Hybrid Model
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Transcript of Hybrid Model
INTRODUCTION: TRANSISTOR MODELING
• To begin analyze of small-signal AC response of BJT amplifier the knowledge of modeling the transistor is important.• The input signal will determine whether it’s a small
signal (AC) or largesignal (DC) analysis.• The goal when modeling small-signal behavior is to make of a transistor that work for small-signal enough to “keep things linear” (i.e.: not distort too much) [3]• There are two models commonly used in the small signal analysis:
a) re modelb) hybrid equivalent model
How does the amplification be done?
• Conservation; output power of a system cannot be large than its input and the efficiency cannot be greater than 1.
• The input dc plays the important role for the amplification to contribute its level to the ac domain where the conversion will become as η=Po(ac)/Pi(dc)
Disadvantages
• Re model– Fails to account the output impedance level of
device and feedback effect from output to input
• Hybrid equivalent model– Limited to specified operating condition in
order to obtain accurate result
VS
VCC
C1
C2
C3
+
-
Vo
RS
Vi
+
-RE
RCR1
R2
VS
+
-
Vo
RS
V i
+
-
RCR1
R2
•I/p coupling capacitor s/c• Large values• Block DC and pass AC signal • Bypass
capacitor s/c•Large values
DC supply “0” potential
Voltage-divider configuration under AC analysis
Redraw the voltage-divider configuration after removing dc
supply and insert s/c for the capacitors
• O/p coupling capacitor s/c• Large values• Block DC and pass AC signal
VS
RSR2 R1 Rc
Transistor small-signal ac
equivalent cct
Vo
Zi
Ii
Zo
Io
Vi
+ +
- -
B
E
C
Redrawn for small-signal AC analysis
Modeling of BJT begin
HERE!
VS
+
-
Vo
RS
V i
+
-
RCR1
R2
AC bias analysis :
1) Kill all DC sources
2) Coupling and Bypass capacitors are short cct. The effect of these capacitors is to set a lower cut-off frequency for the cct.
3) Inspect the cct (replace BJTs with its small signal model:re or hybrid).
4) Solve for voltage and current transfer function, i/o and o/p impedances.
IMPORTANT PARAMETERS
• Input impedance, Zi• Output impedance, Zo• Voltage gain, Av• Current gain, Ai
Input Impedance, Zi(few ohms MΩ)
The input impedance of an amplifier is the value as a load when connecting a single source to the I/p of terminal of the amplifier.
VS Two-portsystem
Vi
Rsense
IiZi
+
-
Determining Zi
+
-
sense
isi
R
VVI
−=
i
ii
I
VZ =
Two port system-determining input impedance Zi
• The input impedance of transistor can be approximately determined using dc biasing because it doesn’t simply change when the magnitude of applied ac signal is change.
Output Impedance, Zo (few ohms 2MΩ)
The output impedance of an amplifier is determined at the output terminals looking back into the system with the applied signal set to zero.
Two-portsystem
Rsource
Vs=0V
Rsense
V
+
-
+
-
Io
ZoVo
Determining Zo
sense
oo
R
VVI
−=
o
oo
I
VZ =
cctopen become ZRZ oLo ⇒≥R LZ o=R o
Iam p lifie r
IR o
IL
RoL
Lo
II
RRFor
≥≥
Voltage Gain, AV
• DC biasing operate the transistor as an amplifier. Amplifier is a system that having the gain behavior. • The amplifier can amplify current, voltage and power.• It’s the ratio of circuit’s output to circuit’s input.• The small-signal AC voltage gain can be determined by:
i
ov
V
VA =
VS AvNLVi
Rsource
Zi
+
-
+
-Vo
+
-
Determining the no load voltage gain
By referring the network below the analysis are:
cct)(open ΩRi
oLvNL
V
VA
load no
∞==
vNLARZ
Z
V
VA
:resistance sourcewith
si
i
s
ovs
+==
Current Gain, Ai
• This characteristic can be determined by:
i
oi
I
IA =
BJTamplifier
Vi
Zi
+
-
Vo
+
-
Ii
RL
Determining the loaded current gain
Io
L
ivi
R
ZAA −=
Li
io
ii
Lo
RV
ZV
Z/V
R/V −=−=
L
oo
R
VI −=
re TRANSISTOR MODEL
• employs a diode and controlled current source to duplicate the behavior of a transistor.• BJT amplifiers are referred to as current-controlled devices.
Common-Base Configuration
Common-base BJT transistorre modelre equivalent cct.
Hybrid Equivalent Model
• re model is sensitive to the dc level of operation that result input resistance vary with the dc operating point
• Hybrid model parameter are defined at an operating point that may or may not reflect the actual operating point of the amplifier
Hybrid Equivalent Model
The hybrid parameters: hie, hre, hfe, hoe are developed and used to model the transistor. These parameters can be found in a specification sheet for a transistor.
Determination of parameter
0VVo
i12
0VVi
i11
o12i11i
o
o
V
Vh
I
Vh
VhIhV
====
====
====
====
++++====
0AIo
o22
0VVo
i21
o
o22i21O
o
o
V
Ih
I
Ih
, 0VV Solving
VhIhI
====
====
====
====
====++++====
H22 is a conductance!
General h-Parameters for any Transistor Configuration
hi = input resistancehr = reverse transfer voltage ratio (Vi/Vo)hf = forward transfer current ratio (Io/Ii)ho = output conductance
Common emitter hybrid equivalent circuit
Common base hybrid equivalent circuit
Simplified General h-Parameter Model
The model can be simplified based on these approximations:
hr ≅ 0 therefore hrVo = 0 and ho ≅ ∞ (high resistance on the output)
Simplified
Common-Emitter re vs. h-Parameter Model
hie = βrehfe = βhoe = 1/ro