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Dominant Model - RF and Microwave Engineering - Lecture Notes, Study notes of Electrical Engineering

Bharat Ratna Dr. B. R. Ambedkar UniversityElectrical Engineering

These are the Lecture Notes of RF and Microwave Engineering which includes Small Signal Analysis, Parameter Model, Invariant, Reinterpret, Low Frequencies, Frequency Dependent, Relationships, Related, Frequency Dependent Component etc. Key important points are: Dominant Model, Small Signal Analysis, Parameter Model, Invariant, Reinterpret, Low Frequencies, Frequency Dependent, Relationships, Related, Frequency Dependent Component

Typology: Study notes

2012/2013

Uploaded on 03/23/2013

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High-Frequency Models: BJT 1
HIGH-FREQUENCY MODELS OF THE BJT
• The dominant model used for small-signal analysis of a BJT in the forward-active region, the
h-parameter model as presented in Chapter 3, does not contain frequency sensitive elements
and is therefore invariant with respect to changes in frequency. It is therefore necessary to
introduce a new BJT model or to reinterpret an old model to include frequency-dependent
terms using the Ebers-Moll model as a basis for creating the new model.
• In the forward-active region and at low frequencies the Ebers-Moll Model can be replaced by
the linear two-port model shown in Figure 10.4-2. This model is known as the hybrid-π
model. It is similar to the h-parameter model used previously in this text, but has particular
utility when frequency-dependent terms are included.
r
µ
m
gV
π
E
r
rb
π
V
π
+
−
B C
r
o
Figure 10.4-2 Low-frequency Hybrid-π BJT Model
• The relationships between h-parameter and hybrid-π models are related to the h-parameter
model parameters by: • As will be seen in
Section 10.7, the
hybrid-π model is
also useful in
modeling FETs.
• The frequency-dependent component of transistor behavior is based on the capacitive
component of p-n junction impedance. Once the capacitive nature of a p-n junction is
known, a frequency dependent model for a BJT can be obtained.
Modeling a p-n Junction Diode at High Frequencies
• The charge buildup in the semiconductor region near a p-n junction under a voltage bias,
causes a significant buildup of electrical charge on each side of the junction which exhibits
acts as a capacitance. It is modeled as a capacitor shunting the dynamic resistance of the
junction (Figure 10.4-3).
r
C
d
j
Figure 10.4-3 High-frequency model of a p-n junction
• In most electronic applications the p-n junction capacitance is dominated by the diffusion of
carriers in the depletion regions. A good analytic approximation of this depletion
capacitance, Cj, is given by:
()
m
V
jo
j
d
C
C
−
≈1, (10.4-2)
where,
gh
r
m
fe
==
π
η
I
V
c
t
, rgm
π
βη β
==
Ft
c
F
V
I,
rh
o
oe
≈=
1V
I
A
c
, r h r
bie
=−
π
.
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High-Frequency Models: BJT 1

H IGH-FREQUENCY MODELS OF THE BJT

  • The dominant model used for small-signal analysis of a BJT in the forward-active region, the h -parameter model as presented in Chapter 3, does not contain frequency sensitive elements and is therefore invariant with respect to changes in frequency. It is therefore necessary to introduce a new BJT model or to reinterpret an old model to include frequency-dependent terms using the Ebers-Moll model as a basis for creating the new model.
  • In the forward-active region and at low frequencies the Ebers-Moll Model can be replaced by the linear two-port model shown in Figure 10.4-2. This model is known as the hybrid-π model. It is similar to the h -parameter model used previously in this text, but has particular utility when frequency-dependent terms are included. r μ

g V m π

E

r

rb π V π

−

B C

ro

Figure 10.4-2 Low-frequency Hybrid-π BJT Model

  • The relationships between h -parameter and hybrid-π models are related to the h -parameter model parameters by: - As will be seen in Section 10.7, the hybrid-π model is also useful in modeling FETs.
  • The frequency-dependent component of transistor behavior is based on the capacitive component of p-n junction impedance. Once the capacitive nature of a p-n junction is known, a frequency dependent model for a BJT can be obtained.

Modeling a p-n Junction Diode at High Frequencies

  • The charge buildup in the semiconductor region near a p-n junction under a voltage bias, causes a significant buildup of electrical charge on each side of the junction which exhibits acts as a capacitance. It is modeled as a capacitor shunting the dynamic resistance of the junction (Figure 10.4-3). r

C

d

j Figure 10.4-3 High-frequency model of a p-n junction

  • In most electronic applications the p-n junction capacitance is dominated by the diffusion of carriers in the depletion regions. A good analytic approximation of this depletion

capacitance, C (^) j , is given by:

V m

jo j (^) d

C

C

where,

g

h m r = fe =

I

V

c t

, r π g (^) m

= (^) F t= c

V F

I

r o hoe

1 V

I

A c

, rb = hie − r π.

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High-Frequency Models: BJT 2

C (^) jo = small-signal junction capacitance at zero voltage bias,

ψ o = junction built-in potential, and

m = junction grading coefficient (0.2 < m ≤ 0.5).

  • A plot the junction capacitance as described by Equation 10.4-2 is shown in Figure 10.4-4.

V

C (^) j

C (^) jo ψ ο d Figure 10.4-4 p-n Junction Depletion Capacitance

Modeling the BJT at High Frequencies in the Forward-Active Region

  • In order to model the BJT at high frequencies, the hybrid-π model of Figure 10.4-2 is altered by shunting each p-n junction dynamic resistance with an appropriate junction capacitance.

r

r (^) b π C π

C μ

V π g V m π

− E

B C

ro

Figure 10.4-5 The High-Frequency Hybrid-π Model of a BJT

  • The junction capacitance, C μ, is relatively independent of quiescent conditions. Typical manufacturer data sheets provide a value for C μ at a given reverse bias (typically, VCB = 5 or 10 V).
  • The forward-biased base-emitter junction exhibits greater variation with bias conditions: its junction capacitance, C π , must therefore be determined with greater caution.
  • In order to correlate these measurements with the hybrid-π parameters, an ac equivalent circuit of the test circuit must be created (Figure 10.4-7).
  • The gain-bandwidth product: the product of short-circuit current gain,

( ) ( ) π(^ π μ)^ π(^ π μ)

π

j r C C

h j r C C

r A (^) I gm fe

at a particular frequency and that

frequency has constant value for all frequencies greater than π(^ π μ)

r C + C

3 dB is a common

description: π(^ π μ)^ π μ

C C

g r C C

h (^) fe m

T.^ (10.4-6)

  • Manufacturers data sheets will either provide a value for ωT or provide the gain at some other high frequency. The gain-bandwidth is given by: ωT = Am ωm (10.4-7) where ωm is the frequency at which the manufacturer made the gain measurement and Am is the gain at that frequency.

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