EXPERIMENT 7 NEGATIVE FEEDBACK and APPLICATIONS

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1 PH315 A. La osa EXPEIMENT 7 NEGATIE FEEDBACK and APPLICATIONS I. PUPOSE: To use various types o eedback with an operational ampliier. To build a gaincontrolled ampliier, an integrator, and a dierentiator. II. THEOETICAL CONSIDEATIONS II.1 FEEDBACK In control systems, eedback consists in comparing the output o the system with the desired output and making a correction accordingly. 1 Negative eedback Negative eedback is the process o coupling a portion o the output back into the input, as a way to cancel part o the input. This process, it turns out, has the eect o reducing the gain o the ampliier, but, in exchange, it improves other characteristics including reedom rom distortion and nonlinearity, latness in the requency response, and predictability. In act, as more negative eedback is used, the resultant ampliier s characteristics becomes less dependent on the characteristics o the original openloop ampliier Positive eedback We have learned rom our C ilter experiment that a phase lag exists between the input and output voltages, which increases as more components are added into the circuit. I a negative eedbackloop circuit were to accumulate large enough phase lag (i.e. greater than 180 o ), then positive eedback occurs (the circuit ends u being an oscillator.) II.2 The GOLDEN ULES (OPEATIONAL AMPLIFIE) When implemented as part o a negative eedback external network, the behavior o the op amp can be predicted (or many practical purposes) based on two simple rules: 2 ule I The output attempts to do whatever is necessary as to produce that the external eedback brings the dierential input voltage close to zero. ule II The inputs draw no current. Dierential input voltage v v i i = = A (v v ) CC CC /A ~ 120 CC /A CC Ampliying region (v v ) A=A O Fig. 1 Let: Working model o an op amp. ight: egion o linear ampliication o the op amp when operating in a negative eedback network.

2 oltage Gain (in db) oltage Gain (in db) III. EXPEIMENTAL CONSIDEATIONS Applications o negative eedback with operational ampliiers See additional inormation (technical terminology) contained in the ile Operational Ampliiers posted in the website o this course. = 100 k Beore perorming the experiments CC = 12 listed below, review the data sheet o the op amp you are using. In particular, CC check = 12 the slwe rate (it is 0.3 /s or the LM358AP). This I parameter (that tell you how ast tye opamp responds to an input signal) will allow you to estimate the requency bandwidth response o your circuit. gain and close loop gain Gain (in db) v Lowpass_unitygainBandwidth I o v dB Frequency Fig.2. = 100 k Unitygain I T bandwidth A OL = Gain (in db) Close loop voltage 3dB gain Close loop bandwidth Frequency Ideal close loop gain: A CL =10 3 Fig.3 and close loop. T Unitygain bandwidth o = 1 k A CL = Lowpass_unitygainBandwidth = 10 3 k v v CC = out 12 CC =

3 III.1 The Inverting Ampliier Since v is grounded, then ule I implies v = 0. Accordingly, the current through o is equal to I o = / o ; and the current through is then equal to I = /. Since no current lows into the op amp inputs (ule II) we should have I o = I ; that is, / o = /, or simply, out o in a) Construct the circuit shown in Fig, 2, and veriy that indeed the is equal to /. Using a square wave (100 m amplitude) as an input, make two Bode plots, o corresponding to two dierent gains (10 and 100 or example). Check i the 3dB value depends on the gain. b) eriy that i the input signals were interchanged, the circuit will not work. = 100 k o = 10 k I o v v I Fig. 4 DC inverted ampliier circuit. III.2 The Noninverting Ampliier ule I implies v = At the same time, v is part o a voltage divider: v = [ /( 1 2 ] 1 Equating these two expressions, we obtain, 1 2 out 1

4 1 = 2 k 2 = 20 k 1 A CC Fig. 5 Noninverting ampliier. 2 a) Construct the circuit shown in Fig, 3, whose input is a DC voltage, and veriy that the voltage gain is indeed equal to 1 ( 2 / 1 ). Using a square wave (100 m amplitude) as an input, make two Bode plots, corresponding to two dierent gains (10 and 100 or example). Check i the 3dB value depends on the gain. b) Construct the circuit shown in Fig, 4, whose input is an ac signal. Notice the highpass ilter has been added. Choose such that the 3dB point requency o the highpass ilter is 70 Hz. Make a Bode plot o the output voltage vs requency. C= 0.22 F Highpass ilter 1 = 2 k 2 = 20 k Fig. 6 Noninverting ampliier with a highpass ilter at the input. III.3 Dierential Ampliier a) Apply the golden rules to demonstrate that the output voltage o the circuit shown in Fig. 5 is 2 given by, ( 2 1 ). 1 b) Build the circuit shown in Fig, 5 and veriy i the output voltage varies according to the expression given in part a) above.

5 = 20 k 1 = 2 k Fig. 7 Dierential ampliier. III.4 Integrator Op amps allow to make integrators without the restriction that <.(as required when using only and C components.) Since v is grounded, the input v acts as a virtual ground. The current I passing through the resistor is then given by, I = / The current through the capacitor is given by, d d I C ( q) ( 0 ) C dt dt dout C dt ule II implies that I = I C, in dout C dt This implies, 1 t ( t) t ( t') dt' C C= 0.01 F q q = 1 k I Fig. 8 Integrator. I C

6 a) Implement an integrator circuit (Fig.6). Since charging eects can cause serious osets, a parallel resistor p may be needed (to prevent any long term voltage shit at the input). Try dierent values or p. (100K, 1 M). See Fig. 7. b) Test your circuit using a square signal o 1 khz at the input. Investigate the eect o changing the various parameters. p = 1 k C= 0.01 F Fig. 9 Integrator. III.5 Dierentiator The circuitry is similar to the integrator but with the and C reversed. The current through the capacitor is given by, d d I C ( q) ( t C) dt dt din C dt The current through the resistor is given by, I = (0 / ule II implies that I = I C, din out C dt This implies, d out( t) C dt in a) Implement an dierentiator circuit. Test the circuit with triangle waves at the input.

7 = 1 k C= 0.01 F q q I C I Fig. 9 Dierentiator 1 2 (Chapter 4) Horowitz and Hills, The Art o Electronics. 2 nd Ed.; Cambridge University Press (1990). (Page 177) Horowitz and Hills,