1. Active Analogue Circuits Year 2 B. Todd Huffman

2. CP2 Circuit Theory Revision Lecture Basics, Kirchoff’s laws, Thevenin and Norton’s theorem, Capacitors, Inductors AC theory, complex notation, LCR circuits Passive Sign Convention (NEW!!!) Example of PSC use (also NEW) Good Texts: Electronics Course Manual for 2 nd year lab. “Art of Electronics” by Horowitz and Hill October 2013 Todd Huffman

3. Passive Sign Convention Passive devices ONLY - Learn it; Live it; Love it! R=Resistance Ω[ohms] Which way does the current flow, left or right? Two seemingly Simple questions: Voltage has a ‘+’ side and a ‘-’ side (you can see it on a battery) on which side should we put the ‘+’? On the left or the right? Given V=IR, does it matter which sides for V or which direction for I?

4. V0V0 I R1R1 R2R2 R3R3 -V 0 +IR 1 +IR 2 +IR 3 =0 + + + + – – – – –V 0 +IR 1 +IR 2 +IR 1 I1I1 I3I3 I2I2 I4I4 I 1 +I 2 –I 3 –I 4 =0 Kirchoff’s laws

5. Capacitors C +Q -Q Q = CV Capacitors resist change in voltage Capacitors in series Capacitors in parallel Stored energy stored in form of electric field C1C1 C2C2 CNCN

6. Inductors Inductors in series Inductors in parallel Stored energy stored in form of magnetic field L “back emf” Self- inductance Inductors resist a change of current L1L1 L2L2

7. AC circuit theory Voltage represented by complex exponential Impedance relates current and voltage V=ZI in complex notation: Resistance  R Inductance  jL Capacitance 1/jC and combinations thereof Impedance has magnitude and phase represented by real component of easily shown from Q=VC

8. Current is given by So |Z| gives the ratio of magnitudes of V and I, and  give the phase difference by which current lags voltage

9. Op-amps Gain is very large (A) Inputs draw no current (Z IN =) Feedback  v + =v – V OUT + – v+v+ v–v– V IN R1R1 R2R2 Non-Inverting Amplifier Circuit + V OUT V IN R1R1 Inverting Amplifier Circuit R2R2 – v–v– v+v+ i i

10. First Non-ideal model + - A(  )  V + VV Instead of infinite gain, the device has finite, and frequency dep. Gain. V0V0 - +

11. A(  ) behaves like an RC filter. Magnitude |A(  )| Phase  A (  ) With a gain factor of over a million; and a roll-off around  = 1 rad/s A(  ) ≈ 10 6 /(1+j  )

12. Model of this non-ideal gain curve V x = A 0 V 1 KCL (V 2 – V x )/R + j  CV 2 = 0 – Substitute expression for Vx above and some algebra V 2 (1 + j  CR) = A 0 V 1 V 2 /V 1 = A 0 /(1 + j  CR) ≡ A(  ) A0A0 R CV1V1 V2V2 VxVx Note: Also Draw filter on Blackboard

13. How does this effect our negative feedback circuits? KVL V R1 –  V – V in = 0 V R2 +  V + V 0 = 0 KCL V R1 /R 1 = V R2 /R 2 And also the Gain relationship  VA(  ) = V 0 Solve on board + V OUT V IN R1R1 Inverting Amplifier Circuit R2R2 – v–v– v+v+ i i

14. The Transistor!

15. Simple Transistor Model It can be a “switch” – Flow is “on” one way – Flow is “off” the other way It can be an amplifier – The flow is proportional to the amount you turn the valve. – If you turn the valve fast enough you can communicate in Morse- Code-litres

16. Bipolar Junction Transistor curves On black board!

17. v BE Model works for npn and pnp (follow passive sign conv. on resistor) + – First Transistor Small Signal Model g m v BE  /g m base collector emitter Typical npn form shown