18Lab 10: Feedback and OscillationU.C. Davis Physics 116AINTRODUCTIONThis lab consists of two parts. Both showsome property of feedback. The Wien bridgeoscillator illustrates how a feedback amplifier canbecome an oscillator. The class B output stageexperiment shows how negative feedback canreduce distortion.1. WIEN BRIDGE OSCILLATORHere, positive feedback is demonstrated byturning an op amp into an oscillator. Thecondition for oscillation in a feedback amplifieris discussed in Sec. 10.4 of Bobrow. Thiscircuit, the Wien bridge oscillator, is covered inpp. 695-697.The gain of a feedback amplifier, AF, isgiven by AAABF=+1,where A is the amplifier gain and B is the gain ofthe feedback network (assumed to providenegative feedback). The loop gain is defined asthe product, AB. The amplifier becomes anoscillator (a circuit which produces an output atsome frequency with no external input) if AB=-1,so that the denominator on the right vanishes. This property of feedback amplifiers is usedin the basic Wien bridge oscillator shown in Fig.1. We now calculate the oscillation frequency,the frequency at which AB = -1._+ out vR2R1}}Z1Z2RRCCFigure 1: Wien bridge oscillator.The two resistors R1 and R2 determine thegain, ARR=+121, of a noninvertingamplifier. The two complex impedancesZjCR11=+ω and ZRjCRjC211=+ωωprovide positive feedback since they feed backinto the + input. To be consistent with ourformula for AF (negative feedback), we need aminus sign in the expression for B (positivefeedback means B is negative):BBjZZZ==−+()ω212.To have an oscillator, AB = -1. This putsconditions on R, C and ω and on A. For yourreport, prove BRCRC j R C=−−−ωωω31222().For AB = -1, we need ω = 1/RC (since theimaginary part of the result is zero) so B = -1/3.Thus we choose R1 and R2 so that A = 3.Unfortunately, this oscillator will notproduce a clean sinusoidal output because theamplitude will build up until the amplifiernonlinear region is reached. We need to introduceadditional components to keep the amplitudeconstant and within in the linear range of the op-amp, as is described on the next page.19_+ out vR'R'}}Z1Z20.8 0.810k ΩR' 60.15 R'RCCRFigure 2: Wien bridge oscillator with controlled amplitude.We now modify the circuit (as shown inFig. 2, above) by setting the gain slightly toohigh and adding another resistor which isconnected in parallel with the feedback resistorwhen some maximum amplitude (set by the twozener diodes) is exceeded. This reduces the gainuntil the amplitude falls below the Zenerthreshold again. In this way, the outputamplitude remains fairly stable near the Zenerthreshold. The value of R' is about 6k and theintended values of the fractional R's are:633RRR'= k0.8 '= 47000.15 '=1kΩΩΩAdjust the potentiometer to get differentamplitudes of oscillation. Find the frequency andamplitude of the maximum amplitudeoscillation. For your lab report, sketch thiswaveform and measure its frequency. Comparethis to the theoretical value.2. CLASS B OUTPUT STAGE ANDREDUCTION OF DISTORTIONWITH NEGATIVE FEEDBACKThis section demonstrates a push-pull orclass B amplifier. It is described in Bobrow, pp.629-635. The purpose of such an amplifier is toget a greater output power while using lesspower supply power. Look at the circuit of figure 3. Compare theoutput waveform with the feedback resistor R2connected to points A and vout in the circuit.Note the very obvious "crossover distortion" inthe A configuration and the much improvedoutput in the vout configuration. Try toqualitatively explain why the first configurationhas this distortion and why it is improved by thesecond configuration._+vout100k 10kΩΩin Ato A or voutΩ330+15V-15V2N39042N3906R 1= 1kΩR2Figure 3: Inverting amplifier with class B output stage.Connect R2 to vout to observe the effect of negative feedback in reducing