Physics 116A NotesFall 2004

David E. Pellett

Draft v.0.9

• Notes Copyright 2004 David E. Pellett unless stated otherwise.

• References:

– Text for course:Fundamentals of Electrical Engineering, second edition, by LeonardS. Bobrow, published by Oxford University Press (1996)

– Others as noted

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Physics 116A, BJT Basics: Outline

• Bipolar Junction Transistor (BJT) fabrication (diagram)

• BJT regions of operation

• BJT active region behavior and Ebers-Moll model

• Overview of simple BJT amplifiers

• Q-point analysis

• Small signal AC analysis

• A simple small signal AC BJT model

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BJT Regions of Operation

• VBE ≡ VB −VE, VCE ≡ VC −VE, voltage polarities are for npn

Diode Biases BC Reverse BC ForwardBE Reverse Cutoff Region

VBE < 0.5 V• BJT acts like openswitch

Reverse Active Regionor Inverse Region

• Usually to be avoided

BE Forward Active RegionVBE ∼ 0.7 VVCE > 0.2 V

• BJT acts like dependentcurrent source

Saturation RegionVBE ' 0.8 V

• BJT acts like closedswitch

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BJT Active Region OperationThe BE diode is forward biased, base is very thin, BC diode reverse biased

• Consider NPN case (for PNP, substitute ”holes” for ”electrons”)

• IE determined by VBE through diode equation

• Electrons from emitter diffuse across thin base into BC depletion region

• Here, ~E causes them to drift on through BC depletion region

• Geometry such that most electrons from emitter make it to collector:

IC = αIE, α ≈ 0.99

• IC roughly independent of VCE so collector acts as current source

• IB = IE − IC = IE(1− α) ≈ 0.01IE

• Define hFE ≡ IC/IB = αIE/(1− α)IE = α/(1− α) ≈ 100

– Thus BJT acts as dependent current source: IC = hFEIB

– Current amplifier with large current gain

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BJT Active Region IE vs. VBE

• BJT regions – cutoff: VBE < 0.5 V; active: VBE ∼ 0.7 V; saturation:VBE ' 0.8 V

0

5

10

15

20

25

30

35

40

45

50IE vs. VBE for 2N2222A npn BJT (SPICE simulation)

VBE (mV)

I E (m

A)

0 100 200 300 400 500 600 700 800• VCE = 10 V

• I vs V characteristic of a forward-biased diode

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BJT Active Region IC vs. VCE

• BJT in active region for VCE > 0.2 V and IB > 0.

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5IC vs VCE for 2N2222A npn BJT (SPICE simulation)

I C (m

A)

VCE (V)

IB = 8 µA

IB = 0 µA

IB = 4 µA

IB = 12 µA

IB = 16 µA

• Looks like current source in active region: IC = hFEIB, hFE ≈ 160

• Slight slope due to narrowing of base as BC depletion region grows

6

Simple BJT Active Region Model

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Simple BJT Amplifiers

Simple one-BJT amplifier analysis:

• Specify amplifier configuration (one BJT node is shared (common) be-tween the input and output circuit)

– Common collector (emitter follower)

– Common emitter

– Common base

• Specify BJT operating point (quiescent point or “Q point”)

– BJT biasing

• Small signal AC analysis of resulting circuit

– Linearized small signal AC models of BJT

– Small signal AC equivalent circuit

– Use to calculate desired quantities such as Av, Rin.

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Emitter Follower DC Analysis I

(a) VB:

VB = VBE + VE = 0.7 V + IERE

VB = 0.7 V + 2.0 mA× 500 Ω = 1.7 V

(b) IB:

IE = IC + IB = hFEIB + IB = (hFE + 1)IB

IB = IE/(hFE + 1) = 2.0 mA/101 = 20 µA

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Emitter Follower DC Analysis II

VB = 1.7 V, IB = 20 µA. (c) I1:

I1 = IB + I2 = 20 µA + VB/R2

I1 = 20 µA + 1.7 V/8100 Ω = 0.23 mA

(d) R1:R1 = (VCC − VB)/I1 = (10 V − 1.7 V)/0.23 mA = 40 kΩ

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Small Signal AC Analysis

At Q point, VBQ= 1.7 V, IBQ

= 20 µA, IEQ= 2.0 mA, VEQ

= 1.0 V, etc.R1 = 40 kΩ.

• Introduce signals, vi or ii, which are assumed to be small, first-order linearvariations about the Q point

– E.g., VB = VBQ+ vb, where vb is the small signal AC base voltage.

– Like X + ∆X in the calculus ⇒ f(X0 + ∆X) ≈ f(X0) + dfdX|X0

∆X

– Keeping just first-order terms allows us to “linearize” non-linear circuitelements like diodes and transistors

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Small Signal AC Analysis: re for BJT

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A Simple Small Signal AC BJT Model

• Note that re is a small signal AC resistance. It is a linear approximationto the diode curve near the Q point. Also, note that the Q point VBEQ

=0.7 V does not appear in the small signal AC model since it is a constantvoltage.

• We will consider alternate and more detailed models later as needed.

• Next: apply to find voltage gain of emitter follower

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