Lecture 19: Frequency Response

1. Lecture 19:Frequency Response Prof. Niknejad

2. Lecture Outline • Finish: Emitter Degeneration • Frequency response of the CE and CS current amplifiers • Unity-gain frequency T • Frequency response of the CE as voltage amp • The Miller approximation University of California, Berkeley

3. Typical “Discrete” Biasing • A good biasing scheme must be relatively insensitive to transistor parameters (vary with process and temperature) • In this scheme, the base current is given by: • The emitter current: University of California, Berkeley

4. Gain for “Discrete” Design • Let’s derive it by intuition • Input impedance can be made large enough by design • Device acts like follower, emitter=base • This signal generates a collector current Can be made large to couple All of source to input (even with RS) University of California, Berkeley

5. CE Amplifier with Current Input Find intrinsic current gain by driving with infinite source impedance and Zero load impedance… University of California, Berkeley

6. Short-Circuit Current Gain Small-signal short circuit (could be a DC voltage source) Pure input current (RS = 0 ) Substitute equivalent circuit model of transistor and do the “math” University of California, Berkeley

7. Small-Signal Model: Ai Note that ro, Ccs play no role (shorted out) University of California, Berkeley

8. Phasor Analysis: Find Ai KCL at the output node: KCL at the input node: Solve for V : University of California, Berkeley

9. Phasor Analysis for Ai (cont.) Substituting for V Substituting for Z =r || (1/jC) University of California, Berkeley

10. Short-Circuit Current Gain Transfer Function Transfer function has one pole and one zero: Note: Zero Frequency much larger than pole: University of California, Berkeley

11. Magnitude Bode Plot pole Unity current gain 0 dB zero University of California, Berkeley

12. Transition Frequency T Dependence on DC collector current: Base Region Transit Time! Limiting case: University of California, Berkeley

13. Common Source Amplifer: Ai(j) DC Bias is problematic: what sets VGS? University of California, Berkeley

14. CS Short-Circuit Current Gain Transfer function: University of California, Berkeley

15. MOS Unity Gain Frequency • Since the zero occurs at a higher frequency than pole, assume it has negligible effect: Performance improves like L^2 for long channel devices! For short channel devices the dependence is like ~ L^1 Time to cross channel University of California, Berkeley

16. Miller Impedance • Consider the current flowing through an impedance Z hooked up to a “black-box” where the voltage gain from terminal to the other is fixed (as you can see, it depends on Z) University of California, Berkeley

17. Miller Impedance • Notice that the current flowing into Z from terminal 1 looks like an equivalent current to ground where Z is transformed down by the Miller factor: • From terminal 2, the situation is reciprocal University of California, Berkeley

18. Miller Equivalent Circuit Note: • We can “de-couple” these terminals if we can calculate the gain Av across the impedance Z • Often the gain Av is weakly depedendent on Z • The approximation is to ignore Z, calculate A, and then use the decoupled miller caps University of California, Berkeley