# 5.4 - 5.4 Application II Operational Amplifiers Open-Loop...

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74 5.4 Application II: Operational Amplifiers Open-Loop Configuration + Inverting input Non-inverting input + Power supply Output Input for null adjustments Gain = A e out e a e b Normally omit the power supply and null adjustment inputs Characteristics of op-amps Ideal Op-Amps Real Op-Amps (Typical LF411 specs) Infinite gain for all frequencies 2 x 10 5 (depends on frequency, f ) Infinite input impedance, Z in Z in = 10 12 Ω Zero output impedance, Z out 10-50 Ω No phase shift Δφ depends on f No input or output limitations Max. V in = ± 15V, Max. i out =25 mA Zero biasing current 50 pA needed to drive e out to zero when e a =0 Zero voltage offset 0.8 mV No noise generated Noise always a problem. Noise 1/\$ Infinitely fast response Time constant, μ = Ο( 10 2 ) μ sec

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75 Figure 1. 741 Op-Amp. Physical appearance (it's just a chip!) and schematic pin-out. Frequency response of open-loop op-amp Op-amp behaves according to the 1st order equation: () o oa b de eA ee dt μ ⎛⎞ += ⎜⎟ ⎝⎠ where μ = op-amp's time constant ( 160 μ sec) A = Gain of op-amp Arbitrarily set e a = 0 and e b = E b exp i ω t ( i.e. a sine wave), then e o = E o exp i t (what comes out looks pretty much like what comes in) Using 1st order eq. above, oo b iE E A E + = 1 1 o b o b E iA E EA Ei ωμ + = = + We want the modulus of E o /E b , o b E E ( ) 22 1 1 11 1 o b Ai i i μω =⋅ = +− + 1 2 , o b A E ⎧⎫ ⎪⎪ =+ ⎨⎬ ++ ⎩⎭
76 22 1 o b EA E ωμ = + Notice the expected behavior as the frequency of the input signal, ω , increases. Note that this is for open-loop amps only , i.e., no outside networks!

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5.4 - 5.4 Application II Operational Amplifiers Open-Loop...

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