1. L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits” Mc.Graw Hill, 1987, New York npn Bipolar Transistor Low Frequency Characterization Ebers-Moll Equations Parameters: Behaviour of the model 3-terminal element, voltage- controlled, reference? collector base emittor

2. If the reference is chosen as the emittor... L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits” Mc.Graw Hill, 1987, New York Substitute in Ebers-Moll equations Which representation is this?

3. L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits” Mc.Graw Hill, 1987, New York (p. 141)

4. Piecewise-linear model L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits” Mc.Graw Hill, 1987, New York Ideal Model

5. Operational Amplifier (Op-Amp) L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits”, Mc.Graw Hill, 1987, New York

6. o n p Bipolar (µA741)FET (µA740) ~0,2mA~0,1nA L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits”, Mc.Graw Hill, 1987, New York How many terminals does it have? How many equations do we need? Base currents

7. L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits”, Mc.Graw Hill, 1987, New York Ideal Op-Amp -Vd+-Vd+

8. Equivalent model for positive saturation region Equivalent model for negative saturation region

9. Equivalent model for linear region virtual short-circuit

10. Linear Region: + -+ - - + v in vdvd ioio +vo+vo +-+- + -+ - - + v in ioio +vo+vo +-+- vdvd Negative Feedboack Positive Feedback Negative-Positive Feedback Circuits

11. + Saturation Region +vo+vo + E sat v d > 0 + -+ - + v in inin ipip +vo+vo + E sat v d > 0 + -+ - + v in ipip inin Negative FeedbackPositive Feedback

12. - Saturation Region +vo+vo - E sat v d < 0 + -+ - + v in inin ipip +vo+vo - E sat v d < 0 + -+ - + v in ipip inin Negative Feedback Positive Feedback

13. Negative Feedback Circuit Positive Feedback Circuit

14. Some Applications Buffer Aim: No matter how big is the load at the output, the output voltage is the same as the input voltage. Voltage-controlled voltage source valid for

15. Some Applications Buffer Aim: No matter how big is the load at the output, the output voltage is the same as the input voltage. Internal resistance is large for the input and small for the output. This reduces the downloading effect of N 2 onto N 1. Simple analysis.

16. Inverting Amplifier Aim: A signal with small amplitude at the input is amplified at the output with a 180 degree phase shift. Some Applications valid for

17. Non-inverting Amplifier Aim: A signal with small amplitude at the input is amplified at the output without any phase shift. Some Applications valid for

18. Differential Amplifier Aim: Difference between two signals at the input is amplified at the output. Some Applications valid for

19. DC Operating Points N 1-port 2- terminal resistor + _ v i IsIs How many solutions: one more than one no solution + _ v i IsIs + _ v i IsIs unique solution more than one solution

20. + _ v i IsIs no solution Input: value of the independent source Output: voltage or current value of the element under consideration In general, input consists of DC and AC parts. By linearity, one can consider DC and AC solutions seperately. DC operating point is the value of the output when only DC input is considered. How to find DC operating points? ibib iaia NbNb NaNa d1d1 d1’d1’ vbvb vava ++ __ KCL + KVL + EE Solutions of these equations give the DC operating points.

21. L.O. Chua, C.A. Desoer, S.E. Kuh. “Linear and Nonlinear Circuits”, Mc.Graw Hill, 1987, New York Find the DC operating points (E b =2,R b =0.25)

22. Small Signal Analysis + _ v i N VQVQ IQIQ E DC E DC -v m E DC +v m VQVQ IQIQ Find the DC operating point. Find the linearization of the nonlinear element. Assume that the input consists of a DC part and a small AC part: Then the output is If the AC part is small enough we can apply Taylor expansion and consider the linear term only: Linearization

23. Linearization Assumption: Taylor expansion: Small-signal conductivity

24. Find the DC operating points for v R and using the linearization of the nonlinear resistor find an approximate value for v R. 0.02sin(wt)) V (3+

25. Small-Signal Analysis for 2-port nonlinear resistors Find the operating points. Find the linearization of the 2-port. Current-conrolled element equations Operating point

26. Jakobian matrix