Hybrid pi model of a Transistor. And designing of pi model using transistor with internal capacitances & internal resistance default considerations. along with CE short channel current gain with and without load. and also FET analysis its equivalent circuits.in FET analysis we have common source and common drain type of systems along with their equivalent circuits and analysis. capture these images and findout the solution for your hybid pi model high frequncy nature of a transistor. All the best. keep in contact with my linkedin.

1. 1
RAGHU INSTITUTE OF TECHNOLOGY
AUTONOMOUS
DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING
II BTECH II SEMESTER
ELECTRONIC CIRCUIT ANALYSIS
UNIT I
Prepared By:
Mrs. SUSHMI NAIDU,
Mr. M. PAVAN KUMAR,
Assistant Professors
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

2. 2
 Contents:
• Sinusoidal Analysis
• High frequency Roll Off in Av
• Av Roll Off due to Cl
• Frequency response of the CE Stage
• Amplifier Figure Of Merit
• High Frequency BJT model
• Hybrid Pi Model
– Parameters
– Relationships
• Hybrid Pi Model Mid Band
• Hybrid Pi model High Frequency
• CE amplifier
• Mid Band Hybrid pi CE
• Equivalent circuit to find Zo
• High frequency hybrid pi CE amplifier
• High pi CE transconductance model
• Determination of Hybrid pi conductance and capacitance
• High frequency response of CS amplifier
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

3. 3
 References
• “Integrated Electronics”, J. Milliman and C.C. Halkias, Tata
McGraw Hill, 1972
• “Electronic Circuit Analysis- B.V. Rao, K.R.Rjeswari,
P.C.R.Pantulu- Pearson publication
• “Electronic Devices and Circuits” – Salivahanan, Suresh Kumar,
A.Vallavaraj, TATA McGraw Hill
• www.nptel.ac.in
• www.nesoacademy.org
• www.tutorialspoint.com
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

4. 4
 Sinusoidal Analysis
• Any voltage or current in a linear circuit with a sinusoidal
source is a sinusoid of the same frequency (ω).
 We only need to keep track of the amplitude and phase,
when determining the response of a linear circuit to a
sinusoidal source.
• Any time-varying signal can be expressed as a sum of
sinusoids of various frequencies (and phases).
 Applying the principle of superposition:
 The current or voltage response in a linear circuit due to a
time-varying input signal can be calculated as the sum of
the sinusoidal responses for each sinusoidal component of
the input signal.
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

5. 5
 High Frequency “Roll-Off” in Av
• Typically, an amplifier is designed to work over a limited
range of frequencies.
 At “high” frequencies, the gain of an amplifier decreases.
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

6. 6
 Av Roll-Off due to CL
• A capacitive load (CL) causes the gain to decrease at high
frequencies.
 The impedance of CL decreases at high frequencies, so that
it shunts some of the output current to ground.






−=
L
Cmv
Cj
RgA
ω
1
||
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

7. 7
 Frequency Response of the CE
Stage
• At low frequency, the capacitor is effectively an open circuit,
and Av vs. ω is flat. At high frequencies, the impedance of the
capacitor decreases and hence the gain decreases. The
“breakpoint” frequency is 1/(RCCL).
1222
+
=
ωLC
Cm
v
CR
Rg
A
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

8. 8

9. 9
 Amplifier Figure of Merit (FOM)
• The gain-bandwidth product is commonly used to benchmark
amplifiers.
 We wish to maximize both the gain and the bandwidth.
• Power consumption is also an important attribute.
 We wish to minimize the power consumption.
( )
LCCT
CCC
LC
Cm
CVV
VI
CR
Rg
1
1
nConsumptioPower
BandwidthGain
=






=
×
Operation at low T, low VCC, and with small CL  superior FOM
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

10. 10
 High-Frequency BJT Model
• The BJT inherently has junction capacitances which affect its
performance at high frequencies.
Collector junction: depletion capacitance, Cµ
Emitter junction: depletion capacitance, Cje, and also
diffusion capacitance, Cb.
jeb CCC +≡π
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

11. 11
 BJT High-Frequency Model
(cont’d)
• In an integrated circuit, the BJTs are fabricated in the surface
region of a Si wafer substrate; another junction exists
between the collector and substrate, resulting in substrate
junction capacitance, CCS.
BJT cross-section BJT small-signal model
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

12. 12

13. 13
 Hybrid Model PI
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

14. 14
 Hybrid Model Pi Parameters
• Parasitic Resistances
• rb = rb’b = ohmic resistance – voltage drop in base region
caused by transverse flow of majority carriers, 50 ≤ rb ≤ 500
• rc = rce = collector emitter resistance – change in Ic due to
change in Vc, 20 ≤ rc ≤ 500
• rex = emitter lead resistance
– important if IC very large, 1 ≤ rex ≤ 3
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

15. 15
 Hybrid Model Pi Parameters
• Parasitic Capacitances
• Cje0 = Base-emitter junction (depletion layer)
capacitance, 0.1pF ≤ Cje0 ≤ 1pF
• Cµ0 = Base-collector junction capacitance, 0.2pF ≤ Cµ0 ≤
1pF
• Ccs0 = Collector-substrate capacitance, 1pF ≤ Ccs0 ≤ 3pF
• Cje = 2Cje0 (typical)
• ψ0 =.55V (typical)
• τF = Forward transit time of minority carriers,
average of lifetime of holes and electrons, 0ps ≤ τF ≤
530ps
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

16. 16
 Hybrid Model Pi Parameters
• rπ = rb’e = dynamic emitter resistance – magnitude
varies to give correct low frequency value of Vb’e for Ib
• rµ = rb’c = collector base resistance – accounts for
change in recombination component of Ib due to
change in Vc which causes a change in base storage
• cπ = Cb’e = dynamic emitter capacitance – due to Vb’e
stored charge
• cµ = Cb’c = collector base transistion capacitance (CTC)
plus Diffusion capacitance (Cd) due to base width
modulation
• gmVπ = gmVb’e = Ic – equivalent current generator
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

17. 17
 Hybrid Pi Relationships
C
m
T
T
C
m
C B
I
g =
V
k T
V = = 26mV @ 300 K
q
I
g =
26mV
(26mV) ( ) 26mV
r = =
I I
π
°
β
 = gm r
π
c mπ
π
β v
i = = g v
r
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

18. 18
 Hybrid Pi Relationships
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

19. 19
 Hybrid Model Pi Mid Band
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

20. 20
 Hybrid Model Pi High Freq.
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

21. 21
 Common Emitter Amplifier - Complete
Hybrid PI
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

22. 22
 Mid Band Hybrid PI Common
Emitter
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

23. 23
 Equivalent Circuit to find ZO
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

24. 24
 High Frequency Hybrid PI CE Amp
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

25. 25
 Hybrid - π Common Emitter
Transconductance Model
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

26. 26
 Determination of Hybrid-
xConductances
• Determination of Hybrid-x Conductances
gm
is directly proportiortal to IC
is also inversely proportiortal to T.
For PNP transistor, IC
is negative
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

27. 27
 Hybrid - π Capacitances
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

28. 28
 High frequency model parameters
of a BJT in terms of low frequency
hybrid parameters
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

29. 29
• The High frequency model parameters of a BJT in
terms of low frequency hybrid parameters is given
below:
• Transconductance gm = Ic/Vt
• Internal Base node to emitter resistance rb’e =
hfe/ gm = (hfe* Vt )/ Ic
• Internal Base node to collector resistance rb’e =
(hre* rb’c) / (1- hre) assuming hre << 1 it reduces to rb’e =
(hre* rb’c)
• Base spreading resistance rbb’ = hie – rb’e = hie – (hfe* Vt )/ Ic
• Collector to emitter resistance rce = 1 / ( hoe –
(1+ hfe)/rb’c)
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

30. 30
 Collector Emitter Short Circuit
Current Gain
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

31. 31
FET: Analysis of common Source
and common drain Amplifier
circuits at high frequencies

32. 32
 High frequency response of
Common source amplifier
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

33. 33
 High frequency response of
Common source amplifier
SUSHMINAIDU, M.PAVAN ECA Dept of ECE RIT‖ ‖ ‖

34. 34
GATE QUESTIONS
• Consider the bode plot shown in figure. Assume that all the poles and zeros are real valued.
The value of fH – fL (in Hz) is ____________ (2015)
• Consider the common collector amplifier in the
figure (bias circuitry ensures that the transistor operates
in forward active region, but has been omitted for
simplicity). Let IC be the collector current, VBE be the
base emitter voltage and VT be the thermal voltage.
Also, gm and ro are the small signal Transconductance
and output resistance of the transistor, respectively.
Which one of the following conditions ensures a nearly
constant small signal voltage gain for a wide range of
values of RE? (2014)

35. 35
END OF UNIT 1