BJT Circuit Configurations

BJT Circuit Configurations

R

V

~

_~

~

R

v

V

v

R

R

R

V

R

v

Common base Common emitter Common collector

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

V_CE, 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 I_base = 40 μA, I_coll = 4 mA for any E_C-E greater than 1.5 V R_L

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, V_CC = I_RL×R_L + V_CE;

V_CE, V CC CE RL L

V

V

I

R

−

=

I

= I

For I_b = 40 μA and V_CC = 13V, the collector current I_C = 4 mA For I_b = 75 μA and V_CC = 14V, the collector current I_C = 4 mA

V_CE R_L V_CC

BJT amplifier gain analysis: 1

1. Input circuit

The input voltage has two components: the DC bias and the AC signal V_in

Time DC bias

AC signal amplitude

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

BJT amplifier gain analysis: 2

2. Output circuit

The collector current has two components too. I_C

Time DC current

AC current amplitude

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

V_CE, V

BJT amplifier gain analysis: 3

The resistance of the B-E junction is very low when V

≥ V

≈ V

≈ 0.7 V.

Hence the base current I

≅ (V

-V

)/R1 = (V

-V

+V

)/R

The collector current I

does not depend on the collector voltage if the latter is high

enough.

Hence, I

≅ β I

;

The voltage drop across the load resistance R

: V

= I

R

;

The output voltage V

= V

- V

= V

- I

R

;

V

= V

- I

R

= V

-

β I

R

= V

-

β R

(V

-V

+V

)/R

;

In signal amplifiers only AC component of the output voltage is important:

V

= -

β R

V

/R

;

The amplifier voltage gain:

k

= V

/V

= -

β R

/R

;

BJT amplifier gain analysis: 4

Common emitter gain summary:

Current gain: k

=

β

Voltage gain:

k

= V

/V

= -

β R

/R

;

Power gain: k

= k

× k

=

-

β

×

R

/R

Base resistance and emitter current crowding in BJTs

The voltage drop along the base layer

V_bb = r_bb I_b,where r_bb is called the base spreading resistance.

1

1

I

=

I

⎛

⎜

e

− =

⎞

⎟

I

⎛

⎜

_⎜

e

−

⎞

⎟

_⎟

⎝

⎠

_⎝

_⎠

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

The p-n junction current decreases rapidly when the voltage drops by ΔV_bb ~ V_th = kT/q max e th b b b b e

d

V

I R

I

t W

ρ

Δ

=

≈

Emitter current crowding in BJTs (cont.)

1

qN

ρ

μ

=

From these,

V t W

V

d

q N

t W

I

ρ

I

μ

Δ ≈

=

d

V

I R

I

t W

ρ

Δ

=

≈

th e b b e b b

V

d

q N

t W

I

μ

Δ ≈

Estimate the effective emitter

length, Δd

for the BJT having

the following parameters:

I

= 50 μA;

N

= 10

_cm

μ

= 400 cm

_/V-s

W

= 0.1 μm

t

= 100 μm

Δd

= 3.33 e-4 cm = 3.33 μm

Base narrowing (Early effect)

The depletion width of the p-n junction depends on the applied voltage:

(Here W is the depletion region width not the width of the base as in BJT!)

In the BJT, this effect means that the effective width of the base is less than W

:

W

= W

- X

- X

where W

is the physical thickness of the base,

x

and x

are the depletion region widths from the emitter and collector sides.

The depletion widths are given by (N

>>N

):

2

/

1

0

(

)

2

⎥

⎦

⎤

⎢

⎣

⎡

−

=

b

be

bi

deb

N

q

V

V

x

εε

2

/

1

2

0

(

)

2

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

₊

=

b

c

cb

bi

dcb

qN

N

V

V

x

εε

x

is usually the most important factor since the voltage applied to collector is

high.

The doping level in collector, N

has to be lower than that of the base, N

, to

reduce the Early effect:

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

In the gain expression, W should be replaced with W

:

The Early effect decreases the output resistance, and hence the voltage

gain of BJTs.

2

L

W

β

=

The punch-through breakdown voltage V

:

Punchthrough breakdown in BJTs

-- the result of the Early effect

W = x

_dcb

(

)

N

N

N

N

W

q

V

=

+

2

εε

BJT Model

• Gummel-Poon model used in SPICE and other

simulators

I

_e

= I

_c

+ I

_b

1

I

α

I

α

=

−

Hence,

where

α

is called a common base current gain

I_e I_c

I_b

Applying KCL to the BJT terminals:

Collector – emitter current relationship:

c e

I

=

α

I

(

)

c

c

b

I

=

α

I

+

I

I

=

β

I

Common emitter current

gain is defined as:

β =

α

1

− α

α =

β

1

+ β

Simplified Gummel-Poon BJT equivalent circuit

• Emitter junction:

exp

1

I

V

I

n V

β

⎡

_⎛

_⎞

⎤

=

_⎢

_⎜

_⎟

−

_⎥

⎝

⎠

⎣

⎦

• Collector junction:

exp

1

I

V

I

n V

β

⎡

_⎛

_⎞

⎤

=

_⎢

_⎜

_⎟

−

_⎥

⎝

⎠

⎣

⎦

α

_i

I

_c

α

n

I

e

I

_c

I

_e

Base

Emitter

Ideal diode

Ideal diode

Collector

Leakage diode

Leakage diode

α

_i

I

_c

α

n

I

e

I

_c

I

_e

Base

Emitter

Ideal diode

Ideal diode

Collector

Leakage diode

Leakage diode

Gummel-Poon BJT equivalent circuit accounting

for the leakage currents

•Emitter –base leakage

diode

:

exp

1

V

I

I

n V

⎡

_⎛

_⎞

⎤

=

_⎢

_⎜

_⎟

−

_⎥

⎝

⎠

⎣

⎦

Collector –base leakage diode

_

exp

1

V

I

I

n V

⎡

_⎛

_⎞

⎤

=

_⎢

_⎜

_⎟

−

_⎥

⎝

⎠

⎣

⎦