Chapter6 - Review of Passive and Active RF Lumped Components

Chapter 6 (November 2016) © 2012-2016 by Fabian Kung Wai Lee 1
6- Passive and Active RF
Lumped Components
The information in this work has been obtained from sources believed to be reliable.
The author does not guarantee the accuracy or completeness of any information
presented herein, and shall not be responsible for any errors, omissions or damages
as a result of the use of this information.
References
• [1] Ludwig R., Bretchko P., “RF circuit design - theory and applications”, 2000,
Prentice Hall.
• [2] Laverghetta T.S., "Practical Microwaves", 1996, Prentice-Hall.
• [3] Robertson I. D., Lucyszyn S. (Editors), “RFIC and MMIC design and
technology”, 2001, IEE Circuits, Devices and Systems Series 13.
• [4] Gray P. R., Meyer R. G., “Analysis and design of analog intergrated
circuits”, 3rd Edition, 1993, John-Wiley & Sons. Note: 5th (2009) edition of this
book is available with newer materials.
• [5] Millman J., Halkias C. C.,”Integrated electronics”, 1972, McGraw-Hill.
• [6] Massobrio G., Antognetti P., “Semiconductor device modeling with SPICE”,
2nd edition 1993, McGraw-Hill.
• [7] Sze S. M., “Semiconductor devices – physics and technology”, 3rd edition
2012, John-Wiley & Sons.
• [8] Gilmore R., Besser L.,”Practical RF circuit design for modern wireless
systems”, Vol. 1 & 2, 2003, Artech House.
• [9]* D.M. Pozar, “Microwave engineering”, 4th Edition, 2011 John-Wiley &
Sons.

Agenda
• Passive lumped components at RF.
• Surface-mounted packaging.
• A review of bipolar junction transistor (BJT) operation and model.
• Overview of other active RF components.
• Biasing circuit design for BJT and basic amplifier circuit.
• Frequency response for basic amplifier circuit (S-parameters).
• Appendix – examples of active RF circuits.
1.0 Lumped Components at
Radio Frequency (RF)

Passive Lumped Components for
Medium Frequency (up to 300MHz)
Coil inductor
with Ferrite core
Multilayer
ceramic capacitor
Coil inductor
with air core
Carbon/metal
film resistor
Effect of Packaging
• How the component is packaged is very important at high frequencies.
• When a component is energized (e.g. voltage and current applied):
• To reduce unwanted lead inductance and capacitance, a smaller
package size with shorter leads is preferred. This results in the birth of
surface-mounted technologies (SMT). SMT also enable miniaturization
of the physical circuits.
CLead
Llead
Magnetic flux linkage
Electric field
linkage
A Resistor

Passive Lumped Components at RF (1)
• At radio frequencies a component is not what it appears to be.
• For instance consider a resistor in leaded package:
Cp
LR RLlead
Cp
RLlead
R
Ideally:
A more accurate representation would be:
Note: Make sure you
understand the meaning
of ‘lumped’, and its opposite,
the ‘distributed’.
  









p
leadpractical
RCj
R
LjZ


1
 
 
R
I
V
Zideal 


Or
|Z|
Resistive Capacitive Inductive
f
Z
Resistive Capacitive Inductive
f
-90o
0o
90o
• The magnitude and phase of the resistor’s impedance as a function of
frequency:
Only in this range will the component
behave as an ideal resistor, usually fres is < 250MHz for leaded resistors
Self-resonance
Self-resonance
frequency, fres
  









p
leadpractical
RCj
R
LjZ


1
Llead
Cp
R

• For a capacitor:
Llead
Clead
Rplate Lplate
C Rdiel
Llead Rs C
101
102
103
104
105
101 102
f (MHz)
|Zc| (m)
101 102
f (MHz)
Zc
-90o
-45o
0o
45o
90o
470pF
ceramic
0.15F
Tantalum
470pF
ceramic
0.15F
Tantalum
Self-Resonance
Capacitive response

Lead inductance and resistance
• Approximate model for a practical inductor:
R
C1 C2
L
C3
Parasitic
capacitance
to ground
plane
Parasitic
capacitance
to ground plane
Capacitance between
the windings of the
inductor
Skin effect loss
on the winding
Nominal inductance
   CjL LjRZ  1
//
 21
L
R
LCres 
See this interesting video by Keysights:
https://www.youtube.com/watch?v=fwD_82dzsx8

Surface-Mounted Package
• Surface-mount technology (SMT) was developed in the 1960s and
became widely used in the late 1980s. Much of the pioneering work in
this technology was done at the then IBM.
• Instead of leads, components were mechanically redesigned to have
small metal tabs or end caps to be directly soldered to the surface of
the PCB.
• Components became much smaller. Elimination of leads also reduces
parasitic inductance and capacitance or the component, allowing
operation at higher frequency.
PCB
Copper pad
Surface-mounted packageMetal
tab
Soldering
Who Determines the Package Dimension ?
• A package dimension and style is usually determined by the needs of the
electronic industry.
• Usually a dominant component manufacturing company will introduce a
new package type based on current needs. The mechanical design will
be proposed to a standard making body.
• If sufficient players adopt the package, it will become an accepted
standard and a formal document is drafted to describe its characteristics.
• At present in North America the standards for SMT and other
components is drafted by the JEDEC Solid State Technology Association
(JEDEC - Joint Electron Device Engineering Council ),
http://www.jedec.org/ . JEDEC members consist of electronics and
semiconductor companies worldwide.
• JEDEC also works closely with Electronic Industries Association of
Japan (EIAJ) to focus on similar package outlines from each organization
into one world-wide standard package outline.

Active Lumped Component - Bipolar
Junction Transistor
TO-92 packages
SOT-23 package
SOT-143
E
BC
2N3904
Medium Freq.
200MHz
BFG520
EHF
9GHz
BFR92A
UHF
5GHz
BF199
UHF
500MHz
E
C
B
C
B E
E-Line package
ZTX313
Medium Freq.
300MHz
B
E
C
E
E
B
C
SMT components usually comes in a strip
(which in turn is wounded on a reel)
Passive Lumped Components for Ultra High
Frequencies (UHF) (>300MHz) Application
Other standard sizes
are:
- 0402, smaller
than 0603.
- 0201, even smaller
than 0402.
- 1210, bigger than
0805.
Multilayer electrolytic
capacitor (1206)
Aluminium oxide 0805
80mils
50mils
Thin film inductor
(0603)
Coil inductor
(0805)
Thick film
resistor
Multilayer ceramic capacitor
(0603), NPO dielectric
(0805)
(1206)
(1206),
Y5V dielectric
(0603),
NPO dielectric

More Examples (1)
Inductors Thick film Resistors
Various types of capacitorsTransistors and
MMIC (monolithic
microwave integrated circuit)
0402
0603
0805
1206
1210
SOT-23 SOT-143
Variable
capacitor
86 plastic
package
Various types of diodes
MINIMELF SOD-110
SOD-323Rectifying
diode
Zener diode
RF varactor
RF amplifier
Metal Electrode Faced
More Examples (2)
24 Leads QFNVarious packaging for Piezoelectric
crystal and related components
Various SOIC and QFP packages
32 leads
PLCC
60 leads
TQFP
44 leads
TQFP
Non-standard
package
HC49/U
HC49/4H
surface accoustic wave
(SAW) resonator
Crystal resonator
Crystal resonator
QCC8C

Passive Lumped Components for
Incorporation into PCB and other Substrates
• Lumped components directly incorporated onto the surface of PCB.
Typical for operation in GHz region.
Deposited carbon film,
or semiconductor
Low resistance High resistance
Resistors
Inter-digital Capacitor
Series Single-Loop
Spiral Inductor Series Multi-Loop Spiral Inductor
Air Bridge
Shunt Multi-Loop Spiral Inductor
Via
Microstrip Line
Metal-Insulator-Metal (MIM)
Capacitor
High r dielectric
Bipolar Junction Transistor (BJT)
• Top view of a standard BJT (silicon).
N (Collector)
N (Emitter)
P (Base)
E C
B
Source: R. C. Jaeger, T. N. Blalock, “Microelectronics circuit design”,
2nd edition 2003, McGraw-Hill.
Collector
Base
Emitter
Metal Semiconductor
Contact
Bondwire

RF Bipolar Junction Transistor (RF
BJT)
E
B
Interdigital E and B
contacts
Silicon
Oxide-Nitrite
Insulator
Cross section view of an
NPN RF Transistor
C
P
N
B B BE E
N++
N++
Very thin base region to improve transistor  at high frequency
RF BJT Construction (1)
• Almost all RF transistors are NPN, because mobility of electron is
much higher than hole in Silicon (e = 0.13m2V-1s-1, h = 0.05m2V-1s-1).
The mobility is inversely proportional to the base transit time, .
• The Base thickness is very thin, to improve current gain hfe at high
frequencies. The hfe is related to a parameter known as base transit
time , smaller  yields larger hfe.
• Inter-digital Base and Emitter contacts are employed to reduce base
spreading resistance rb’b and to reduce the noise generated by the
transistor.
• The base transit time  can be reduced further if electrons are
accelerated across the base by electric field (E). This is achieved by
deliberately introducing doping concentration profile in the base.
• Low-cost commercial RF transistors in discrete form can have fT up to
10 GHz. Examples of RF BJT are BFR92A (fT = 5 GHz) and BFG520
(fT = 9 GHz), from NXP Semiconductors (www.nxp.com) and Infineon
Technologies.

RF BJT Construction (2)
N(Collector)
N(Emitter)
P(Base)
ECB
x
Dopant
Concentration
Donor
Acceptor
E
B
C
E field
Electrostatic force on electrons
A doping profile in Base for
NPN transistor:
Doping profile
No doping profile
BJT Operating Regions
• We can view the BJT as 2 back-to-back PN junctions with 4 operating
regions. IC
VCE
B
C
E
IB
IE
 














1
1
CE
BE
BCE
BC
II
II
III
II
Only VCE and IC
are needed to know
the state of the BJT
ACTIVE:
BE forward-biased
BC reverse-biased
IC
VCE0
IB1
IB2
IB3
IB4
IB5
B
C
E
BC junction
BE junction
NPN
Transistor
CUT-OFF:
BE, BC junction reverse-biased
SATURATION:
BE, BC junction forward-biased
INVERSE:
BE reverse-biased
BC forward-biased
IB1
IB2
IB3
IB4
IB5
See this Nov 2013 video for a review:
https://www.youtube.com/watch?v=s69o0AmYyjo

N (Collector)
N (Emitter)
P (Base)
E C B
Small-Signal Model of Transistor at
High Frequency - The Hybrid Pi Model
The Hybrid-Pi Model (Gray & Meyer [4]):
Fixing the d.c. IC, IB and VCE , the response of the transistor for
small variation IC+ic , IB+ib and VCE+vce is given by the
small-signal model. How to fix the d.c. current and voltage,
known as biasing the transistor will be discussed shortly.
IC
VCE0
IB1
IB2
IB3
IB4
IB5
D.C. load line
The Parameters of Hybrid-Pi Model (1)
The Hybrid-Pi model is a fairly
accurate description of the BJT
small-signal response up to GHz
frequency range. You can find more
information on the Hybrid-Pi model
in [4].
Alternatively see the proof by F. Kung on how to get
the hybrid-Pi model of a BJT using Taylor Series
Expansion of the V-I relationship of BE and BC
junctions, March 2000.
• The names of the various parameters:
rbb’ - Base spreading resistance (also given as rx)
gm – Transconductance (it relates voltage to current)
Ce - Emitter capacitance
Cc - Collector capacitance
rb’c - Collector to base resistance (also given as r)
rb’e - Base to emitter resistance (also given as r)
rce - Output resistance (also given as ro)

• Physical explanation of the Hybrid-Pi parameters…
rbb’ The base-spreading resistance – The base region is very thin. Current, which
enters the base region across the emitter junction, must flow through a long
narrow path to reach the base terminal. Hence the ohmic resistance of the base
is very much larger than that of the collector or emitter. The manufacturer of
the transistor usually provides this value.
gm The transconductance – The transconductance is defined as:
26
mA)(inCC
BE
C
m
I
kT
qI
dV
dI
g  at T=25o
, q= electronic charge, 1.602x10-19
C
Where IC is the dc collector current.
Ce The emitter capacitance – Ce represents the sum of the emitter diffusion
capacitance CDE (or base charging capacitance) and the emitter junction
depletion region capacitance CTE.
TEDEe CCC 
CDE is due to finite charge transit time in the emitter PN junction, it is given by
Gray & Meyer [4], chapter 1 and Millman & Halkias [5], chapter 11 as:
mFDE gC 
Where F= forward baised base transit time.
The depletion region capacitance depends on the biasing voltage across the PN
junction and the doping profile of the junction. The expression is rather
lengthy, the interested reader can consult Gray & Meyer [4], chapter 1.
rb’e The input resistance – This resistance is defined by Gray & Meyer [4],
chapter 1:
m
fe
B
EB
eb
g
h
dI
dV
r  '
'
rb’c The collector to base resistance – In active region, the collector junction of a
transistor is reverse biased. Hence when VCE changes, the depletion region
width of the collector junction also changes, this modulates the effective length
of the base and a change in total minority carrier charge Qm stored in the base.
IC is a function of Qm , consequently the collector current also changes. This
effect is modeled by the inclusion of rb’c.
cefecb rhr '
Usually rb’c >> rb’e and can be ignored.
CC The collector capacitance – CC is the depletion region capacitance between
the collector and base PN junction. It is important as Miller effect can greatly
increases its effect.
rce The output resistance – The output resistance is due to base-width
modulation effect or the Early effect. It is given by (Gray & Meyer [4],
chapter 1):
m
A
C
A
ce
kTg
qV
I
V
r 
Where VA is known as the Early voltage and IC is the dc collector current.

Validity of the Hybrid - Pi Model
• The Hybrid-Pi model is only valid under small-signal conditions. Exactly
what do we imply by small-signal is shown below.







T
BE
SC
V
V
II exp





 











 

T
BE
T
BE
S
T
BEBE
SC
V
V
V
V
I
V
VV
II expexpexp'
CCCC IIIi  ' TEBBE VvV  '
EBmEB
T
C
CC vgv
V
I
Ii '' 
T
C
BE
C
BE
C
m
V
I
v
i
dV
dI
g 
Approximate relationship between IC and VBE:
(BJT under active region)
Upon using Taylor’s expansion:













 





 







 
 ...
6
1
2
1
1exp'
32
T
BE
T
BE
T
BE
C
T
BE
CC
V
V
V
V
V
V
I
V
V
II
Say
Let :
BEBEBE VVV 
These higher-order
terms (HOT)
are ignored
Then :
Conditions When Hybrid-Pi Model Can
Be Applied
1. Only valid for small-signal operation, not valid for power amplifier.
2. Extra conditions:
 hfe close to hFE (small-signal current gain similar to large-
signal current gain).
 TEBBE VvV  '
See the book by Millman & Halkias [5], Gray & Meyer [4] for further
information.
Example
Assuming VBE << VT implies VBE < 0.1VT.
VBE must be smaller than 2.6mV
for the hybrid pi model to be accurate.
 
mVVV
Cq
CKT
JKk
q
kT
T 260259.0
10602.1
27about300
10381.1
19
o
123







Useful BJT Figure of Merit (1) - The
Transition Frequency (fT)
• The transition frequency, fT is the frequency where the small signal
current gain io/is of the circuit approaches unity.
• It is dependent on the small signal capacitance Ce and Cc.
• Beyond fT, a transistor is useless as an amplifier (for both current and
voltage amplification). Hence fT fixes the upper usable frequency of a
BJT device.
• fT is a function of D.C. condition, fT(IC, VCE), can you explain why?
Ce
m
T
CC
g
f


2
1
See Gray & Meyer [4]
for derivation,
note that a similar
definition to fT can
also be applied to
FET.
iS
ioThis is the a.c.
equivalent
circuit!





s
o
i
i
10log
0
Log10 fT
Log10 f
Useful BJT Figure of Merit (2) – The
fmax
• Another useful figure of merit is the maximum frequency of oscillation,
fmax.
• This is the maximum frequency where the transistor circuit, with output
connected to the input (with appropriate impedance matching network),
oscillates.
• Typically fmax > fT.
• fmax corresponds to the frequency where maximum available power gain
(Gamax) of the transistor equals to 1.

PN Junction Capacitance and the Base
Transit Time
• The PN junction capacitance can be written as CX = CDX+ CTX for BC
and BE junction, x = C or E.
• CDX is the diffusion capacitance while CTX is the depletion region
capacitance (also called the space charge capacitance).
• CDX is negligible when the PN junction is reverse biased and is the
dominant capacitance when the PN junction is forward biased.
• Thus for a BJT operating in Active Region, CE  CDE and CC  CTC.
• Where CDE = F gm and CTC is given by:
• F is the base transit time (the average life time of minority charge
carrier in base - for NPN transistor this is the average life time of
electrons in the Base before being ‘sucked’ into the Collector region).
• Cjx is the depletion region capacitance when VBX=0 and m and Vjx are
parameters usually determined empirically from measurement. A
smaller F will yield a larger fT.
EorCx
1










 m
jX
BX
jx
TX
V
V
C
C
More on PN Junction Capacitance (1)
• The diffusion capacitance is given by (see Chapter 3, [5], charge-
control description of a PN junction):
• Ihpn is the current component due to injection of holes from P to N
region, while Ienp is the component from injection of electrons from N to
P region. Together they constitute the forward biased current IF .
• Similarly under reverse biased the diffusion capacitance is given by:
• Since Iepn and Ihnp are extremely small, CD is also very small (<10-13
typical).
TV
enpIe
TV
hpnIh
DC





q
kT
TV 
P N
Ihpn
Ienp
IF
PN junction is
Forward biased
+ -
P N
Iepn
Ihnp
IR
PN junction is
Reverse biased
- + TV
hnpIh
TV
epnIe
DC






More on PN Junction Capacitance (2)
• For a typical NPN transistor, the N-type region of the Emitter is highly
doped and P-type region of the Base is lightly doped.
• Thus under forward biased (BE junction forward biased), Ihpn << Ienp, IE
 Iepn. And CDE can be approximated as:
• Recognizing that F = e,
• A plot of CT versus junction voltage is shown below (see Chapter 1,
[4]). Again charge-control description of a PN junction is used to derive
the capacitance. CT
Vjunction
1
m
j
junction
j
T
V
V
C
C










Region where the expression breaks
Down.
0
Cj
See books by Gray & Meyer [4], Millman
& Halkias [5] or any semiconductor device physic text
for further discussion about junction
capacitance and transistor.
TV
CIe
TV
EIe
TV
enpIe
DEC







Fm
TV
CIF
DE gC 



RF Transistor Selection (1)
• Example of how the parameters of RF devices are tabulated in
electronic components catalog.
Adapted from the catalogue
of Farnell Components.
• fT
• Power dissipation
• VCE (max)
• hFE (min)
• Pm(max)
(now known as Element14
in Malaysia)

RF Transistor Selection (2)
Image adapted from
RS Components Malaysia
www.rsmalaysia.com
Other Active Devices – MOSFET and
MESFET (1)
N-channel
Metal-Oxide
Semiconductor
Field Effect Transistor
(MOSFET)
N-channel
Metal-Semiconductor
Field Effect Transistor
(MESFET) (Today this
device is not so popular)
The substrate (usually
made of composite semi-
conductor such as
Gallium Arsenide)
Oxide layer
S DG
n+ n+p
n
Oxide Layer
The substrate
(usually made
of element
semiconductor
such as Silicon)
PN junction contact
Semi-insulating layer (usually undoped semiconductor)
S DG
p
Metal-Semiconductor rectifying contact
Ohmic Metal-Semiconductor
contact

MOSFET and MESFET (2)
• For operating frequency > 2GHz, FET are usually used in place of BJT in
microwave circuits. Typically MESFET is used in both discrete and integrated
circuit form, while MOSFET is only used in integrated circuit.
• Among BJT, MOSFET and MESFET, MESFET has the highest transition
frequency fT and is often used for high-performance RF/microwave circuits:
• (1) FET has better noise characteristic (lower noise figure).
• (2) FET such as MESFET can be constructed from compound semiconductor
such as Gallium Arsenide (GaAs) (the so-called III-V compound) which has
higher electron mobility than Silicon.
• (3) Smaller Gate capacitance in MESFET structure. The Schottky barrier
(Metal-Semiconductor contact) on the Gate of MESFET has smaller
capacitance as compared to the gate oxide capacitance of MOSFET, the PN
junction in JFET or the C of BJT.
• (4) Also ohmic contact on the Drain and Source on MESFET reduces the
corresponding Drain and Source capacitance.
• (2), (3) and (4) contributed to much higher fT in MESFET.
Small-Signal Model for FET
Cgs
G
Cgd
Gmvin rd Cds
D
S
Causes reduction of voltage and current gain
at high frequency
rG rD
rS
rGS
vin
Thus you can see that
for small-signal or
A.C. equivalent circuit,
BJT and FET are more or
less equivalent.

HBT and HEMT (1)
• Most modern high-performance RF/microwave circuits employ FET, for
instance GaAs (Gallium Arsenide) MESFET for operating frequency >
3GHz. GaAs MESFET can operate in excess of 10GHz.
• Since late 1990s, Hetero-junction Bipolar Transistor (HBT) is
introduced commercially. In HBT different semiconductor material is
used for the Base, Emitter and Collector region. For instance P-type
GaAs for Base, N-type GaAs for Collector and N-type AlGaAs for
Emitter. Another example of HBT is the SiGe (Silicon-Germanium) on
Silicon process. Here a compound of SiGe is used for the Base. An
example of discrete SiGe HBT is BFP620 from Infineon Technologies
(www.infineon.com) with fT of 65GHz!
P
N
B B BE E
N++
N++
Si
SiGe
Si
C
An example of SiGe
HBT
HBT and HEMT (2)
• The hetero-junction structure results in valence band discontinuity
between the Base and Emitter of an NPN structure [7].
• This discontinuity reduces the injection of holes from Base to the
Emitter, while allowing the injection of electron from Emitter to Base.
This effect improves emitter efficiency ().
• The emitter efficiency is further improved by being able to construct a
transistor with heavily doped and very thin Base region, thus base-
spreading resistance (rb’b) and base-transit time (F) are reduced.
• Smaller F results in smaller Ce.
Ce
m
T
CC
g
f


2
1

HBT and HEMT (3)
• Hetero-junction approach is also applied to MESFET, in the channel
region of the FET, called Modulation-Doped Field Effect Transistor
(MODFET) [7].
• However since FET operation does not depend on charge injection, but
of charge transport in the channel between the Drain and Source
terminals, the introduction of hetero-junction structure in the channel
serves to increase the electron mobility, allowing very rapid exchange of
electrical signal between Drain and Source. This improves the fT of the
FET.
• Although based on MODFET approach, the resulting FET is usually
called High Electron Mobility Transistor (HEMT). Higher electron
mobility allows the device to response to rapid changes in its Gate.
Effectively this reduces Cgs.
• Such transistor can operate well into the millimeter wave region or in
excess of 100GHz.
HBT and HEMT (4)
• An example of HEMT using GaAs as the substrate.
S DG
Metal
N
Undoped
AlGaAs spacer
 10 nm
Undoped GaAs
Semi-insulating GaAs layer
AlGaAs
Oxide
2D Electron
Gas (2 DEG)
layer
N+
N+
Usually in depletion mode.
But can be designed to work
in both depletion
and enhancement mode

End Notes on Active RF Components
• Since 2006, the CMOS technology, where the main active component
is the MOSFET, is also used extensively for applications up to a few
GHz. This is usually implemented in integrated circuit form.
• For all these active devices, the small-signal equivalent are almost
similar to the hybrid-pi model of the BJT, so in this course we only
concentrate on RF circuit design using BJT. The major difference is in
the way we bias the active devices. FET active devices, which come in
enhancement and depletion mode will require different biasing circuits.
• Also depletion mode device sometimes requires negative d.c. supply.
• Refer to Roberson & Lucyszyn [3], Gilmore & Besser (Vol. II) [8] for
more information. More advanced and updated information can also
be obtained from Sze [7].
2.0 Review of BJT Amplifier
Biasing and S-Parameters
Computation

D.C. Biasing for BJT and FET (1)
• Biasing means putting proper d.c. voltages and currents at a transistor
terminals (Collector, Base, Emitter) so that the device is in the required
operating region, when no a.c. signal is applied.
• A bipolar junction transistor (BJT) has 4 operating regions: Active, Cut-
off, Saturation and Inverse.
• For small-signal amplifier, we bias the transistor in the Active region.
• Small-signal amplifiers is usually of type Class-A, because it needs to
have linear response. IC
VCE0
IB1
IB2
IB3
IB4
IB5
We fix the d.c. current
and voltage, IC, IB and
VCE of a BJT to the
Active Region (BC
junction RB, BE junction
FB)
Key point of BJT biasing
for small-signal
operation, NPN transistor:
VC>VB>VE (Active region)
D.C. Biasing for BJT and FET (2)
• For large-signal amplifier, we may bias the transistor in the Active and
the Cut-off regions, depending on the Class of the amplifier.
• Biasing also applies to field effect transistor (FET), which has 4 distinct
operating regions: Active (also called Saturation), Linear, Cut-off and
Inverse.
• Small-signal FET amplifier is usually biased in Active region.
• Large-signal FET amplifier can be biased in Active and Cut-off regions.
Key point of FET biasing
for small-signal
operation, N-channel:
VD >VG > VS (Active region)
VDS > VGS – VTN
Threshold voltage

BJT Amplifier Configurations
• A transistor is a 3 terminals device. Thus 2 of the terminals can be
used to for signal input and output. The third terminal can be
grounded, usually A.C. grounded with respect to the other terminals.
• This grounded terminal is thus called the common terminal, and hence
the name for transistor amplifier configuration.
• Note that a similar situation exist for FET amplifier, we call these
Common-Source, Common-Drain and Common-Gate FET
amplifiers.
vin
vout
vin
vout
vin vout
Common-Emitter
(CE) Common-Collector
(CC)
Common-Base
(CB)
Can you explain
why there is no
other
permutations?
Typical D.C. Biasing Circuits for BJT
(1)
Vcc
Rb1
Rb2
Rc
Re
• Emitter Feedback Bias (suitable for low frequency up to UHF band):
RF choke Coupling capacitor
Bypass capacitor
Decoupling capacitorBasic biasing network
Input
Output
Common
Emitter
Configuration!
Cc1
Ce
Cd
Vcc
Rb1
Rb2
Rc
Re
Cc2
L1
L2
L3
After adding coupling,
bypass capacitors
and RF chokes.
We usually
use the triangle
symbol to
model amplifier
circuit
This is the basic amplifier
circuit

(2)
• Bypass or decoupling capacitors are used to stabilize the d.c. voltage
and current levels and to isolate RF signals from other circuitry.
• Sometimes these capacitors can be put right after the RF choke to
improve their effectiveness. Vcc
Rb1
Rb2
Rc
Re
Cc2L1
L2
L3
Cd1
Cd2
Cc1
Cd3
Ce
Input
Output
To shunt out RF power
that leaks from RF choke
(3)
• Other forms of Emitter Feedback Bias:
Vcc
Rb1
Rb2
Re
Cc1
Cc2
Ce
L1
L2
L3
Cd Cd
Common emitter
configuration
with no collector
resistor
Common collector
configurationVcc
Rb1
Rb2
Re
Cc1
Cc2
L1
L2
L4
This will allow
higher maximum
voltage swing
at the Collector
terminal

(4)
• Voltage or Collector Feedback Bias (suitable for low frequency up to
microwave band):
Rc
Vcc
Rb
Basic biasing network,
Common Emitter configuration.
After adding coupling,
bypass capacitors
and RF chokes.
Cc1
Cc2
L1
L2
Cd3
Cd2
Vcc
Rb
Input
Output
Rc
Cd1
(5)
• Base Feedback Bias, better DC stability compare to Collector Feedback
Bias (suitable for low frequency up to microwave band):
Basic biasing network,
Common Emitter configuration.

(6)
• Active Bias (suitable for low frequency to microwave band):
Cc1
Cc2
L1
L2
Cd
Vcc
Rb1
Rb2
Rc
Input
Output
RF transistor
Low frequency
transistor
(7)
• Another form of Active Bias using current mirror, popular for high power
application with large Collector current IC. Usually IC >> Iref.
Cc1
Cc2
L1
L2
Cd
Vcc
Rc
Input
Output
Large
RF transistor
Low frequency
and small transistor
Iref
IC
refA
A
C II E
E
2
1

Where:
AE1 = Emitter area
for transistor Q1
AE2 = Emitter area
for transistor Q2Q2 Q1
Note that no resistor in the
high current path
C
BECC
R
VV
refI 


Some Issues Concerning D.C. Biasing
• Biasing network must not interfere with the flow of RF energy during
normal operation. Hence the quality of the bypass capacitors and RF
chokes is vital.
• Temperature stability. Bias point or quiescent point (i.e. IC, VCE) of the
BJT must not change a lot with temperature variation, to ensure that
the performance of the active circuit is not affected by temperature
variation. In this sense, active bias is the most stable, followed by
Emitter bias and voltage feedback bias.
• Compensation for temperature variation using diode in Emitter bias is
available, for instance see Millman & Halkias [5].
• Stability against parameters variation of the BJT. Again active bias
and emitter feedback bias are less susceptible, followed by base
feedback bias and collector feedback bias. See Milman & Halkias [5]
for analysis.
FET Amplifier Biasing
• Due to time constraint we will not focus on field-effect transistor (FET).
• However it needs to be mentioned that the FET amplifier can also be
classified into Common-Source (CS), Common-Gate (CG) and
Common-Drain (CD).
• The DC biasing circuit discussed can also be modified to accommodate
FET based active device. Again for RF/microwave circuits typically N-
channel device is used.
Common-Source
(CS) Common-Drain
(CD)
Common-Gate
(CG)
vin
vout
vin
vout
vin
vout

Example 2.1 - BJT Amplifier Biasing
and Small-Signal Equivalent Circuit
• Determine the quiescent point (Q) of the
transistor and its D.C. stability. Given
hFE(min)=100, hFE(max)= 200.
• Derive the approximate small-signal
equivalent circuit of the following
amplifier schematic. Use hybrid pi model
for the BJT. Given VA=74.03V,
Cjc=3.638pF, Cje=4.493pF, rb’b=10,
hfe=300, Vjc=0.75, m=0.3085, F =
301.2pS.
• If the circuit is going to be used at
430MHz, suggest suitable values for Cc1,
Cc2, Ce and the required RF choke
inductance.
• Finally suggest suitable value for Cd.
Cd
Input
Vcc = 5V
10k
4.7k
470
220
Cc2
L1
L2
L3
Ce
Output
Example 2.1 Solution
Vcc=5V
10k
4.7k
470
220
VB
VE
VC
I1
IC
IB
IE
VVB 60.15
107.4
7.4 

VVV BE 00.16.0 
(1) DC Analysis:
Assuming hFE is large, I1 >> IB.
Assuming transistor is in active
region, VBE = 0.6V.
Using Ohm’s Law: mAI EV
E 545.4
220

Assuming hFE is large, IC >> IB.
mAI
IIII
C
CBCE
545.4

Using Kirchoff’s Voltage Law: VIVV CccC 864.2470 
Verify that transistor is under Active Region:
VVVV CBBC 264.1864.26.1 
Thus BC junction is reverse biased. And in previous slide it has been
shown that BE junction is forward biased, so the transistor is biased
in Active Region, the circuit is destined for Class A operation.
VCE and IC constitute
the Q point

Example 2.1 Solution Cont…
    17.1415011
31971501
31971
/1
/1







eRbRFEh
eRbR
FE
coI
cI
h
(2) D.c. biasing stability analysis (Stability Factor)
(see derivation in Chapter 9 of Millman & Halkias [5]):
0042.0
31971501
220/150
/1
/







eRbRFEh
eRFEh
BEV
cI
   
      
6
2001100
486.1400454.0
max1min
max
min
10272.3 


























FEhFEh
FEhFEhcoI
cI
FEhFEhcI
FEh
cI
     150use,3197 minmax2
1
21
21 
 FEFEFE
bRbR
bRbR
b hhhR
Variation of Ic when Ico changes
Variation of Ic when VBE changes due to temperature change
Variation of Ic due to device parameter variation
(3) Deriving small-signal Hybrid-Pi model parameters:
1
26
545.4
26
1748.0  CI
mg
 kr
mg
feh
eb 682.1'
 kr
CI
AV
ce 288.16
 M886.4' cefecb rhr Can be ignored, considered open circuit

pFgC
CCCC
mFE
DETEDEE
734.53


 
pF
V
V
C
CCCC
m
jc
BC
jc
TCTCDCC 682.2
1
3085.0
75.0
264.11
12-103.638 












Since BE junction is forward biased:
Since BC junction is reverse biased:
The small-signal
equivalent
circuit: 53.734pF
2.682pF
0.1748vb’e 16.288k1.682k
10B B’
E
C
(4) Finding the values of coupling capacitors, bypass capacitor and RF
choke.
Typically, values of L1, L2 and L3 should be chosen such that the reactance of the
inductors is greater than 1000 at the operating frequency. The values Cc1, Cc2 and
Ce are chosen such that the reactance of the capacitors is less than 1 at the
operating frequency. Care must be taken to ensure that the actual component
self-resonance frequency be at least 50% higher than
the operating frequency.
  nHL
fLZL
128.370
10002
6
104302
1000 



  pFC
Z fCC
128.370
1
6
104302
1
2
1




• Thus we can use 390nH (standard value) for L1, L2 and L3. Make sure that the self-
resonance frequency and Q-factor of the chosen practical inductor is sufficient for this
purpose.
• Similarly 390pF is chosen for Cc1, Cc2 and Ce.

D.C. Biasing Design with AppCAD
FEh
cI
BEV
cI
cboI
cI






,,
Download at http://www.avagotech.com/appcad
Characterizing the Frequency Response of
the Basic Amplifier Circuit
• We would like to find out how the circuit will behave if a sinusoidal
voltage of certain frequency is injected into it’s input.
• It is reasonable to expect that the amplifier circuit to behave differently
at different frequencies.
• Of interest is the ratio of the various voltages and currents on the
terminals of the basic amplifier circuit, i.e. the classical parameters.
RL = Zc
ZcZc
Rs = Zc
Vs
V1
V2
I1
I2
Optional
transmission line
Output
impedance
Zo1
2
V
V
VA 
Voltage gain
1
2
I
I
IA 
Current gain
 
 *
1
*
22
IVre
IVre
I
G 
Power gain
1
1
I
V
inZ 
Input Impedance

Summary of Amplifier Parameters
Based on Configurations
• The voltage gain, current gain, input and output impedance of CE, CC
and CB transistor amplifier configurations are summarized here ([4], [5]),
similar conclusions can be derived for FET based amplifiers.
• Each configuration has it uses, for instance CE type amplifier is usually
used for general purpose amplifier. CC is good for buffer or isolation.
CB is typically used in multi-stage amplifiers and oscillators, and for low-
frequency operation, CB can be used as current source for its high output
impedance.
Amplifier
configuration
Voltage
Gain
Current
Gain
Input
Impedance
Output
Impedance
Phase
Output/Input
Voltage
Linearity
CE High High Moderately
high
Moderately
low
180o Moderate
CC  1 High High Low 0o Moderate
CB High  1 Low High 0o High
Two-Stage Amplifiers
• Here we only focus on single-stage amplifier.
• However we would like to mention that two-stages amplifiers are also
very important, as they can combine the individual benefits of single-
stage amplifiers.
• Example of popular two-stages amplifiers are CE-CB (cascade, for
high linearity and high voltage gain), CC-CC (Darlington pair), CE-CE
(for high power gain), CE-CC (to drive high current load or power gain).
• The FET equivalent will be CS-CG, CD-CD, CS-CS and CS-CD.

Characterizing the Frequency Response of
the Amplifier Circuit at RF/Microwave Band
• For amplifier operating at RF and microwave frequencies, a more
convenient set of parameters are the S-parameters.
• The amplifier is considered as a 2-port network, and the S-parameters
s11, s12, s21 and s22 can be measured or derived. Bear in mind here that
we assume the amplifier to be linear or small-signal.
• S-parameters can be reliably measured at RF and microwave
frequencies using instrument called Vector Network Analyzer or
derived from linear circuit analysis.
• Instead of dealing with absolute voltage and current phasors, S-
parameters deal with the ratio of incident and reflected waves. This is
based on the fact that high frequency amplifier can be connected to
transmission lines/waveguides at both its terminals. Of course in the
extreme case the transmission line can be so short that it vanishes.
• The next slide shows how S-parameters are obtained. For more
information please refer to the notes of RF Circuit Design – Passive
Circuit.
Measurement of S-parameter for 2-port
Networks
01
2
21
01
1
11
22 

aa
a
b
s
a
b
s
02
1
12
02
2
22
11 

aa
a
b
s
a
b
s
Measurement of s11 and s21:
Measurement of s22 and
s12:
Zc
ZcZc
Zc
Vs
a1
b1
b2
Port 1 Port 2
b1
Zc
ZcZc
Zc Vs
b2
a2
1
1
1 c
c
ZI
Z
V
a



2
2
2 c
c
ZI
Z
V
a



1
1
1 c
c
ZI
Z
V
b


2
2
2 c
c
ZI
Z
V
b


2221212
2121111
aSaSb
aSaSb


2221212
2121111
aSaSb
aSaSb



Example 2.2 – Computing S-
Parameters from Circuit Simulator
• Here is a screen shot of the schematic drawn using Agilent’s Advanced
Design System (ADS) software.
Setting up small-signal
S-parameters computation
in a commercial simulator
Example 2.2 Cont…
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60.0 2.8
-20
-15
-10
-5
0
5
10
15
-25
20
freq,GHz
dB(S(2,1))
dB(S(1,2))
Note that S-parameters, like
voltage and current phasor,
are complex values.
freq (100.0MHz to 2.700GHz)
S(1,1)
S(2,2)
Complex values of S11 and
S22 versus frequency, plotted
on Smith Chart
Magnitude of S21 and
S12 (in dB) versus frequency, plotted
on XY chart.

Example 2.3 – Obtaining Small-Signal S-
Parameters for BJT Amplifier Analytically
• Consider the circuit of Example 2.1 being terminated with source and
load impedance of Ro. Ignoring the package parasitic, the small-signal
equivalent circuit is as shown below.
Z4
gmV3
R1
Vs/Ro Z3 R5
R2
V1
V3 V2
oce
cCj
eCjeb
bb
bo
RrR
Z
rZ
rR
RRR
//
//
//
5
1
4
1
'3
'2
1







oce
cCj
eCjeb
bb
bo
RrR
Z
rZ
rR
RRR
//
//
//
5
1
4
1
'3
'2
1







Load network
Ce
Cc
gmV3
rce
rb’e
rbb’Ro
Ro
Rb
Vs
Source network
V1 V3 V2
Port 1
Port 2
Example 2.3 Solution
Using Nodal Analysis…
Node 1:
  s
oR
sV
R
V
R
VV
IVGGGV 


32211
1
1
2
31
oR
sV
sRZRR
IGYGG  ,,,,
5
1
5
3
1
3
1
1
1
2
1
2Let
Node 3:    
  0
0
3322412
33234132


VYGVYVG
VYVVYVVG
Node 2:  
    0
0
34254
253324


VYgVGY
VGVgVVY
m
m
(1)
(2)
(3)
From (1):
21
32
1 GG
VGsI
V


 (4)
From (2): 3
54
4
2 VV
GY
mgY


 (5)

Putting (4) & (5) into (2):  






































54
4
2
4
21
2
2
32
21
2
3
3323
54
4
4
21
32
2 0
GY
mgYY
GG
G
GG
sIG
GY
mgY
GG
VGsI
YG
V
VYGVYG
Using (4):
 
 






























































54
4
214323121
2
2
21
1
54
4
2
4
21
2
2
32
2
21
2
21
1
1
GY
mgY
GGYYGYGGG
G
GGoR
sV
GY
mgYY
GG
G
GG
G
GG
sI
V
YG
G
V
Using (5):
  























54
4
214323121
2
54
4
2
GY
mgY
GGYYGYGGGoR
sVG
GY
mgY
V
(6)
(7)
(8)
oR
VsV
I 1
1


oR
V
I 2
2


(9)
(10)
Using the relationship between port voltage, current and the normalized
voltage waves in S-parameter theory (see Chapter 2):
  sRoR
VIRVa
oo 2
1
112
1
1  From (9)
   sRoR
VVIRVb
oo
 12
1
112
1
1 2
    ooo R
V
RoR
VIRVb 2
22
1
222
1
2 2 
02 a

 
 
11
12
54
4
214323121
2
2
21
2
11
112
021
1
11

































GY
mgY
GGYYGYGGG
G
GGoR
sV
V
sV
sVV
aa
b
S
S
Hence:
  




































54
4
214323121
22
54
4
21
22
021
2
21
GY
mgY
GGYYGYGGGoR
G
GY
mgY
sV
V
aa
b
S
S
By injecting the source at output we can obtain expression for s22 and s12.
This is the procedure used by most CAD tools to obtain S-parameters for
linear circuits.
Example 2.4 – A Transistor Biasing
Circuit in Integrated Circuit (IC)
• Here is an example of a active biasing
for a power amplifier circuit. The
transistor on the right is a RF power
transistor. This is an example of active
biasing using a Current Mirror [4].
H02U43_STACK_CAP
Cs1
C=3.007 pF
L=64.0 um
W=52.0 um
Status=Pass
MET2MET1
H02U43_PAD
OUT_PAD1
L=100.0 um
W=100.0 um
Status=Pass
MET1 MET1
H02U43_TFR
TFR_Rstab1
R=159.25 Ohm
L=13.0 um
W=4.0 um
Status=Warning: Width outside validated range
MET1MET1
H02U43_TFR
TFR_RE1
R=2.94 Ohm
L=6.0 um
W=100.0 um
Status=Warning: Length outside validated range
MET1MET1
H02U43_TFR
TFR_B1
R=294 Ohm
L=24.0 um
W=4.0 um
Status=Warning: Width outside validated range
MET1MET1
H02U43_BACKVIA
BACKVIA1
MET1
H02U43_PAD
DC_PAD
L=100.0 um
W=100.0 um
Status=Pass
MET1MET1
H02U43_VBIC
VBIC3
Ta=25
Dev iceName=RQ1A021B2
MET2 MET2
MET1
MET1
H02U43_VBIC
VBIC2
Ta=25
Dev iceName=RQ1A202F2_M2
MET2 MET2
MET1
MET1
H02U43_TFR
TFR1
R=117.6 Ohm
L=24.0 um
W=10.0 um
Status=Pass
MET1MET1
H02U43_STACK_CAP
STACK1_C1
C=1.308 pF
L=36.0 um
W=40.0 um
Status=Pass
MET2MET1
H02U43_PAD
IN_PAD
L=100.0 um
W=100.0 um
Status=Pass
MET1MET1
H02U43_VBIC
VBIC1
Ta=25
Dev iceName=RQ1A021B2
MET2MET2
MET1
MET1
Class-A/AB Single pow er cell unit block:
1 power HBT (2umx20um emitter, 2 fingers)
using TFR resistors with Stack coupling capacitors.
RF Transistor
(HBT)

Appendix 1
Some Do-It-Yourself (DIY)
Active RF Circuits
UHF Low-Noise Amplifier
Supply: 3.0-4.0V
Bandwidth: 850-910 MHz
Transducer Power Gain (GT): 11-12 dB Noise Figure (F): < 1.45
Grounded co-planar
Transmission line
Zener diode
voltage regulator
circuit
BFR92A

L-Band (1.8 GHz) Fixed Frequency
Oscillator
Spiral Inductor
(to set the
oscillation
frequency)
Output
(1-3dBm
into 50Ω)
3.3-4.5V D.C. Power SupplySchottky diode
(Baker’s clamp)
Philips Semiconductor’s BFG520
2.2-2.6 GHz Microwave Voltage-
Controlled Oscillator (VCO)
• Example of microwave oscillator prototype, built on 0.8 mm thick Rogers
4350 substrate with top and bottom side copper.
VCC = 5 -12V
3.3V LDO
VCONTROL = 1-5V
Indicator LED
BFR520
Output

400 to 550 MHz UHF Frequency
Synthesizer Prototype
This is a low-cost frequency synthesizer using a digital phase-locked loop
PLL integrated circuit from National Semiconductor, LMX2306 (now obsoleted).
The voltage controlled oscillator (VCO) is designed using techniques presented in this course.
Microcontroller and buffer
to generate the reference
clock and control signals
for LMX2306.
Ouput
LMX2306
VCO
Loop filter
SMD
prototyping
board by
F. Kung
810 to 930 MHz UHF Frequency
Synthesizer
Crystal
reference
oscillator
Voltage controlled
oscillator
Optional voltage
doubler (for
charge-pump) Optional PIN diode
attenuator
Programmable
Phase-locked Loop IC
To microcontroller-based
Master Unit

MMIC Amplifier and SMT Prototyping
of RF Circuits
MMIC Amplifier
3M Copper tape
2-stage wideband amplifier
RF amplifier
In
Out
In
Out

Chapter6 - Review of Passive and Active RF Lumped Components

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