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Understanding Op-Ampby Karl Eilers, CATCircuitry – Part 2First a correction: in part 1, figure1, the labels on the inputs are reversed.Here is that figure again,with correct labels. Apologies to anyonewho was confused by this.We concluded the discussion in part 1 with the basic differential-input amplifier,figure 2. This is a very commonly used circuit, but it has a couple ofdrawbacks. First, it is impossible to achieve high gain, high input impedance,high precision and low noise. As shown in the earlier article, to havea high gain the ratio of R3 to R1 must be high. This either means R1 mustbe small, resulting in alow input impedance, orR3 must be very large,resulting in noise. Also,if the op-amp uses bipolartransistors, the DCoffset error will be large.(This is discussed inmore detail below.)Second, the resistances of the signal effectively become part of R1 and R2.For example, if R1=10K and RS1 (source resistance 1) = 1K, that effectivelymeans R1=11K. If accurate measurement is important, this is a problem,because it changes the gain of the circuit. Also, if RS1 is not equal to RS2,this upsets the balancing and ruins the common-mode rejection. RS1 notequal to RS2 is a common occurrence in instrumentation, where a balancedcircuit is often used to measure the voltage of an unbalanced source. In thatcase, one of the inputs would be tied to the source’s ground, so either RS1or RS2 would be zero.filters, but op-amp based filters are often better. These are called “activefilters” because they require a DC power source and use amplifying components.In the circuit in figure 4A, gain rises withfrequency. If we first consider the casewhere RS=0, that is, a piece of wire, wewill have a differentiator, whose outputis proportional to the change in inputvoltage over a period of time:Eq. 2 Vo = - Rf C (dVi / dt)WhereVo = output voltageRf = feedback resistor in ohmsC = input capacitor in faradsdVi / dt = change in input voltage per secondNote the negative sign; this circuit gives a negative output for a rising inputsignal.One problem with this design is that the capacitor reactance and thus inputimpedance varies inversely with frequency. Thus the impedance of the signalsource must be low enough so this variation does not affect the results.Also, the output voltage of the differentiator rises with frequency, theoreticallyto infinity, making the circuit susceptible to high frequency noise.We can’t actually build a true differentiator. A circuit whose gain rises withno limit will be too quirky to use in thereal world. In practical circuits, a gainlimit is set by adding RS in series withthe capacitor. At some high frequency,where the reactance of the capacitorequals RS, the slope of the line changesfrom rising to flat, as shown in figure 4B.This is called the “corner” frequency.Eq. 3 Fc = 1 / 2RsCwhere R is in ohms and C in farads. Replace 1 with 10^6 to work in microfaradsand 10^12 to work in picofarads.These problem can be overcome with the circuit of figure 3, the InstrumentationAmplifier (IA). R5 must equal R6 and R8 should equal R9. AssumingR1 = R2 = R3 = R4, the voltage gain is:Eq. 1 Gv = 1 + 2(R5 / R7)R5, 6 and 7 can be low resistance, solving noise and offset problems. Gainis set by a single resistor, R7, and can be made adjustable. If we use FETinputop-amps, input impedance is set by R8 and R9, which are only thereto keep the input voltages from drifting when the IA is not connected toanything. These can be very high-resistance, resulting in an amplifier withhigh impedance inputs on both sides and making source resistance issuesirrelevant.Filters, Differentiators, IntegratorsIn the preceding circuits, all frequencies are treated equally within the opamp’soperating band. But by adding capacitors, op-amps can make excellentfilters too. Inductors, capacitors and resistors alone can make goodAbove the corner frequency, the circuit approximates a conventional invertingamplifier with gain = Rf / Rs.This circuit can also be used to discriminate against low frequencies. Whenused this way, it is called a “high pass filter.” A better name would be a “lowattenuate filter,” because its function is to attenuate frequencies below Fc.For example, in mobile communication radios, the lower range of the humanvoice occupies more modulation than it’s worth. It is customary to pass theaudio signal through a high pass filter to reserve more modulation for thevoice’s higher harmonics, which actually carry information.Whether this circuit is a differentiator or a high pass filter depends on howwe think of it, and what it is designed to do.In the circuit of figure 5A, which is the mirror-image of the one of figure 4A,output falls with frequency. If we first consider the case where RF is an opencircuit, we will have an integrator. With a changing input voltage, the differentiatorshows us its rate of change at a given instant while the integrator8 | The High-Tech News | JAN/FEB2010