ECE 3336 Introduction to Circuits & Electronics

1. ECE 3336 Introduction to Circuits & Electronics Set #14 MORE on Operational Amplifiers Fall 2012, TUE&TH 5:30-7:00 pm Dr. Wanda Wosik

2. Basics of Operational AmplifiersNoninverting Case We will focus on operational amplifiers, specifically on • Ideal Operational Amplifiers, definitions and requirements for their ideal operation in noninverting configuration • Negative Feedback that allows for op-amp to be controlled by external elements

3. Solving Op Amp Circuits As for inverting configuration we will have two assumptions for the analysis and design. We will again treat the op amps as ideal circuits. We will again call these assumptions golden rules. • The first assumption: i- = i+ = 0.results from large resistances at the inputs. Currents do not flow into the op-amp. • The second assumption v+≈v- deals with the output that makes the input voltages equal v+≈v-. This is realized by introducing negative feedback loop, which spans the output and the inverting input. iin=0A negative feedback loop

4. A Note on the Second Assumption The second golden rule v- = v+results in the virtual short, or the summing-point constraint. The constrain refers to the input voltages, which become the same v- = v+ if there is the negative feedback and the open loop gain Av(OL) is large. Without negative feedback, even a small input voltage will cause saturation of the output either at V+ or V-. That depends on the sign of vin. Negative dc power supply NO NEGATIVE FEEDBACK yet Inverting Input Output Noninverting Input This is open loop configuration + dc V supply

5. Op Amp Circuits with the Negative Feedback Loop Negative feedback adds a portion of the output signal to the inverting input. Since the signs of these voltages are opposite, the negative feedback acts as if the signal applied to the input decreases. The net result is that the output voltage can be controlled by the external elements and does not saturate. Negative feedback For ideal op-amps we will apply two golden rules to solve circuits ideal Golden Rules 1)i- = i+ = 0. 2) v- = v+. Virtual short

6. Op Amp in the Non-inverting Configuration These comments are identical as for the inverting configuration An op amp operates in the noninverting configuration when the input voltage is applied to the noninverting terminal. RF is the feedback resistor Rs is the source resistor • There is a negative feedback thanks to RF • Negative feedback gives the virtual short:v-=v+. Since v+=Vs also v-=Vs. • The op-amp does not draw currents iin=0A ideal Av(OL)≈∞

7. Solving op-amp in the Non-Inverting Configuration Closed Loop As earlier, to find vout we have to find vRF. To find vRF we have to know current iFwhich can be calculated from is. The current is is given by the voltage v-=Vs and Rs. Since we have golden rules (iin=0, v+=v-) v+=vS 0A ideal 0A Av(OL)≈∞ v+=vS Closed loop voltage GAIN:

8. Significance of the Closed Loop Gain The negative feedback loop, combined with ideal properties of the op-amp (high open loop gain 105-107 and large input resistance) ensures that • the gain does not depend on the op amp • the gain is the determined by a ratio of two resistors connected to the op-amp. No phase change ideal

9. Voltage Follower Golden rules apply: v+=v- and iin=0A • Important application of the noninverting configuration is obtained when there is no resistance in the negative feedback loop. RF=0Ω So, the voltage at the input is the same as the voltage at the output vout=vS. Do we gain anything here by doing that? VS ideal VS We do! We have a very large input resistance of this circuit: • Such op-amps do not showloading effects (i.e. voltage drop due to low resistance connected to an output of a circuit). • They work as voltage follower but they also act as impedance buffers.

10. The Differential Amplifier • This is a combination of inverting and noninverting configuration. As earlier we have negative feedback and the op-amp is ideal. i2=-i1 v-=v+ iin=0 Group and arrange:

11. Instrumentation Amplifier (IA) IA are made as integrated circuits Now use the results from differential op-amp vout1 iin=0 iin=0 v1 iR1 v2 iin=0 vout2 Advantages: Very high input resistance Very high common-mode-rejection-ratio CMMR (goal: CMMR  for perfectly matched resistors. That results in vout≈0V for v1=v2)

12. Integrator The integrating circuit was used earlier Now we add the op-amp and we get an integrator. It also constitutes a part of an analog computer The Golden Rules are used for the op-amp Now we integrate both sides and we have the integrator Virtual short

13. Differentiator The differentiating circuit was used earlier Now we add the op-amp and we get a differentiator. It also constitutes a part of an analog computer. The Golden Rules are used for the op-amp

14. Active Filters • The concept of frequency dependence of the signals seen in the filters (remember that we had |H(j)|max=1 for those filters) is here combined with the signal amplification. • We will use here the negative feedback configuration • We will also use impedances instead of resistors • We still have the same golden rules: • no input currents (high Rin) • virtual short

15. Active Low-Pass Filter The voltage gain ALP is calculated using Golden Rules Amplification Cutoff frequency 0V Amplification So the cutoff frequency is also the 3dB frequency (as before) -3dB Phase is just like for the simple filter

16. Negative feedback Inverting configuration Active High-Pass Filter The voltage gain calculated using Golden Rules cutoff Amplification -3dB 3dB frequency Phase: Phase is just like for the simple high pass filter

17. Op-Amp as a Level Shifter A useful circuit to adjust DC voltage level = to remove the DC offset from the signal Use the superposition principle (one source at a time) 220kΩ 10kΩ inverting noninverting Power supply We can design such precision voltage sources using Rp We want this to be equal 0V That gives Vref=1.714V Potentiometer

18. Negative feedback Inverting configuration Active Band-Pass Filter The voltage gain ABP is again calculated using Golden Rules Three characteristic frequencies Relations between the frequencies Magnitude of ABP @1 1 is the unity gain frequency

19. Characteristic Frequencies in the Band-Pass Filters The voltage gain has 3 characteristic frequencies: 1, LP and HP =0 =0 Gain around LP -3dB Gain around HP -3dB Cancel off 0 So LP and HP are 3dB frequencies while 1 is the unity gain frequency

20. Bode Plots for the Active Band-Pass Filter We can plot the magnitude of the voltage gain as a function of frequency Linear scale dB scale LP HP LP HP 1 1 Relations between the frequencies 45° -45° The phase is like for simple bandpass filters LP HP

21. Limitations of the Op-Amps Saturation of the voltage at the output occurs at about ±Vs. Small signals at the input are required

22. Limitations of the Op-Amps Frequency Response Limits refer to the voltage gain of the open loop and closed loop configuration Open loop gain decreases very quickly with frequency The voltage gain decreases in the closed loop configuration but the cutoff frequency increases The gain-bandwidth product is constant K

23. Limitations of the Op-Amps Slew rate limitation of op-amp means that the op-amp output voltage does not respond with the same slope as the input signal Increasing frequency means faster changing or steeper slopes at the zero crossing Slew rate is limited by the frequency and amplitude product As the result of limited slew there is a distortion of the output signal.