1 / 29

Lecture 15: Small Signal Modeling

Lecture 15: Small Signal Modeling. Prof. Niknejad. Lecture Outline. Review: Diffusion Revisited BJT Small-Signal Model Circuits!!! Small Signal Modeling Example: Simple MOS Amplifier. Large signal. Notation Review.

kert
Download Presentation

Lecture 15: Small Signal Modeling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lecture 15:Small Signal Modeling Prof. Niknejad

  2. Lecture Outline • Review: Diffusion Revisited • BJT Small-Signal Model • Circuits!!! • Small Signal Modeling • Example: Simple MOS Amplifier University of California, Berkeley

  3. Large signal Notation Review • Since we’re introducing a new (confusing) subject, let’s adopt some consistent notation • Please point out any mistakes (that I will surely make!) • Once you get a feel for small-signal analysis, we can drop the notation and things will be clear by context (yeah right! … good excuse) small signal Quiescent Point (bias) DC (bias) small signal (less messy!) transconductance Output conductance University of California, Berkeley

  4. Half go left, half go right Wp Diffusion Revisited • Why is minority current profile a linear function? • Recall that the path through the Si crystal is a zig-zag series of acceleration and deceleration (due to collisions) • Note that diffusion current density is controlled by width of region (base width for BJT): • Decreasing width increases current! Density here fixed by potential (injection of carriers) Physical interpretation: How many electrons (holes) have enough energy to cross barrier? Boltzmann distribution give this number. Density fixed by metal contact University of California, Berkeley

  5. Diffusion Capacitance • The total minority carrier charge for a one-sided junction is (area of triangle) • For a one-sided junction, the current is dominated by these minority carriers: Constant! University of California, Berkeley

  6. Diffusion Capacitance (cont) • The proportionality constant has units of time • The physical interpretation is that this is the transit time for the minority carriers to cross the p-type region. Since the capacitance is related to charge: Distance across P-type base Diffusion Coefficient Mobility Temperature University of California, Berkeley

  7. BJT Transconductance gm • The transconductance is analogous to diode conductance University of California, Berkeley

  8. Transconductance (cont) • Forward-active large-signal current: • Differentiating and evaluating at Q = (VBE, VCE ) University of California, Berkeley

  9. BJT Base Currents Unlike MOSFET, there is a DC current into the base terminal of a bipolar transistor: To find the change in base current due to change in base-emitter voltage: University of California, Berkeley

  10. Small Signal Current Gain • Since currents are linearly related, the derivative is a constant (small signal = large signal) University of California, Berkeley

  11. Input Resistance rπ • In practice, the DC current gain F and the small-signal current gain o are both highly variable (+/- 25%) • Typical bias point: DC collector current = 100 A MOSFET University of California, Berkeley

  12. Output Resistance ro Why does current increase slightly with increasing vCE? Collector (n) Base (p) Emitter (n+) Answer: Base width modulation (similar to CLM for MOS) Model: Math is a mess, so introduce the Early voltage University of California, Berkeley

  13. Graphical Interpretation of ro slope~1/ro slope University of California, Berkeley

  14. BJT Small-Signal Model University of California, Berkeley

  15. BJT Capacitors • Emitter-base is a forward biased junction  depletion capacitance: • Collector-base is a reverse biased junction  depletion capacitance • Due to minority charge injection into base, we have to account for the diffusion capacitance as well University of California, Berkeley

  16. Core Transistor External Parasitic BJT Cross Section • Core transistor is the vertical region under the emitter contact • Everything else is “parasitic” or unwanted • Lateral BJT structure is also possible University of California, Berkeley

  17. Base Collector Emitter Core BJT Model • Given an ideal BJT structure, we can model most of the action with the above circuit • For low frequencies, we can forget the capacitors • Capacitors are non-linear! MOS gate & overlap caps are linear Reverse biased junction Fictional Resistance (no noise) Reverse biased junction & Diffusion Capacitance University of California, Berkeley

  18. Complete Small-Signal Model “core” BJT Reverse biased junctions Real Resistance (has noise) External Parasitics University of California, Berkeley

  19. Circuits! • When the inventors of the bipolar transistor first got a working device, the first thing they did was to build an audio amplifier to prove that the transistor was actually working! University of California, Berkeley

  20. Modern ICs • First IC (TI, Jack Kilby, 1958): A couple of transistors • Modern IC: Intel Pentium 4 (55 million transistors, 3 GHz) Source: Intel Corporation Used without permission Source: Texas Instruments Used without permission University of California, Berkeley

  21. Supply “Rail” A Simple Circuit: An MOS Amplifier Input signal Output signal University of California, Berkeley

  22. Selecting the Output Bias Point • The bias voltage VGS is selected so that the output is mid-rail (between VDD and ground) • For gain, the transistor is biased in saturation • Constraint on the DC drain current: • All the resistor current flows into transistor: • Must ensure that this gives a self-consistent solution (transistor is biased in saturation) University of California, Berkeley

  23. Finding the Input Bias Voltage • Ignoring the output impedance • Typical numbers: W = 40 m, L = 2 m, RD = 25k, nCox = 100 A/V2, VTn = 1 V, VDD = 5 V  University of California, Berkeley

  24. Applying the Small-Signal Voltage Approach 1. Just use vGS in the equation for the total drain current iD and find vo Note: Neglecting charge storage effects. Ignoring device output impedance. University of California, Berkeley

  25. Solving for the Output Voltage vO University of California, Berkeley

  26. Small-Signal Case • Linearize the output voltage for the s.s. case • Expand (1 + x)2 = 1 + 2x + x2 … last term can be dropped when x << 1 Neglect University of California, Berkeley

  27. “DC” Small-signal output Linearized Output Voltage For this case, the total output voltage is: The small-signal output voltage: Voltage gain University of California, Berkeley

  28. Plot of Output Waveform (Gain!) Numbers: VDD/ (VGS – VT) = 5/ 0.32 = 16 output input mV University of California, Berkeley

  29. There is a Better Way! • What’s missing: didn’t include device output impedance or charge storage effects (must solve non-linear differential equations…) • Approach 2. Do problem in two steps. • DC voltages and currents (ignore small signals sources): set bias point of the MOSFET ... we had to do this to pick VGS already • Substitute the small-signal model of the MOSFET and the small-signal models of the other circuit elements … • This constitutes small-signal analysis University of California, Berkeley

More Related