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

Department of Information Engineering358 Gain of this amplifier? VV

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

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

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

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)

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- VV

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

Department of Information Engineering365 Practical circuits A better solution

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

Department of Information Engineering367 V1V1 V2V2 V3V3 I

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