Department of EECS University of California, Berkeley EECS 105 Fall 2003, Lecture 19 Lecture 19: Frequency Response Prof. Niknejad

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley 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

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley 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:

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley 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 R S )

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley CE Amplifier with Current Input Find intrinsic current gain by driving with infinite source impedance and Zero load impedance…

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Short-Circuit Current Gain Small-signal short circuit (could be a DC voltage source) Pure input current (R S = 0  ) Substitute equivalent circuit model of transistor and do the “math”

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Small-Signal Model: A i Note that r o, C cs play no role (shorted out)

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Phasor Analysis: Find A i KCL at the output node: KCL at the input node: Solve for V  :

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Phasor Analysis for A i (cont.) Substituting for V  Substituting for Z  = r  || (1/j  C  )

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Short-Circuit Current Gain Transfer Function Transfer function has one pole and one zero: Note: Zero Frequency much larger than pole:

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Magnitude Bode Plot 0 dB pole Unity current gain zero

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Transition Frequency  T Limiting case: Dependence on DC collector current: Base Region Transit Time!

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Common Source Amplifer: A i (j  ) DC Bias is problematic: what sets V GS ?

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley CS Short-Circuit Current Gain Transfer function:

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley 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

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley 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)

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley 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

EECS 105 Fall 2003, Lecture 19Prof. A. Niknejad Department of EECS University of California, Berkeley Miller Equivalent Circuit We can “de-couple” these terminals if we can calculate the gain A v 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 Note: