1. Announcements Tuesday’s Lecture next week is cancelled –October 18 th Assignment 4 is active, due in my mailbox by 5pm Friday (October 14 th ) Mid-term Thursday, October 27 th

2. Project Dates Project Description - one paragraph, plus circuit diagrams and web links – email to me by Tuesday Nov 1st Guidelines and a few useful links are here: http://www.physics.udel.edu/~jholder/Phys645/Lab/Projects.ht m. There are many more sites if you search the web (e.g. google “hobby electronics”) http://www.physics.udel.edu/~jholder/Phys645/Lab/Projects.ht m Kits are allowed, but circuits must be assembled on the prototyping board. $50 maximum budget. Once approved, I will need a complete parts list, with digikey or radioshack catalog part numbers. I will place the orders, but FINDING THE CORRECT COMPONENTS AND GETTING THEM IN TIME IS YOUR RESPONSIBILITY!!! Note that most basic components (resistors, capacitors etc.) are available in the lab. The project should (ideally) contain both analog and digital You should work with your lab partner, but individual reports are required for the projects. The project counts for 20% of your final grade (I grade them) I will leave copies of some good past projects in the lab (please don’t take them away)

3. Lecture 12 Overview Op amp circuits –amplifiers –Adding/ Subtracting –Integrating Circuit –Differentiating Circuit –Active Filters

4. Recap: Opamps DC coupled, very high gain, differential amplifier. Feed part of the output back into the inverting input to get stable operation in the linear amplification region Golden rules under negative feedback: The voltage at the inputs is the same (v + =v - ) No current flows into the opamp (i + =i - =0)

5. Op amp circuit 2: Inverting Amplifier Signal and feedback resistor, connected to inverting (-) input. v + =v - connected to ground v + grounded, so:

6. Op amp circuit 3: Summing Amplifier Same as previous, but add more voltage sources

7. Summing Amplifier Applications Adds signals from a number of waveforms Applications - audio mixer http://wiredworld.tripod.com/tronics/mixer.html Can use unequal resistors to get a weighted sum For example - could make a 4 bit binary - decimal converter 4 inputs, each of which is +1V or zero Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights)

8. Op amp circuit 4: A non-inverting amplifier Feedback resistor still to inverting input, but no voltage source on inverting input (note change of current flow) Input voltage to non-inverting input

9. Op amp circuit 5: Differential Amplifier (subtractor) Useful terms: if both inputs change together, this is a common-mode input change if they change independently, this is a normal-mode change A good differential amp has a high common-mode rejection ratio (CMMR)

10. Differential Amplifier applications Very useful if you have two inputs corrupted with the same noise Subtract one from the other to remove noise, remainder is signal Many Applications : e.g. an electrocardiagram measures the potential difference between two points on the body The AD624AD is an instrumentation amplifier - this is a high gain, dc coupled differential amplifier with a high input impedance and high CMRR (the chip actually contains a few opamps) http://www.picotech.com/applications/ecg.html

11. How do we build a voltage integrator? So, use a capacitor to get v O as a function of ∫i dt. Need to convert input voltage v I to current. Resistor works poorly (current through resistor depends on output voltage) This is what we want: Output voltage = input voltage integrated over time Remember the capacitor? Circuit element which integrates current

12. First Attempt: Use a resistor For a good integrator RC>>1, v OUT <<v IN But v O must be small compared to v R

13. Op-amp approach Converts the input voltage to a current, which is what we need for an integrator. For a constant input voltage, the circuit sends a constant current through the load, regardless of its resistance. voltage controlled current source "virtual ground"

14. Op-amp integrator

16. Integrator Application: Ramp Generator Integrator response to a constant voltage: V IN V OUT t This is a ramp generator - very useful in timing circuits... V V What's the integrator response to a square wave?

17. Integrator Application: Ramp Generator Integrator response to a constant voltage: V IN V OUT t t This is a ramp generator - very useful in timing circuits......Useful for waveform generators: V V V IN V OUT What's the integrator response to a square wave?

18. What does this do?

19. Op-amp differentiator

20. Differentiator Differentiator response to a square wave?:

21. Differentiator Application: edge detection Differentiator response to a square wave?: The differentiator is good at detecting edges, or transitions - very useful in digital circuits. V IN V OUT t N.B. Don't confuse the differentiator with a differential amplifier (subtractor)!

22. Other "mathematical operator" circuits can be easily constructed: Logarithm Antilogarithm Multiplier Divider Square root function

23. What about complex impedances?

24. Active low-pass filter e.g. R F /R S =10; 1/R F C F =1 Max Amplification: R F /R S Low pass factor: 1/(1+ jωR F C F ) Cut-off frequency (-3dB = 1/√2) when ωR F C F =1, ie ω 0 =1/R F C F

25. Active high-pass filter e.g. R F /R S =10; 1/R F C F =1 Max Amplification: R F /R S High pass factor: 1/(1+ 1/jωR S C S ) Cut-off frequency: ωR F C F =1

26. Active band-pass filter Combine the two: Advantages of active filters: 1)no inductors (large, pick-up) 2)buffered (high input impedance, low output impedance) – so filter performance independent of source and load; can cascade filters