1. EE105 Fall 2007Lecture 5, Slide 1Prof. Liu, UC Berkeley Lecture 5 OUTLINE BJT (cont’d) – Transconductance – Small-signal model – The Early effect – BJT operation in saturation mode Reading: Chapter 4.4.3-4.5 ANNOUNCEMENTS HW1 will be considered as extra credit. HW3 is posted, due Tuesday 9/18

2. EE105 Fall 2007Lecture 5, Slide 2Prof. Liu, UC Berkeley Notes on PN Junctions Typically, pn junctions in IC devices are formed by counter-doping. The equations provided in class (and in the textbook) can be readily applied to such diodes if – N A  net acceptor doping on p-side (N A -N D ) p-side – N D  net donor doping on n-side (N D -N A ) n-side V D (V) I D (A)

3. EE105 Fall 2007Lecture 5, Slide 3Prof. Liu, UC Berkeley Transconductance, g m The transconductance (g m ) of a transistor is a measure of how well it converts a voltage signal into a current signal. It will be shown later that g m is one of the most important parameters in integrated circuit design.

4. EE105 Fall 2007Lecture 5, Slide 4Prof. Liu, UC Berkeley Visualization of Transconductance g m can be visualized as the slope of the I C vs. V BE curve. The slope (hence g m ) increases with I C.

5. EE105 Fall 2007Lecture 5, Slide 5Prof. Liu, UC Berkeley Transconductance and I C For a given V BE swing (  V), the resulting current swing about I C2 is larger than it is about I C1. – This is because g m is larger when V BE = V B2.

6. EE105 Fall 2007Lecture 5, Slide 6Prof. Liu, UC Berkeley Transconductance and Emitter Area When the BJT emitter area is increased by a factor n, I S increases by the factor n.  For a fixed value of V BE, I C and hence g m increase by a factor of n.

7. EE105 Fall 2007Lecture 5, Slide 7Prof. Liu, UC Berkeley Derivation of Small-Signal Model The BJT small-signal model is derived by perturbing the voltage difference between two terminals while fixing the voltage on the third terminal, and analyzing the resultant changes in terminal currents. – This is done for each of the three terminals as the one with fixed voltage. – We model the current change by a controlled source or resistor.

8. EE105 Fall 2007Lecture 5, Slide 8Prof. Liu, UC Berkeley Small-Signal Model: V BE Change

9. EE105 Fall 2007Lecture 5, Slide 9Prof. Liu, UC Berkeley Small-Signal Model: V CE Change Ideally, V CE has no effect on the collector current. Thus, it will not contribute to the small-signal model. It can be shown that V CB ideally has no effect on the small-signal model, either.

10. EE105 Fall 2007Lecture 5, Slide 10Prof. Liu, UC Berkeley Small-Signal Model: Example 1 The small-signal model parameters are calculated for the DC operating point, and are used to determine the change in I C due to a change in V BE.

11. EE105 Fall 2007Lecture 5, Slide 11Prof. Liu, UC Berkeley Small-Signal Model: Example 2 In this example, a resistor is placed between the power supply and collector, to obtain an output voltage signal. Since the power supply voltage does not vary with time, it is regarded as ground (reference potential) in small- signal analysis.

12. EE105 Fall 2007Lecture 5, Slide 12Prof. Liu, UC Berkeley The Early Effect In reality, the collector current depends on V CE : – For a fixed value of V BE, as V CE increases, the reverse bias on the collector-base junction increases, hence the width of the depletion region increases. Therefore, the quasi- neutral base width decreases, so that collector current increases.

13. EE105 Fall 2007Lecture 5, Slide 13Prof. Liu, UC Berkeley Early Effect: Impact on BJT I-V Due to the Early effect, collector current increases with increasing V CE, for a fixed value of V BE.

14. EE105 Fall 2007Lecture 5, Slide 14Prof. Liu, UC Berkeley Early Effect Representation

15. EE105 Fall 2007Lecture 5, Slide 15Prof. Liu, UC Berkeley Early Effect and Large-Signal Model The Early effect can be accounted for, by simply multiplying the collector current by a correction factor. The base current does not change significantly.

16. EE105 Fall 2007Lecture 5, Slide 16Prof. Liu, UC Berkeley Early Effect and Small-Signal Model

17. EE105 Fall 2007Lecture 5, Slide 17Prof. Liu, UC Berkeley Summary of BJT Concepts

18. EE105 Fall 2007Lecture 5, Slide 18Prof. Liu, UC Berkeley BJT in Saturation Mode When the collector voltage drops below the base voltage, the collector-base junction is forward biased. Base current increases, so that the current gain (I C /I B ) decreases.

19. EE105 Fall 2007Lecture 5, Slide 19Prof. Liu, UC Berkeley Large-Signal Model for Saturation Mode

20. EE105 Fall 2007Lecture 5, Slide 20Prof. Liu, UC Berkeley BJT Output Characteristics The operating speed of the BJT also drops in saturation.

21. EE105 Fall 2007Lecture 5, Slide 21Prof. Liu, UC Berkeley Example: Acceptable V CC Range In order to prevent the BJT from entering very deeply into saturation, the collector voltage must not fall below the base voltage by more than 400 mV.

22. EE105 Fall 2007Lecture 5, Slide 22Prof. Liu, UC Berkeley Deep Saturation In deep saturation, the BJT does not behave as a voltage-controlled current source. V CE is ~constant.