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lecture 2&3: Amplifiers The heart of EE Lecture outline Ideal Op-Amp Reading: Negative Feedback 1)Hambley Ch 1,2, section 8.1 Application to Filters 2) Lab 2 handout Linear systems Bode plots Op-amp nonidealities Positive feedback Amplifiers They are everywhere: Music, Computers, Sensors Used to turn a small voltage into a bigger voltage that can be manipulated easily. Some filtering is used as well. amplifiers give gain Simple amp-1 input and 1 output Gain, A=Vout/Vin Example If the amplifier above gives an output voltage of 1000V with an input voltage of 50V, what is the gain? ideal operational-amplifier (op-amp) http://www.youtube.com/watch?v=TQB1VlLBgJE Inputs draw no current-infinite input impedace Vout=A(Vplus-Vminus) A-open loop gain. A is ideally infinity-How is this useful? Output can provide as much voltage/current as needed-zero output impedance negative feedback Negative feedback (NF) tries to reduce the difference with NF, Vplus=Vminus ALWAYS summing point constraints virtual ground. Inverting amplifier Input goes into Vminus input-INVERTING input Gain, Ainv=-R2/R1, gain is negative because inverting inverting amplifier Vplus=Vminus Inputs draw no current Non-inverting amplifier Input goes into Vplus input-NON-INVERTING input Gain, Ainv=1+R2/R1, gain is positive unity gain buffer Gain is 1 i.e. Vin=Vout Used to isolate one side from the other Real op-amps http://www.national.com/mpf/LM/LM324.html#Overview Quad LM324 Single LM741 Output voltage determined by rails (power supply) Open loop gain not infinity Inputs draw small amount of current-nA’s or less bandpass Filter amplifier f1=0.3Hz, f2=10Hz High freq., cap is short, low freq., cap is open frequency<f1 all caps are open. What is the gain? F1<Frequency<F2 C1 is short. C2 is open. What is the gain?-midband gain. frequency>f2 All caps are shorts What is the gain? linear systems T(s) has zeros when T(s)=0 T(s) has poles when T(s)=infinity linear systems Any voltage signal can be represented by a sum of sinusoidal voltage signalsFourier/Laplace theorems If s=jω, the input voltage is represented by: V0exp(jωt)= V0exp(st) Allows us to use algebra instead of differential eqns. RLC circuit, for example. t t t t filter op-amp What is T(s)? filter op-amp zero at s=0 poles at 1/R1C1 and 1/R2C2 What happens at the zero? At the poles? bode plots Frequency response on log/log axes x-axis frequency on log scale y-axis gain in decibels (dB) gain in dB=20log|Vo/Vi| 20dB/decade will appear often. Can sketch quickly without doing too much math bode plot rules See Hambley section 8.1 Zeros of transfer function +20dB/decade increase in gain starting at zero phase contribution at zero frequency is +45° Total phase change is 90° attained at 10 times zero freq. Poles of transfer function -20dB/decade decrease in gain starting at zero phase contribution at pole frequency -45° Total phase change is -90° attained at 10 times pole freq. bode plot errors Bode magnitude plot only has straight lines not true near break frequencies ~3dB error Bode phase plot only has straight lines not true for phase near break frequencies ~5° error Bode plot of filter Zero at s=0, poles at s=1/R1C1 and 1/R2C2 Gain at midband =R2/R1or 20log(R2/R1) dB midband, inverted output so phase=180° bode plot of filter 180 135 90 op-amp non-idealities Slew rate -maximum rate of change of voltage at output-arises from compensating capacitor i.e. dv/dt|max If input voltage changes too quickly, op-amp can’t keep up-leads to distortion of output. Gain-bandwith product-high frequency, lower gain. AOLfOL=ACLfCL HINT for prelab! Eqn 2.39 Unity gain frequency Positive feedback http://en.wikipedia.org/wiki/Schmitt_trigger Amplifies differences, so output is always +/-Vcc Schmitt trigger Standard Schmitt Inverting Schmitt Switches between 2 output rails +/-M. Switch when inputs equal each other Use resistors to control this Inverting and non-inverting Schmitt triggers inverting schmitt trigger Vtrigger=+/-VR2/(R1+R2) Input into inverting input Schmitt application Does this represent inverting or non-inverting Schmitt? To minimize switching too often in noisy environment e.g. Thermostat-switch only when T=+/-1degree EE SHORT: Tubes vs. OpAmps http://www.youtube.com/watch?v=PbJ1GZMi_ho Old amplifiers used tubes-BIG! New amplifiers use op-amps. Compact, high performance more transfer functions & Timer circuits frequency response cont.