Bipolar transistor amplifiers

1. List of Tables

Table 1, “BJT small-signal parameters”
Table 2, “Definitions for Table [t-bjt-amplifiers]”
Table 3, “Bipolar single-transistor amplifier types”

2. Introduction

3. Tables and terminology

Table 1. BJT small-signal parameters
Symbol	Name	Definition
\(g_m\)	transconductance	\(\dfrac{I_C}{V_T} = \dfrac{\alpha}{r_e}\)
\(r_e\)	intrinsic emitter resistance	\(\dfrac{\alpha\, V_T}{I_C} = \dfrac{\alpha}{g_m}\)
\(r_\pi\)	intrinsic base resistance	\(\dfrac{\beta\, V_T}{I_C} = \dfrac{\beta}{g_m}\)
\(r_o\)	intrinsic output resistance	\(\dfrac{V_A}{I_C}\)
\(\beta\)	alternate	\(g_m r_\pi\)
\(A_0\)	intrinsic voltage gain	\(g_m r_o = \dfrac{V_A}{V_T}\)

Table 2. Definitions for Table [t-bjt-amplifiers]
Symbol	Name
\(\boldsymbol{Z}_i\)	Impedance looking into transistor input terminal. Does not include the bias network.
\(\boldsymbol{Z}_o\)	Impedance looking into transistor output terminal. Does not include the bias network.
\(A_{v\emptyset}\)	Open-circuit voltage gain, no external load attached.
\(\boldsymbol{Z}_B\)	Impedance of the bias network at the base node looking away from the transistor. Does not include source or load impedances.
\(\boldsymbol{Z}_E\)	Impedance of the bias network at the emitter node looking away from the transistor. Does not include source or load impedances.
\(\boldsymbol{Z}_C\)	Impedance of the bias network at the collector node looking away from the transistor. Does not include source or load impedances.
\(\boldsymbol{Z}_s\)	Output impedance of the source driving the amplifier.
\(\boldsymbol{Z}_L\)	Load impedance seen by the amplifier.

Table 3. Bipolar single-transistor amplifier types
In	Out	Name	\(\boldsymbol{Z}_i\)^†	\(\boldsymbol{Z}_o\)	V-Gain: \(\boldsymbol{A_{v\emptyset}}\)
B	E	EF emitter follower / CC common-collector	\(\left(\beta + 1\right) \left(r_e + Z_E \!\parallel\! Z_L \right)\)	\(r_e + \dfrac{Z_B \!\parallel\! Z_s}{\left(\beta + 1\right)}\)	\(\dfrac{\alpha\, Z_E}{r_e + \alpha\, Z_E}\)
B	C	CE common-emitter	\(\left(\beta + 1\right) \left(r_e + Z_E\right)\)	\(r_o + (1 + A_0) \bigl(Z_E \parallel \left(r_\pi + Z_B \!\parallel\! Z_s \right) \bigr)\)	\(\dfrac{-\alpha\, Z_o \!\parallel\! Z_C}{Z_E + r_e}\)
E	C	CB common-base	\(r_e + \dfrac{Z_B}{\left(\beta + 1\right)}\)	\(r_o + (1 + A_0) \bigl(Z_E \parallel Z_s \parallel \left(r_\pi + Z_B \right) \bigr)\)	\(\dfrac{\left\lbrack 1 + A_0 \left(\dfrac{r_\pi}{Z_B + r_\pi}\right)\right\rbrack Z_C}{Z_C + r_o}\)
E	B	(not useful)
C	B	(not useful)
C	E	(not useful)
^† \(r_o\) is rarely significant here.

Be careful about the definitions in order to properly use the above tables.

Figure 1. Common-Emitter impedances

Figure 2. Common-Collector / Emitter-Follower impedances

Figure 3. Common-Base impedances

4. Small-signal models

Figure 4. Bipolar small-signal model connections

Figure 5. Hybrid pi model

Figure 5, “Hybrid pi model” presents the popular hybrid-pi small-signal model of a bipolar transistor for low frequencies.

Figure 6. T model

Figure 6, “T model” is an alternate small-signal model. Be careful of the base current in this model and properly do KCL! Both models will give exactly the same answer — it makes no real difference which one you choose. However, it does sometimes help the analysis / algebra to choose one over the other, depending on the amplifier type. We will use the hybrid pi model most of the time.

5. Single transistor amplifiers

5.1. Emitter follower / common collector

TODO

Wikipedia: Common collector

5.2. Common emitter

TODO

Wikipedia: Common emitter

5.3. Common base

TODO

Wikipedia: Common base

5.4. Current source

Labeled in AoE Figure 2.40, p.91 as another one of the basic transistor circuits. Mentioned here for completeness, but this is the amplifier chapter.

5.5. Switch

The last of the basic transistor circuits in [AoE].

6. Two transistor amplifiers

Given the three fundamental amplifier types possible with a transistor, the next extension is to construct amplifiers with two transistors.

CE-CE CE-CB	cascode
CE-EF CB-CE CB-CB CB-EF EF-CE EF-CB	single-ended LTP
EF-EF	Darlington pair

Sziklai pair

References

[[[341-notes]]] D. White, ECE 341 Class notes 2019 folder, https://drive.google.com/drive/folders/1vzdLxzTUAC6xXF6YjVcDRuy_BKR7gzDz?usp=sharing
[[[341-docs]]] D. White, ECE 341 reference documents folder, https://drive.google.com/folderview?id=0B5O5cSaA0tEQYVpaSnJxMGFrdHM
[AoE] P. Horowitz and W. Hill, The Art of Electronics 3rd ed. (affiliate link), Cambridge University Press, 2015. https://artofelectronics.net
[L-AoE] T. Hayes, Learning the Art of Electronics: A Hands-On Lab Course (affiliate link), Cambridge University Press, 2016. https://learningtheartofelectronics.com
[LEC] Tony R. Kuphaldt, Lessons in Electric Circuits, Source version: https://www.ibiblio.org/kuphaldt/electricCircuits/, All About Circuits version: https://www.allaboutcircuits.com/textbook/
[CL-book] Michael F. Robbins, CircuitLab, Ultimate Electronics: Practical Circuit Design and Analysis, https://www.circuitlab.com/textbook/
[TCA] Alfred D. Gronner, Transistor Circuit Analysis, Simon & Schuster, 1970, https://archive.org/details/TransistorCircuitAnalysis
[CMOS VLSI] Neil Weste and David Harris, CMOS VLSI Design - A Circuit and Systems Perspective, 4th edition. Addison-Wesley, 2011. http://pages.hmc.edu/harris/cmosvlsi/4e/index.html
[Guidebook] D. White, Guidebook for Electronics II. https://agnd.net/valpo/341/guidebook
[Gummel-Poon] H.K. Gummel, H.C. Poon, An Integral Charge Control Model of Bipolar Transistors. Bell System Technical Journal, 49: 5. May-June 1970 pp 827-852. https://archive.org/details/bstj49-5-827
[ROHM] ROHM Semiconductor, Electronics Basics, http://www.rohm.com/web/global/en_index
[vishay-e-series] Vishay, Standard Series Values in a Decade for Resistances and Capacitances, https://www.vishay.com/docs/28372/e-series.pdf