lecture 2&3: Amplifiers The heart of EE

Lecture outline Ideal Op-Amp Negative Feedback Application to Filters Linear systems Bode plots Op-amp nonidealities Positive feedback Reading: 1)Hambley Ch 1,2, section 8.1 2) Lab 2 handout

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) 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 Output voltage determined by rails (power supply) Open loop gain not infinity Inputs draw small amount of current-nA’s or less Quad LM324 Single LM741

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 signals- Fourier/Laplace theorems If s=jω, the input voltage is represented by: V 0 exp(jωt)= V 0 exp(st) Allows us to use algebra instead of differential eqns. RLC circuit, for example. t t tt

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 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. See Hambley section 8.1

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

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. A OL f OL =A CL f CL HINT for prelab! Eqn 2.39 Unity gain frequency

Positive feedback Amplifies differences, so output is always +/-Vcc

Schmitt trigger 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 Standard Schmitt

inverting schmitt trigger Vtrigger=+/-VR2/(R1+R2) Input into inverting input

Schmitt application To minimize switching too often in noisy environment e.g. Thermostat-switch only when T=+/-1degree Does this represent inverting or non-inverting Schmitt?

EE SHORT: Tubes vs. Op- Amps Old amplifiers used tubes-BIG! New amplifiers use op-amps. Compact, high performance

more transfer functions & Timer circuits frequency response cont.