as the supply voltages. Exceeding the specified maximum can degrade or destroy the op-amp.
 
 

l  Output impedance; output swing versus load resistance

Output impedance R_o means the op-amp's intrinsic output impedance without feedback. For the 741 it is about 75 ohms, but with some low-power op-amps it can be as high as several thousand ohms. Feedback lowers the output impedance into insignificance (or raises it, for a current source); so what usually matters more is the maximum output current, with typical values of 20mA or so. This is frequently given as a graph of output voltage swing V_om as a function of load resistance, or sometimes just a few values for typical load resistances. For the ubiquitous 741, output swings to within about 2 volts of V_CC and V_EE are possible into load resistances greater than about 2k. Load resistances significantly less than that will permit only a small swing. Some op-amps can produce output swings all the way down to the negative supply (e.g., the LM358), a particularly ` useful feature for circuits operated from a single positive supply, since output swings all the way to ground are then possible. Finally, op-amps with MOS transistor outputs (e.g., the CA3130 and CA3160) can swing all the way to both supply rails.
 
 

l  Voltage gain and phase shift

Typically the voltage gain A_vo at dc is 100,000 to 1,000,000 (often specified in' decibels), dropping to unity gain at a frequency (called f_T) of 1 MHz to 10MHz. This is usually given as a graph of open-loop voltage gain as a function of frequency. For internally compensated op-amps this graph is simply a 6dB/octave rolloff beginning at some fairly low frequency (for the 741 it begins at about 100Hz), an intentional characteristic necessary for stability, as you will see in Section 3.31. This rolloff (the same as a simple RC low-pass filter) results in a constant 90° lagging phase shift from input to output (open-loop) at all frequencies above the beginning of the rolloff, increasing to 120 ° to 160 ° as the open-loop gain approaches unity. Since a 180° phase shift at a frequency where the voltage gain equals 1 will result in positive feedback (oscillations), the term "phase margin" is used to specify the difference between the phase ' shift at f_T and 180 ° .
 
 

Input offset voltage

Op-amps don't have perfectly balanced input stages, owing to manufacturing variations. If you connect the two inputs together for zero input signal, the output will usually saturate at either V_CCor V_EE(you can't predict which). The difference in input voltages necessary to bring the output to zero is called the input offset voltage V_os (it's as if there were a battery of that voltage in series with one of the inputs). Usually op-amps make provision for trimming the input offset vottage to zero. For a 741 you use a 10k pot between pins 1 and 5, with the wiper connected to V_EE.

Of greater importance for precision applications is the drift of the input offset voltage with temperature and time, since any initial offset can be trimmed to zero. A 741 has a typical offset voltage of 2mV (6mV maximum) and unspecified coefficients of offset drift with temperature and time. The OP-07, a precision op-amp, is laser-trimmed for a typical offset of 30 microvolts, with temperature coefficient TCV_osof 0.2mV/°C and long-term drift of 0.2mV/month.
 
 

Slew rate

The op-amp "compensation" capacitance and small internal drive currents act together to limit the rate at which the output can change, even when a large input unbalance occurs. This limiting speed is usually specified as slew rate or slewing rate (SR). For the 741 it is 0.5V/ms; a high-speed op-amp might slew at 100V/ms, and the LH0063C "damn fast buffer" slews at 6000V/ms. The slew rate limits the amplitude of a sine-wave output swing above some critical frequency (the frequency at which the full supply swing requires the maximum slew rate of the opamp), thus explaining the "output voltage swing as a function of frequency" graph. A sine wave of frequency f hertz and amplitude A volts requires a minimum slew rate of 2pAf volts per second.

For externally compensated op-amps the slew rate depends on the compensation network used. In general, it will be lowest for "unity gain compensation," increasing to perhaps 30 times faster for x 100 gain compensation. This is discussed further in Section 3.31.
 
 

Temperature dependence

All these parameters have some temperature dependence. However, this usually doesn't make any difference, since small variations in gain, for example, are almost entirely compensated by feedback. Furthermore, the variations of these parameters with temperature are typically small compared with the variations from unit to unit.

The exceptions are input offset voltage and input offset current. This will matter, particularly if you've trimmed the offsets approximately to zero, and will appear as drifts in the output. When high precision is important, a low-drift "instrumentation" opamp should be used, with external loads kept above 10k to minimize the horrendous effects on input-stage performance caused by temperature gradients.

For completeness, we should mention here that op-amps are also limited in common-mode rejection ratio (CMRR), power-supply rejection ratio (PSRR), input noise voltage and current (e_n , i_n) and output crossover distortion. These become significant limitations only in connection with precision circuits and low-noise amplifiers.
 

3.12 Effects of op-amp limitation on circuit behavior

Let's go back and look at the inverting amplifier with these limitations in mind. You will see how they affect performance, and you will learn how to design effectively in spite of them. With the understanding you will get from this example, you should be able to handle other op-amp circuits. Figure 3.28 shows the circuit again.
 

Figure 3-28

 

Open-loop gain

Because of finite open-loop gain, the voltage gain of the amplifier with feedback (closedloop gain) will begin dropping at a frequency where the open-loop gain approaches R₂/R₁ (Fig. 3.29). For garden-variety op-amps like the 741, this means that you're dealing with a relatively low frequency amplifier; the open-loop gain is down to 1000 at 1 kHz, and f_T is 1MHz. Note that the closed-loop gain is always less than the open-loop gain; this means, for instance, that a x 1000 amplifier built with a 741 will show a noticeable falloff of gain for frequencies approaching 1kHz. Later in the chapter (Section 3.24), when we deal with transistor feedback circuits with finite open-loop gains, we will have a more accurate statement of this behavior.
 

Figure 3-29

 

Slew rate

Because of limited slew rate, the maximum sine-wave output swing drops above a certain frequency. Figure 3.30 shows the curve for a 741, with its 0.5V/ms slew rate. For slew rate S, the output amplitude is limited to A (pp) <= S/pf for a sine wave of frequency f, thus explaining the 1/f dropoff of the curve. The flat portion of the curve reflects the power-supply limits of output voltage swing.
 

Figure 3-30

 

Output current

Because of limited output current capability, an op-amp's output swing is reduced for small load resistances. Figure 3.31 shows the graph for a 741. For precision applications it is a good idea to avoid large output currents in order to prevent on-chip thermal gradients produced by excessive power dissipation in the output stage.
 

Figure 3-31

 

Offset voltage

Because of input offset voltage, a zero input produces an output of V_out=G_dcV_os. For an inverting amplifier with voltage gain of 100 built with a 741, the output could be as large as ±0.6 volt when the input is grounded (V_os = 6mV max). Solutions:

1. If you don"t need gain at dc, use a capacitor to drop the gain to unity at dc, as in the RIAA amplifier circuit earlier. In this case you could do that by capacitively coupling the input signal.
2. Trim the voltage offset to zero using the manufacturer's recommended trimming network.
3. Use an op-amp with smaller V_os.

Because of finite input current, zero input voltage still won't give zero output, even if the input offset voltage is trimmed to zero. The inverting input terminal sees a driving impedance of R₁||R₂, so the bias current produces a voltage V_in = I_B(R₁|| R₂), which is then amplified by the gain at dc, -R₂/R₁. For a 741 connected with R₁= 100k and R₂=1MW, the output (for grounded input) could be as large as 10 x 200nA x 91 k, or 0.18 voIt (G_dcI_BR_unbalance;  I_B =200nA max).
 

Figure 3-32

To minimize the effects of input bias current, it is a good idea to ensure that both inputs see the same dc driving resistance, as in Figure 3.32. In this case, 9.1k is chosen as the parallel resistance of 10k and 100k. In addition, it is best to keep the resistance of the feedback network small enough so that bias current doesn't produce large offsets; typical values for the resistance seen from the op-amp inputs are 1k to 100k or so. A third cure involves dropping the gain to unity at dc, as before. If you're still in trouble with errors produced by bias current, use an op-amp with lower bias current. The inexpensive LM308 has I_B=1.5nA (typ), its improved cousin (the LM 11) has I_B=25pA (typ), the popular LF355-LF357 seriés of FET-input op-amps has I_B=30pA, and the recent CA3140 and CA080 series, priced at under a dollar, have I_B = 10pA (typ).
 

Input offset current

Because of input offset current, even a circuit with balanced input impedances at dc will suffer some output offset. This differential effect is usually quite a bit smaller than the output offset produced by input bias current with unbalanced input resistances, so it is worth balancing the input resistances. If the remaining output offset is too large for a given application, the only solution (besides lower resistances in the feed back network) is a lower input current opamp.
 
 

Limitations imply tradeoffs

The limitations of op-amp performance we have talked about will have an influence on component values in nearly all circuits. For instance, the feedback resistors must be large enough so that they don't load the output significantly, but they must not be so large that input bias current produces sizable offsets. High impedances in the feedback network also increase susceptibility to capacitive pickup of interfering signals and increase the loading effects of stray capacitance. These tradeoffs typically dictate resistor values of 2k to 100k with generalpurpose op-amps like the 741.

Similar sorts of tradeoffs are involved in almost all electronic design, including the simplest circuits constructed with transistors. For instance, the choice of quiescent current in a transistor amplifier is limited at the high end by device dissipation, increased input current, excessive supply current, and reduced current gain, whereas the lower limit of operating current is limited by leakage current, reduced current gain, and reduced speed (from stray capacitance in combination with the high resistance values). For these reasons you typically wind up with collector currents in the range of a few tens of microamps to a few tens of milliamps (higher for power circuits, sometimes a bit lower in "micropower" applications).
 
 
 

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