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Department of Information Engineering357 Feedback Op amp golden rules Approximations: 1.Voltage difference between the two inputs is zero 2.Input draws no current Why? –V OUT = A V IN –If V OUT is around 10V, A=10,000, then V IN ~ 1mV, voltage difference ~ 1mV (close to zero) –FET draws virtually zero input current V IN V OUT

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Department of Information Engineering358 Gain of this amplifier? VV

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Department of Information Engineering359 An easier method Because A is so large that V ~ 0 (known as virtual earth) V ~ 0

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Department of Information Engineering360 Inverting amplifier Input impedance (R IN )? –V ~ 0, so R IN = R 1 Important –gain is determined by external parameters that we can control (the resistors) –gain (A) of the op amp can be non-linear, its exact value is not important, as long as it is very large

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Department of Information Engineering361 Negative feedback Feedback MUST be applied to the –ve terminal (–ve feedback), so that V ~ 0 (IMPORTANT) A) Works B) Doesn’t Work

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Department of Information Engineering362 Positive feedback +ve V IN produces large +ve V OUT –+ve V OUT produces +ve V which produces an even larger +ve output. –output reaches max +ve supply voltage very quickly useless as an amplifier (but good as a switch, small +ve signal produces large maximum output)

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Department of Information Engineering363 Non-inverting amplifier R IN ? –infinite ! V-? –V- ~ V IN (V ~ 0) Current through R 1 ? –I=V IN / R 1 Output voltage? – V- VV

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Department of Information Engineering364 Voltage follower Left side circuit (work) –If output is too large, then feedback to the –ve terminal will reduce output to a equilibrium level until V ~ 0 Right side circuit (doesn’t work) –If output is too large, then feedback to the +ve terminal will make the output even larger until saturation

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Department of Information Engineering365 Practical circuits A better solution

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Department of Information Engineering366 Practical circuits Summing circuit (an adder) V IN V OUT

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Department of Information Engineering367 V1V1 V2V2 V3V3 I

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Department of Information Engineering368 Practical circuits (a simple digital-to-analog converter) V OUT = A+2B-3C

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