BJT Circuit Configurations

RL

Vcc

~ ~ ~

Rs

vs

Vcc

vs

Rs

RLRL

VccRs

vs

Common base Common emitter Common collector

Vbe

Common emitter current gain

BJT Current-Voltage Characteristics

Very small base current (~5-75 μA) causes much higher collector current (up to 7.5 mA).The current gain is ~ 100

VCE, V

VCE, V

BJT amplifier circuit analysis: Operating point

Collector current depends on two circuit parameters:the base current and the collector voltage.At high collector voltage the collector current depends on the base current only.For Ibase = 40 μA, Icoll = 4 mA for any EC-E greater than 1.5 V

RL

BJT amplifier circuit analysis: Operating point

For an arbitrary collector voltage, collector current can be found using the KVL.The KVL for the collector – emitter circuit, VCC = IRL×RL + VCE;

VCE, V

CC CERL

L

V VIR−

= The RL current depends linearly on the collector voltage VCE

Resistor RL and the C-E circuit of BJT are connected in series, hence IRL = IC

For Ib = 40 μA and VCC = 13V, the collector current IC = 4 mAFor Ib = 75 μA and VCC = 14V, the collector current IC = 4 mA

VCE

RL

VCC

BJT amplifier gain analysis: 1

1. Input circuitThe input voltage has two components: the DC bias and the AC signal

Vin

TimeDC bias

AC signal amplitude

DC voltage component biases the base-emitter p-n junction in the forward directionAC component is the input signal to be amplified by the BJT.

BJT amplifier gain analysis: 2

2. Output circuitThe collector current has two components too.

IC

TimeDC current

AC current amplitude

DC and AC collector currents flow through the BJT in accordance with its I-V characteristics

VCE, V

Base current

BJT amplifier gain analysis: 3

The resistance of the B-E junction is very low when VBE ≥ VBE0 ≈ Vbi≈ 0.7 V. Hence the base current IB ≅ (Vin-VBE0)/R1 = (VinDC-VBE0+VinAC)/R1

The collector current IC does not depend on the collector voltage if the latter is high enough.Hence, IC ≅ β IB;The voltage drop across the load resistance R2: V2= IC R2;The output voltage Vout = VCC - V2 = VCC - IC R2;Vout = VCC - IC R2 = VCC - β IB R2 = VCC - β R2(VinDC-VBE0+VinAC)/R1;In signal amplifiers only AC component of the output voltage is important:

VoutAC = - β R2VinAC/R1;

The amplifier voltage gain: kV = VoutAC/VinAC= - β R2/R1;

VCE, V

BJT amplifier gain analysis: 4

Common emitter gain summary:

Current gain: kI = β

Voltage gain: kV = VoutAC/VinAC= - β R2/R1;

Power gain: kP = kV × kI = - β2 × R2/R1

VCE, V

BJT design and factors affecting the performance

Base resistance and emitter current crowding in BJTsThe voltage drop along the base layerVbb = rbb Ib,where rbb is called the base spreading resistance.

1 1TH

VqVVkT

S SI I e I e⎛ ⎞⎛ ⎞

= − = −⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

The length of the edge region, Δde, where most of the emitter current flows may be estimated from:

The p-n junction current decreases rapidly when the voltage drops by ΔVbb ~ Vth = kT/q

maxe

th b b b be

dV I R It W

ρ Δ= ≈

Δde

Emitter current crowding in BJTs (cont.)

1b

b bqNρ

μ=

From these,

th e the b b e b

b b b

V t W Vd q N t WI I

μρ

Δ ≈ =

maxe

th b b b be

dV I R It W

ρ Δ= ≈

Δde

the b b e b

b

Vd q N t WI

μΔ ≈

Example

Estimate the effective emitter length, Δde for the BJT having the following parameters:Ib = 50 μA;Nb = 1017 cm-3

μb = 400 cm2/V-sWb = 0.1 μm te = 100 μm

Δde = 3.33 e-4 cm = 3.33 μm

Δde

Large periphery B JT Design

Base narrowing (Early effect) The depletion width of the p-n junction depends on the applied voltage:

(Here W is the depletion region widthnot the width of the base as in BJT!)

In the BJT, this effect means that the effective width of the base is less than Wb:Weff = Wb - Xdeb - Xdcbwhere Wb is the physical thickness of the base,xdeb and xdcb are the depletion region widths from the emitter and collector sides.The depletion widths are given by (Ne>>Nb):

2/10 )(2

⎥⎦

⎤⎢⎣

⎡ −=

b

bebideb Nq

VVx

εε

2/1

20 )(2

⎥⎥⎦

⎤

⎢⎢⎣

⎡ +=

b

ccbbidcb

qNNVV

xεε

xdcb is usually the most important factor since the voltage applied to collector is high.The doping level in collector, NDC has to be lower than that of the base, NAB, to reduce the Early effect:

NC << NB

Due to Early effect the effective base thickness depends on the collector voltage.

In the gain expression, W should be replaced with Weff:

The Early effect decreases the output resistance, and hence the voltage gain of BJTs.

2

22 p

receff

L

Wβ =

The punch-through breakdown voltage Vpt:

Punch-through breakdown in BJTs -- the result of the Early effect

W = xdcb

( )c

bcbpt N

NNNWqV +=

0

2

2εε

BJT Model• Gummel-Poon model used in SPICE and other

simulators

Ie = Ic + Ib

1c bI Iαα

=−

Hence,

where α is called a common base current gain

Ie Ic

Ib

Applying KCL to the BJT terminals:

Collector – emitter current relationship:

c eI Iα=

( )c c bI I Iα= +

c bI Iβ=Common emitter current gain is defined as:

β =α

1−α

α =β

1+ β

The last two expressions link common emitter and common base current gains

Simplified Gummel-Poon BJT equivalent circuit

• Emitter junction:

exp 1se bebe

F F th

I VIn Vβ

⎡ ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

• Collector junction:

exp 1sc bcbc

R R th

I VIn Vβ

⎡ ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

αiIc αnIe

IcIe

Base

Emitter CollectorIdeal diode Ideal diode

Leakage diodeLeakage diode

Vth = kT/q = 0.026 V at 300 K

αiIc αnIe

IcIe

Base

Emitter CollectorIdeal diode Ideal diode

Leakage diodeLeakage diode

Gummel-Poon BJT equivalent circuit accounting for the leakage currents

•Emitter –base leakage diode:

_ exp 1beLeak be se

E th

VI In V

⎡ ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

Collector –base leakage diode:

_ exp 1bcLeak bc sc

C th

VI In V

⎡ ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦